#include <MoFEM.hpp>
#include <petsc/private/petscimpl.h>
#include <FreeSurfaceOps.hpp>

Classes
struct	TSPrePostProc
	Set of functions called by PETSc solver used to refine and update mesh. More...

struct	FreeSurface

struct	Monitor
	[Push operators to pipeline] More...

Typedefs
template<int DIM>
using	ElementsAndOps = PipelineManager::ElementsAndOpsByDim< SPACE_DIM >

using	DomainEle = ElementsAndOps< SPACE_DIM >::DomainEle

using	DomainParentEle = ElementsAndOps< SPACE_DIM >::DomainParentEle

using	DomainEleOp = DomainEle::UserDataOperator

using	BoundaryEle = ElementsAndOps< SPACE_DIM >::BoundaryEle

using	BoundaryParentEle = ElementsAndOps< SPACE_DIM >::BoundaryParentEle

using	BoundaryEleOp = BoundaryEle::UserDataOperator

using	SideEle = ElementsAndOps< SPACE_DIM >::FaceSideEle

using	SideOp = SideEle::UserDataOperator

using	PostProcEleDomain = PostProcBrokenMeshInMoab< DomainEle >

using	PostProcEleDomainCont = PostProcBrokenMeshInMoabBaseCont< DomainEle >

using	PostProcEleBdyCont = PostProcBrokenMeshInMoabBaseCont< BoundaryEle >

using	EntData = EntitiesFieldData::EntData

using	AssemblyDomainEleOp = FormsIntegrators< DomainEleOp >::Assembly< A >::OpBase

using	AssemblyBoundaryEleOp = FormsIntegrators< BoundaryEleOp >::Assembly< A >::OpBase

using	OpDomainMassU = FormsIntegrators< DomainEleOp >::Assembly< A >::BiLinearForm< I >::OpMass< BASE_DIM, U_FIELD_DIM >

using	OpDomainMassH = FormsIntegrators< DomainEleOp >::Assembly< A >::BiLinearForm< I >::OpMass< BASE_DIM, 1 >

using	OpDomainMassP = OpDomainMassH

using	OpDomainMassG = OpDomainMassH

using	OpBoundaryMassL = FormsIntegrators< BoundaryEleOp >::Assembly< A >::BiLinearForm< I >::OpMass< BASE_DIM, 1 >

using	OpDomainAssembleVector = FormsIntegrators< DomainEleOp >::Assembly< A >::LinearForm< I >::OpBaseTimesVector< BASE_DIM, SPACE_DIM, 1 >

using	OpDomainAssembleScalar = FormsIntegrators< DomainEleOp >::Assembly< A >::LinearForm< I >::OpBaseTimesScalar< BASE_DIM >

using	OpBoundaryAssembleScalar = FormsIntegrators< BoundaryEleOp >::Assembly< A >::LinearForm< I >::OpBaseTimesScalar< BASE_DIM >

template<CoordinateTypes COORD_TYPE>
using	OpMixScalarTimesDiv = FormsIntegrators< DomainEleOp >::Assembly< A >::BiLinearForm< I >::OpMixScalarTimesDiv< SPACE_DIM, COORD_TYPE >

using	BoundaryNaturalBC = NaturalBC< BoundaryEleOp >::Assembly< A >::LinearForm< I >

using	OpFluidFlux = BoundaryNaturalBC::OpFlux< NaturalMeshsetType< BLOCKSET >, 1, 1 >

Enumerations
enum	FR { F , R }

Functions
int	main (int argc, char *argv[])
	Main function for free surface simulation.

Variables
static char	help [] = "...\n\n"

int	coord_type = EXECUTABLE_COORD_TYPE

constexpr int	BASE_DIM = 1

constexpr int	SPACE_DIM = 2

constexpr int	U_FIELD_DIM = SPACE_DIM

constexpr AssemblyType	A = AssemblyType::PETSC

constexpr IntegrationType	I

FTensor::Index< 'i', SPACE_DIM >	i

FTensor::Index< 'j', SPACE_DIM >	j

FTensor::Index< 'k', SPACE_DIM >	k

FTensor::Index< 'l', SPACE_DIM >	l

constexpr auto	t_kd = FTensor::Kronecker_Delta_symmetric<int>()

int	order = 3
	approximation order

int	nb_levels = 4

int	refine_overlap = 4

constexpr bool	debug = true

auto	get_start_bit

auto	get_current_bit
	dofs bit used to do calculations

auto	get_skin_parent_bit = []() { return 2 * get_start_bit() + 2; }

auto	get_skin_child_bit = []() { return 2 * get_start_bit() + 3; }

auto	get_projection_bit = []() { return 2 * get_start_bit() + 4; }

auto	get_skin_projection_bit = []() { return 2 * get_start_bit() + 5; }

double	a0 = 980

double	rho_m = 0.998

double	mu_m = 0.010101 * 1e2

double	rho_p = 0.0012

double	mu_p = 0.000182 * 1e2

double	lambda = 73
	surface tension

double	W = 0.25

double	h = 0.03

double	eta = h

double	eta2 = eta * eta

double	md = 1e-2

double	eps = 1e-12

double	tol = std::numeric_limits<float>::epsilon()

double	rho_ave = (rho_p + rho_m) / 2

double	rho_diff = (rho_p - rho_m) / 2

double	mu_ave = (mu_p + mu_m) / 2

double	mu_diff = (mu_p - mu_m) / 2

double	kappa = (3. / (4. * std::sqrt(2. * W))) * (lambda / eta)

auto	integration_rule = [](int, int, int) { return 2 * order + 1; }

auto	cylindrical
	Coordinate system scaling factor.

auto	wetting_angle_sub_stepping
	Wetting angle sub-stepping for gradual application.

auto	my_max = [](const double x) { return (x - 1 + std::abs(x + 1)) / 2; }
	Maximum function with smooth transition.

auto	my_min = [](const double x) { return (x + 1 - std::abs(x - 1)) / 2; }
	Minimum function with smooth transition

auto	cut_off = [](const double h) { return my_max(my_min(h)); }
	Phase field cutoff function.

auto	d_cut_off
	Derivative of cutoff function.

auto	phase_function
	Phase-dependent material property interpolation.

auto	d_phase_function_h
	Derivative of phase function with respect to h.

auto	get_f = [](const double h) { return 4 * W * h * (h * h - 1); }
	Double-well potential function.

auto	get_f_dh = [](const double h) { return 4 * W * (3 * h * h - 1); }
	Derivative of double-well potential.

auto	get_M0 = [](auto h) { return md; }
	Constant mobility function M₀

auto	get_M0_dh = [](auto h) { return 0; }
	Derivative of constant mobility.

auto	get_M2
	Degenerate mobility function M₂

auto	get_M2_dh = [](auto h) { return -md * 2 * h; }
	Derivative of degenerate mobility M₂

auto	get_M3
	Non-linear mobility function M₃

auto	get_M3_dh
	Derivative of non-linear mobility M₃

auto	get_M = [](auto h) { return get_M0(h); }

auto	get_M_dh = [](auto h) { return get_M0_dh(h); }

auto	get_D
	Create deviatoric stress tensor.

auto	kernel_oscillation
	Oscillating interface initialization.

auto	kernel_eye
	Eye-shaped interface initialization

auto	capillary_tube
	Capillary tube initialization.

auto	bubble_device
	Bubble device initialization.

auto	init_h
	Initialisation function.

auto	wetting_angle = [](double water_level) { return water_level; }
	Wetting angle function (placeholder)

auto	bit = [](auto b) { return BitRefLevel().set(b); }
	Create bit reference level.

auto	marker = [](auto b) { return BitRefLevel().set(BITREFLEVEL_SIZE - b); }
	Create marker bit reference level

auto	get_fe_bit
	Get bit reference level from finite element.

auto	get_global_size
	Get global size across all processors.

auto	save_range
	Save range of entities to file.

auto	get_dofs_ents_by_field_name
	Get entities of DOFs by field name - used for debugging.

auto	get_dofs_ents_all
	Get all entities with DOFs in the problem - used for debugging.

static boost::weak_ptr< TSPrePostProc >	tsPrePostProc

Typedef Documentation

◆ AssemblyBoundaryEleOp

using AssemblyBoundaryEleOp = FormsIntegrators<BoundaryEleOp>::Assembly<A>::OpBase

Definition at line 130 of file free_surface.cpp.

◆ AssemblyDomainEleOp

using AssemblyDomainEleOp = FormsIntegrators<DomainEleOp>::Assembly<A>::OpBase

Definition at line 129 of file free_surface.cpp.

◆ BoundaryEle

using BoundaryEle = ElementsAndOps<SPACE_DIM>::BoundaryEle

Definition at line 117 of file free_surface.cpp.

◆ BoundaryEleOp

using BoundaryEleOp = BoundaryEle::UserDataOperator

Definition at line 119 of file free_surface.cpp.

◆ BoundaryNaturalBC

using BoundaryNaturalBC = NaturalBC<BoundaryEleOp>::Assembly<A>::LinearForm

Definition at line 154 of file free_surface.cpp.

◆ BoundaryParentEle

using BoundaryParentEle = ElementsAndOps<SPACE_DIM>::BoundaryParentEle

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 118 of file free_surface.cpp.

◆ DomainEle

using DomainEle = ElementsAndOps<SPACE_DIM>::DomainEle

Definition at line 114 of file free_surface.cpp.

◆ DomainEleOp

using DomainEleOp = DomainEle::UserDataOperator

Definition at line 116 of file free_surface.cpp.

◆ DomainParentEle

using DomainParentEle = ElementsAndOps<SPACE_DIM>::DomainParentEle

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 115 of file free_surface.cpp.

◆ ElementsAndOps

template<int DIM>

using ElementsAndOps = PipelineManager::ElementsAndOpsByDim<SPACE_DIM>

Definition at line 112 of file free_surface.cpp.

◆ EntData

using EntData = EntitiesFieldData::EntData

Definition at line 127 of file free_surface.cpp.

◆ OpBoundaryAssembleScalar

using OpBoundaryAssembleScalar = FormsIntegrators<BoundaryEleOp>::Assembly< A>::LinearForm::OpBaseTimesScalar<BASE_DIM>

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 146 of file free_surface.cpp.

◆ OpBoundaryMassL

using OpBoundaryMassL = FormsIntegrators<BoundaryEleOp>::Assembly< A>::BiLinearForm::OpMass<BASE_DIM, 1>

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 139 of file free_surface.cpp.

◆ OpDomainAssembleScalar

using OpDomainAssembleScalar = FormsIntegrators<DomainEleOp>::Assembly< A>::LinearForm::OpBaseTimesScalar<BASE_DIM>

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 144 of file free_surface.cpp.

◆ OpDomainAssembleVector

using OpDomainAssembleVector = FormsIntegrators<DomainEleOp>::Assembly< A>::LinearForm::OpBaseTimesVector<BASE_DIM, SPACE_DIM, 1>

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 142 of file free_surface.cpp.

◆ OpDomainMassG

using OpDomainMassG = OpDomainMassH

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 138 of file free_surface.cpp.

◆ OpDomainMassH

using OpDomainMassH = FormsIntegrators<DomainEleOp>::Assembly<A>::BiLinearForm::OpMass<BASE_DIM, 1>

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 135 of file free_surface.cpp.

◆ OpDomainMassP

using OpDomainMassP = OpDomainMassH

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 137 of file free_surface.cpp.

◆ OpDomainMassU

using OpDomainMassU = FormsIntegrators<DomainEleOp>::Assembly<A>::BiLinearForm::OpMass<BASE_DIM, U_FIELD_DIM>

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 133 of file free_surface.cpp.

◆ OpFluidFlux

using OpFluidFlux = BoundaryNaturalBC::OpFlux<NaturalMeshsetType<BLOCKSET>, 1, 1>

Definition at line 155 of file free_surface.cpp.

◆ OpMixScalarTimesDiv

template<CoordinateTypes COORD_TYPE>

using OpMixScalarTimesDiv = FormsIntegrators<DomainEleOp>::Assembly< A>::BiLinearForm::OpMixScalarTimesDiv<SPACE_DIM, COORD_TYPE>

Definition at line 150 of file free_surface.cpp.

◆ PostProcEleBdyCont

using PostProcEleBdyCont = PostProcBrokenMeshInMoabBaseCont<BoundaryEle>

Definition at line 125 of file free_surface.cpp.

◆ PostProcEleDomain

using PostProcEleDomain = PostProcBrokenMeshInMoab<DomainEle>

Definition at line 123 of file free_surface.cpp.

◆ PostProcEleDomainCont

using PostProcEleDomainCont = PostProcBrokenMeshInMoabBaseCont<DomainEle>

Definition at line 124 of file free_surface.cpp.

◆ SideEle

using SideEle = ElementsAndOps<SPACE_DIM>::FaceSideEle

Definition at line 120 of file free_surface.cpp.

◆ SideOp

using SideOp = SideEle::UserDataOperator

Definition at line 121 of file free_surface.cpp.

Enumeration Type Documentation

◆ FR

enum FR

Enumerator
F
R

Definition at line 624 of file free_surface.cpp.

624{ F, R }; // F - forward, and reverse

R

@ R

Definition free_surface.cpp:624

F

@ F

Definition free_surface.cpp:624

Function Documentation

◆ main()

int main	(	int	argc,
		char *	argv[]
	)

Main function for free surface simulation.

Parameters

argc	Number of command line arguments
argv	Array of command line argument strings

Returns: Exit code (0 for success)

Main driver function that:

Initializes MoFEM/PETSc and MOAB data structures
Sets up logging channels for debugging output
Registers MoFEM discrete manager with PETSc
Creates mesh database (MOAB) and finite element database (MoFEM)
Runs the complete free surface simulation
Handles cleanup and finalization

Command line options are read from param_file.petsc and command line. Python initialization is optional (controlled by PYTHON_INIT_SURFACE).

[Register MoFEM discrete manager in PETSc]

[Register MoFEM discrete manager in PETSc

[Create MoAB]

< mesh database

< mesh database interface

[Create MoAB]

[Create MoFEM]

< finite element database

< finite element database interface

[Create MoFEM]

[FreeSurface]

Definition at line 2855 of file free_surface.cpp.

                                 {
 
#ifdef PYTHON_INIT_SURFACE
  Py_Initialize();
#endif
 
  // Initialisation of MoFEM/PETSc and MOAB data structures
  const char param_file[] = "param_file.petsc";
  MoFEM::Core::Initialize(&argc, &argv, param_file, help);
 
  // Add logging channel for example
  auto core_log = logging::core::get();
  core_log->add_sink(LogManager::createSink(LogManager::getStrmWorld(), "FS"));
  LogManager::setLog("FS");
  MOFEM_LOG_TAG("FS", "free surface");
 
  try {
 
    //! [Register MoFEM discrete manager in PETSc]
    DMType dm_name = "DMMOFEM";
    CHKERR DMRegister_MoFEM(dm_name);
    //! [Register MoFEM discrete manager in PETSc
 
    //! [Create MoAB]
    moab::Core mb_instance;              ///< mesh database
    moab::Interface &moab = mb_instance; ///< mesh database interface
    //! [Create MoAB]
 
    //! [Create MoFEM]
    MoFEM::Core core(moab);           ///< finite element database
    MoFEM::Interface &m_field = core; ///< finite element database interface
    //! [Create MoFEM]
 
    //! [FreeSurface]
    FreeSurface ex(m_field);
    CHKERR ex.runProblem();
    //! [FreeSurface]
  }
  CATCH_ERRORS;
 
  CHKERR MoFEM::Core::Finalize();
 
#ifdef PYTHON_INIT_SURFACE
  if (Py_FinalizeEx() < 0) {
    exit(120);
  }
#endif
}

Variable Documentation

◆ A

constexpr AssemblyType A = AssemblyType::PETSC

constexpr

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 107 of file free_surface.cpp.

◆ a0

double a0 = 980

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 186 of file free_surface.cpp.

◆ BASE_DIM

constexpr int BASE_DIM = 1

constexpr

Definition at line 103 of file free_surface.cpp.

◆ bit

auto bit = [](auto b) { return BitRefLevel().set(b); }

Create bit reference level.

Parameters

b	Bit number to set

Returns: BitRefLevel with specified bit set

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 506 of file free_surface.cpp.

506{ return BitRefLevel().set(b); };

MoFEM::Types::BitRefLevel

std::bitset< BITREFLEVEL_SIZE > BitRefLevel

Bit structure attached to each entity identifying to what mesh entity is attached.

Definition Types.hpp:40

◆ bubble_device

auto bubble_device

Initial value:

= [](double x, double y, double z) {
  return -tanh((-0.039 - x) / (eta * std::sqrt(2)));
}

Bubble device initialization.

Parameters

x	X-coordinate
y	Y-coordinate (unused)
z	Z-coordinate (unused)

Returns: Phase field value (-1 to 1)

Creates vertical interface for bubble formation device

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 465 of file free_surface.cpp.

                                                      {
  return -tanh((-0.039 - x) / (eta * std::sqrt(2)));
};

◆ capillary_tube

auto capillary_tube

Initial value:

= [](double x, double y, double z) {
  constexpr double water_height = 0.;
  return tanh((water_height - y) / (eta * std::sqrt(2)));
  ;
}

Capillary tube initialization.

Parameters

x	X-coordinate (unused)
y	Y-coordinate
z	Z-coordinate (unused)

Returns: Phase field value (-1 to 1)

Creates horizontal interface at specified water height

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 450 of file free_surface.cpp.

                                                       {
  constexpr double water_height = 0.;
  return tanh((water_height - y) / (eta * std::sqrt(2)));
  ;
};

◆ coord_type

int coord_type = EXECUTABLE_COORD_TYPE

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 101 of file free_surface.cpp.

◆ cut_off

auto cut_off = [](const double h) { return my_max(my_min(h)); }

Phase field cutoff function.

Parameters

h	Phase field value

Returns: Constrained value in [-1, 1]

Constrains phase field values to physical range [-1,1] with smooth cutoff

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 264 of file free_surface.cpp.

264{ return my_max(my_min(h)); };

h

double h

Definition free_surface.cpp:195

my_max

auto my_max

Maximum function with smooth transition.

Definition free_surface.cpp:248

my_min

auto my_min

Minimum function with smooth transition

Definition free_surface.cpp:255

◆ cylindrical

auto cylindrical

Initial value:

= [](const double r) {
  if (coord_type == CYLINDRICAL)
    return 2 * M_PI * r;
  else
    return 1.;
}

Coordinate system scaling factor.

Parameters

r	Radial coordinate

Returns: Scaling factor for integration

Returns 2πr for cylindrical coordinates, 1 for Cartesian. Used to scale integration measures and force contributions.

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 221 of file free_surface.cpp.

                                      {
  if (coord_type == CYLINDRICAL)
    return 2 * M_PI * r;
  else
    return 1.;
};

◆ d_cut_off

auto d_cut_off

Initial value:

= [](const double h) {
  if (h >= -1 && h < 1)
    return 1.;
  else
    return 0.;
}

Derivative of cutoff function.

Parameters

h	Phase field value

Returns: Derivative of cutoff function

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 271 of file free_surface.cpp.

                                    {
  if (h >= -1 && h < 1)
    return 1.;
  else
    return 0.;
};

◆ d_phase_function_h

auto d_phase_function_h

Initial value:

= [](const double h, const double diff) {
  return diff;
}

Derivative of phase function with respect to h.

Parameters

h	Phase field value (unused in linear case)
diff	Difference between phase values

Returns: Derivative value

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 298 of file free_surface.cpp.

                                                                {
  return diff;
};

◆ debug

constexpr bool debug = true

constexpr

Definition at line 170 of file free_surface.cpp.

◆ eps

double eps = 1e-12

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 201 of file free_surface.cpp.

◆ eta

double eta = h

Examples: mofem/tutorials/fun-2/plot_base.cpp, and mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 196 of file free_surface.cpp.

◆ eta2

double eta2 = eta * eta

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 197 of file free_surface.cpp.

◆ get_current_bit

auto get_current_bit

Initial value:

= []() {
  return 2 * get_start_bit() + 1;
}

dofs bit used to do calculations

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 175 of file free_surface.cpp.

                            {
  return 2 * get_start_bit() + 1;
}; ///< dofs bit used to do calculations

◆ get_D

auto get_D

Initial value:

= [](const double A) {
  FTensor::Ddg<double, SPACE_DIM, SPACE_DIM> t_D;
  t_D(i, j, k, l) = A * ((t_kd(i, k) ^ t_kd(j, l)) / 4.);
  return t_D;
}

Create deviatoric stress tensor.

Parameters

A	Coefficient for tensor scaling

Returns: Fourth-order deviatoric tensor D_ijkl

Constructs deviatoric part of fourth-order identity tensor: D_ijkl = A * (δ_ik δ_jl + δ_il δ_jk)/2 Used in viscous stress calculations for fluid flow

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 394 of file free_surface.cpp.

                                {
  FTensor::Ddg<double, SPACE_DIM, SPACE_DIM> t_D;
  t_D(i, j, k, l) = A * ((t_kd(i, k) ^ t_kd(j, l)) / 4.);
  return t_D;
};

◆ get_dofs_ents_all

auto get_dofs_ents_all

Initial value:

= [](auto dm) {
  auto prb_ptr = getProblemPtr(dm);
  std::vector<EntityHandle> ents_vec;
 
  MoFEM::Interface *m_field_ptr;
  CHKERR DMoFEMGetInterfacePtr(dm, &m_field_ptr);
 
  auto dofs = prb_ptr->numeredRowDofsPtr;
  ents_vec.reserve(dofs->size());
 
  for (auto d : *dofs) {
    ents_vec.push_back(d->getEnt());
  }
 
  std::sort(ents_vec.begin(), ents_vec.end());
  auto it = std::unique(ents_vec.begin(), ents_vec.end());
  Range r;
  r.insert_list(ents_vec.begin(), it);
  return r;
}

Get all entities with DOFs in the problem - used for debugging.

Parameters

dm	PETSc DM object containing the problem

Returns: Range of all entities containing any DOFs

Extracts all mesh entities that have degrees of freedom for any field. Useful for debugging mesh partitioning and DOF distribution.

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 598 of file free_surface.cpp.

                                     {
  auto prb_ptr = getProblemPtr(dm);
  std::vector<EntityHandle> ents_vec;
 
  MoFEM::Interface *m_field_ptr;
  CHKERR DMoFEMGetInterfacePtr(dm, &m_field_ptr);
 
  auto dofs = prb_ptr->numeredRowDofsPtr;
  ents_vec.reserve(dofs->size());
 
  for (auto d : *dofs) {
    ents_vec.push_back(d->getEnt());
  }
 
  std::sort(ents_vec.begin(), ents_vec.end());
  auto it = std::unique(ents_vec.begin(), ents_vec.end());
  Range r;
  r.insert_list(ents_vec.begin(), it);
  return r;
};

◆ get_dofs_ents_by_field_name

auto get_dofs_ents_by_field_name

Initial value:

= [](auto dm, auto field_name) {
  auto prb_ptr = getProblemPtr(dm);
  std::vector<EntityHandle> ents_vec;
 
  MoFEM::Interface *m_field_ptr;
  CHKERR DMoFEMGetInterfacePtr(dm, &m_field_ptr);
 
  auto bit_number = m_field_ptr->get_field_bit_number(field_name);
  auto dofs = prb_ptr->numeredRowDofsPtr;
  auto lo_it = dofs->lower_bound(FieldEntity::getLoBitNumberUId(bit_number));
  auto hi_it = dofs->upper_bound(FieldEntity::getHiBitNumberUId(bit_number));
  ents_vec.reserve(std::distance(lo_it, hi_it));
 
  for (; lo_it != hi_it; ++lo_it) {
    ents_vec.push_back((*lo_it)->getEnt());
  }
 
  std::sort(ents_vec.begin(), ents_vec.end());
  auto it = std::unique(ents_vec.begin(), ents_vec.end());
  Range r;
  r.insert_list(ents_vec.begin(), it);
  return r;
}

Get entities of DOFs by field name - used for debugging.

Parameters

dm	PETSc DM object containing the problem
field_name	Name of field to extract entities for

Returns: Range of entities containing DOFs for specified field

Extracts all mesh entities that have degrees of freedom for the specified field. Useful for debugging and visualization of field distributions across the mesh.

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 566 of file free_surface.cpp.

                                                                {
  auto prb_ptr = getProblemPtr(dm);
  std::vector<EntityHandle> ents_vec;
 
  MoFEM::Interface *m_field_ptr;
  CHKERR DMoFEMGetInterfacePtr(dm, &m_field_ptr);
 
  auto bit_number = m_field_ptr->get_field_bit_number(field_name);
  auto dofs = prb_ptr->numeredRowDofsPtr;
  auto lo_it = dofs->lower_bound(FieldEntity::getLoBitNumberUId(bit_number));
  auto hi_it = dofs->upper_bound(FieldEntity::getHiBitNumberUId(bit_number));
  ents_vec.reserve(std::distance(lo_it, hi_it));
 
  for (; lo_it != hi_it; ++lo_it) {
    ents_vec.push_back((*lo_it)->getEnt());
  }
 
  std::sort(ents_vec.begin(), ents_vec.end());
  auto it = std::unique(ents_vec.begin(), ents_vec.end());
  Range r;
  r.insert_list(ents_vec.begin(), it);
  return r;
};

◆ get_f

auto get_f = [](const double h) { return 4 * W * h * (h * h - 1); }

Double-well potential function.

Parameters

h	Phase field value

Returns: Free energy density f(h) = 4W*h*(h²-1)

Double-well potential with minima at h = ±1 (pure phases) and maximum at h = 0 (interface). Controls interface structure.

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 312 of file free_surface.cpp.

312{ return 4 * W * h * (h * h - 1); };

W

double W

Definition free_surface.cpp:192

◆ get_f_dh

auto get_f_dh = [](const double h) { return 4 * W * (3 * h * h - 1); }

Derivative of double-well potential.

Parameters

h	Phase field value

Returns: f'(h) = 4W*(3h²-1)

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 319 of file free_surface.cpp.

319{ return 4 * W * (3 * h * h - 1); };

◆ get_fe_bit

auto get_fe_bit

Initial value:

= [](FEMethod *fe_ptr) {
  return fe_ptr->numeredEntFiniteElementPtr->getBitRefLevel();
}

Get bit reference level from finite element.

Parameters

fe_ptr Pointer to finite element method

Returns: Current bit reference level of the element

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 520 of file free_surface.cpp.

                                       {
  return fe_ptr->numeredEntFiniteElementPtr->getBitRefLevel();
};

◆ get_global_size

auto get_global_size

Initial value:

= [](int l_size) {
  int g_size;
  MPI_Allreduce(&l_size, &g_size, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
  return g_size;
}

Get global size across all processors.

Parameters

l_size Local size on current processor

Returns: Global sum of sizes across all processors

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 529 of file free_surface.cpp.

                                      {
  int g_size;
  MPI_Allreduce(&l_size, &g_size, 1, MPI_INT, MPI_SUM, MPI_COMM_WORLD);
  return g_size;
};

◆ get_M

auto get_M = [](auto h) { return get_M0(h); }

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 382 of file free_surface.cpp.

382{ return get_M0(h); };

get_M0

auto get_M0

Constant mobility function M₀

Definition free_surface.cpp:326

◆ get_M0

auto get_M0 = [](auto h) { return md; }

Constant mobility function M₀

Parameters

h	Phase field value (unused)

Returns: Constant mobility value

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 326 of file free_surface.cpp.

326{ return md; };

md

double md

Definition free_surface.cpp:200

◆ get_M0_dh

auto get_M0_dh = [](auto h) { return 0; }

Derivative of constant mobility.

Parameters

h	Phase field value (unused)

Returns: Zero (constant mobility)

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 333 of file free_surface.cpp.

333{ return 0; };

◆ get_M2

auto get_M2

Initial value:

= [](auto h) {
  return md * (1 - h * h);
}

Degenerate mobility function M₂

Parameters

h	Phase field value

Returns: M₂(h) = md*(1-h²)

Mobility that vanishes at pure phases (h = ±1)

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 342 of file free_surface.cpp.

                         {
  return md * (1 - h * h);
};

◆ get_M2_dh

auto get_M2_dh = [](auto h) { return -md * 2 * h; }

Derivative of degenerate mobility M₂

Parameters

h	Phase field value

Returns: M₂'(h) = -2*md*h

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 351 of file free_surface.cpp.

351{ return -md * 2 * h; };

◆ get_M3

auto get_M3

Initial value:

= [](auto h) {
  const double h2 = h * h;
  const double h3 = h2 * h;
  if (h >= 0)
    return md * (2 * h3 - 3 * h2 + 1);
  else
    return md * (-2 * h3 - 3 * h2 + 1);
}

Non-linear mobility function M₃

Parameters

h	Phase field value

Returns: Piecewise cubic mobility function

Smooth mobility function with different behavior for h >= 0 and h < 0

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 360 of file free_surface.cpp.

                         {
  const double h2 = h * h;
  const double h3 = h2 * h;
  if (h >= 0)
    return md * (2 * h3 - 3 * h2 + 1);
  else
    return md * (-2 * h3 - 3 * h2 + 1);
};

◆ get_M3_dh

auto get_M3_dh

Initial value:

= [](auto h) {
  if (h >= 0)
    return md * (6 * h * (h - 1));
  else
    return md * (-6 * h * (h + 1));
}

Derivative of non-linear mobility M₃

Parameters

h	Phase field value

Returns: M₃'(h) with sign-dependent cubic behavior

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 374 of file free_surface.cpp.

                            {
  if (h >= 0)
    return md * (6 * h * (h - 1));
  else
    return md * (-6 * h * (h + 1));
};

◆ get_M_dh

auto get_M_dh = [](auto h) { return get_M0_dh(h); }

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 383 of file free_surface.cpp.

383{ return get_M0_dh(h); };

get_M0_dh

auto get_M0_dh

Derivative of constant mobility.

Definition free_surface.cpp:333

◆ get_projection_bit

auto get_projection_bit = []() { return 2 * get_start_bit() + 4; }

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 180 of file free_surface.cpp.

180{ return 2 * get_start_bit() + 4; };

◆ get_skin_child_bit

auto get_skin_child_bit = []() { return 2 * get_start_bit() + 3; }

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 179 of file free_surface.cpp.

179{ return 2 * get_start_bit() + 3; };

◆ get_skin_parent_bit

auto get_skin_parent_bit = []() { return 2 * get_start_bit() + 2; }

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 178 of file free_surface.cpp.

178{ return 2 * get_start_bit() + 2; };

◆ get_skin_projection_bit

auto get_skin_projection_bit = []() { return 2 * get_start_bit() + 5; }

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 181 of file free_surface.cpp.

181{ return 2 * get_start_bit() + 5; };

◆ get_start_bit

auto get_start_bit

Initial value:

= []() {
  return nb_levels + 1;
}

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 172 of file free_surface.cpp.

                          {
  return nb_levels + 1;
}; //< first refinement level for computational mesh

◆ h

double h = 0.03

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 195 of file free_surface.cpp.

◆ help

char help[] = "...\n\n"

static

Definition at line 17 of file free_surface.cpp.

◆ I

constexpr IntegrationType I

constexpr

Initial value:

=

IntegrationType::GAUSS

Definition at line 108 of file free_surface.cpp.

◆ i

FTensor::Index<'i', SPACE_DIM> i

Definition at line 158 of file free_surface.cpp.

◆ init_h

auto init_h

Initial value:

= [](double r, double y, double theta) {
 
  return capillary_tube(r, y, theta);
  
}

Initialisation function.

Note: If UMs are compiled with Python to initialise phase field "H" surface.py function is used, which has to be present in execution folder.

Examples: mofem/tutorials/vec-4/shallow_wave.cpp, and mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 476 of file free_surface.cpp.

                                                   {
#ifdef PYTHON_INIT_SURFACE
  double s = 1;
  if (auto ptr = surfacePythonWeakPtr.lock()) {
    CHK_THROW_MESSAGE(ptr->evalSurface(r, y, theta, eta, s),
                      "error eval python");
  }
  return s;
#else
  // return bubble_device(r, y, theta);
  return capillary_tube(r, y, theta);
  // return kernel_eye(r, y, theta);
#endif
};

◆ integration_rule

auto integration_rule = [](int, int, int) { return 2 * order + 1; }

Examples: mofem/atom_tests/hcurl_check_approx_in_2d.cpp, mofem/atom_tests/hcurl_curl_operator.cpp, mofem/atom_tests/hdiv_check_approx_in_3d.cpp, mofem/atom_tests/hdiv_divergence_operator.cpp, mofem/atom_tests/scalar_check_approximation.cpp, mofem/atom_tests/test_broken_space.cpp, mofem/tutorials/adv-2/thermo_elastic.cpp, mofem/tutorials/adv-4/dynamic_first_order_con_law.cpp, mofem/tutorials/adv-5/seepage.cpp, mofem/tutorials/clx-0/helmholtz.cpp, mofem/tutorials/fun-1/integration.cpp, mofem/tutorials/scl-10/initial_diffusion.cpp, mofem/tutorials/scl-10/photon_diffusion.cpp, mofem/tutorials/scl-6/heat_equation.cpp, mofem/tutorials/scl-7/wave_equation.cpp, mofem/tutorials/vec-1/eigen_elastic.cpp, mofem/tutorials/vec-2/src/NonlinearElasticExample.hpp, mofem/tutorials/vec-3/nonlinear_dynamic_elastic.cpp, mofem/tutorials/vec-4/approx_sphere.cpp, mofem/tutorials/vec-4/shallow_wave.cpp, mofem/tutorials/vec-5/free_surface.cpp, mofem/tutorials/vec-7/adjoint.cpp, and mofem/tutorials/vec-9/src/ArcLengthExample.hpp.

Definition at line 211 of file free_surface.cpp.

211{ return 2 * order + 1; };

order

int order

approximation order

Definition free_surface.cpp:166

◆ j

FTensor::Index<'j', SPACE_DIM> j

Definition at line 159 of file free_surface.cpp.

◆ k

FTensor::Index<'k', SPACE_DIM> k

Definition at line 160 of file free_surface.cpp.

◆ kappa

double kappa = (3. / (4. * std::sqrt(2. * W))) * (lambda / eta)

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 209 of file free_surface.cpp.

◆ kernel_eye

auto kernel_eye

Initial value:

= [](double r, double y, double) {
  constexpr double y0 = 0.5;
  constexpr double R = 0.4;
  y -= y0;
  const double d = std::sqrt(r * r + y * y);
  return tanh((R - d) / (eta * std::sqrt(2)));
}

Eye-shaped interface initialization

Parameters

r	Radial coordinate
y	Vertical coordinate
unused	Z-coordinate (unused in 2D)

Returns: Phase field value (-1 to 1)

Creates circular droplet centered at (0, y0) with radius R

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 433 of file free_surface.cpp.

                                                 {
  constexpr double y0 = 0.5;
  constexpr double R = 0.4;
  y -= y0;
  const double d = std::sqrt(r * r + y * y);
  return tanh((R - d) / (eta * std::sqrt(2)));
};

◆ kernel_oscillation

auto kernel_oscillation

Initial value:

= [](double r, double y, double) {
  constexpr int n = 3;
  constexpr double R = 0.0125;
  constexpr double A = R * 0.2;
  const double theta = atan2(r, y);
  const double w = R + A * cos(n * theta);
  const double d = std::sqrt(r * r + y * y);
  return tanh((w - d) / (eta * std::sqrt(2)));
}

Oscillating interface initialization.

Parameters

r	Radial coordinate
y	Vertical coordinate
unused	Z-coordinate (unused in 2D)

Returns: Phase field value (-1 to 1)

Creates circular interface with sinusoidal perturbations:

Base radius R with amplitude A
n-fold symmetry oscillations
Uses tanh profile for smooth interface

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 414 of file free_surface.cpp.

                                                         {
  constexpr int n = 3;
  constexpr double R = 0.0125;
  constexpr double A = R * 0.2;
  const double theta = atan2(r, y);
  const double w = R + A * cos(n * theta);
  const double d = std::sqrt(r * r + y * y);
  return tanh((w - d) / (eta * std::sqrt(2)));
};

◆ l

FTensor::Index<'l', SPACE_DIM> l

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 161 of file free_surface.cpp.

◆ lambda

double lambda = 73

surface tension

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 191 of file free_surface.cpp.

◆ marker

auto marker = [](auto b) { return BitRefLevel().set(BITREFLEVEL_SIZE - b); }

Create marker bit reference level

Parameters

b	Bit number from end

Returns: BitRefLevel with bit set from end

Definition at line 513 of file free_surface.cpp.

513{ return BitRefLevel().set(BITREFLEVEL_SIZE - b); };

BITREFLEVEL_SIZE

#define BITREFLEVEL_SIZE

max number of refinements

Definition definitions.h:232

◆ md

double md = 1e-2

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 200 of file free_surface.cpp.

◆ mu_ave

double mu_ave = (mu_p + mu_m) / 2

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 206 of file free_surface.cpp.

◆ mu_diff

double mu_diff = (mu_p - mu_m) / 2

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 207 of file free_surface.cpp.

◆ mu_m

double mu_m = 0.010101 * 1e2

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 188 of file free_surface.cpp.

◆ mu_p

double mu_p = 0.000182 * 1e2

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 190 of file free_surface.cpp.

◆ my_max

auto my_max = [](const double x) { return (x - 1 + std::abs(x + 1)) / 2; }

Maximum function with smooth transition.

Parameters

x	Input value

Returns: max(x, -1) with smooth transition

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 248 of file free_surface.cpp.

248{ return (x - 1 + std::abs(x + 1)) / 2; };

◆ my_min

auto my_min = [](const double x) { return (x + 1 - std::abs(x - 1)) / 2; }

Minimum function with smooth transition

Parameters

x	Input value

Returns: min(x, 1) with smooth transition

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 255 of file free_surface.cpp.

255{ return (x + 1 - std::abs(x - 1)) / 2; };

◆ nb_levels

int nb_levels = 4

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 167 of file free_surface.cpp.

◆ order

int order = 3

approximation order

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 166 of file free_surface.cpp.

◆ phase_function

auto phase_function

Initial value:

= [](const double h, const double diff, const double ave) {
  return diff * h + ave;
}

Phase-dependent material property interpolation.

Parameters

h	Phase field value (-1 to 1)
diff	Difference between phase values (phase_plus - phase_minus)
ave	Average of phase values (phase_plus + phase_minus)/2

Returns: Interpolated material property

Linear interpolation: property = diff * h + ave Used for density and viscosity interpolation between phases

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 288 of file free_surface.cpp.

                                                                              {
  return diff * h + ave;
};

◆ refine_overlap

int refine_overlap = 4

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 168 of file free_surface.cpp.

◆ rho_ave

double rho_ave = (rho_p + rho_m) / 2

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 204 of file free_surface.cpp.

◆ rho_diff

double rho_diff = (rho_p - rho_m) / 2

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 205 of file free_surface.cpp.

◆ rho_m

double rho_m = 0.998

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 187 of file free_surface.cpp.

◆ rho_p

double rho_p = 0.0012

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 189 of file free_surface.cpp.

◆ save_range

auto save_range

Initial value:

= [](moab::Interface &moab, const std::string name,
                     const Range r) {
  MoFEMFunctionBegin;
  if (get_global_size(r.size())) {
    auto out_meshset = get_temp_meshset_ptr(moab);
    CHKERR moab.add_entities(*out_meshset, r);
    CHKERR moab.write_file(name.c_str(), "MOAB", "PARALLEL=WRITE_PART",
                           out_meshset->get_ptr(), 1);
  }
  MoFEMFunctionReturn(0);
}

Save range of entities to file.

Parameters

moab	MOAB interface for mesh operations
name	Output filename
r	Range of entities to save

Returns: MoFEMErrorCode Success/failure code

Saves entities to HDF5 file if range is non-empty globally

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 544 of file free_surface.cpp.

                                    {
  MoFEMFunctionBegin;
  if (get_global_size(r.size())) {
    auto out_meshset = get_temp_meshset_ptr(moab);
    CHKERR moab.add_entities(*out_meshset, r);
    CHKERR moab.write_file(name.c_str(), "MOAB", "PARALLEL=WRITE_PART",
                           out_meshset->get_ptr(), 1);
  }
  MoFEMFunctionReturn(0);
};

◆ SPACE_DIM

constexpr int SPACE_DIM = 2

constexpr

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 104 of file free_surface.cpp.

◆ t_kd

constexpr auto t_kd = FTensor::Kronecker_Delta_symmetric<int>()

constexpr

Examples: mofem/atom_tests/matrix_function.cpp, mofem/tutorials/adv-0/plastic.cpp, mofem/tutorials/adv-0/src/PlasticOps.hpp, mofem/tutorials/adv-0/src/PlasticOpsGeneric.hpp, mofem/tutorials/adv-0/src/PlasticOpsLargeStrains.hpp, mofem/tutorials/adv-0/src/PlasticOpsSmallStrains.hpp, mofem/tutorials/adv-4/dynamic_first_order_con_law.cpp, mofem/tutorials/adv-5/seepage.cpp, mofem/tutorials/vec-1/eigen_elastic.cpp, mofem/tutorials/vec-2/src/HenckyOps.hpp, mofem/tutorials/vec-4/approx_sphere.cpp, mofem/tutorials/vec-4/shallow_wave.cpp, mofem/tutorials/vec-5/free_surface.cpp, mofem/tutorials/vec-6/plate.cpp, mofem/users_modules/adolc-plasticity/src/ADOLCPlasticityMaterialModels.hpp, mofem/users_modules/basic_finite_elements/elasticity/elasticity.cpp, mofem/users_modules/basic_finite_elements/nonlinear_elastic_materials/src/NeoHookean.hpp, mofem/users_modules/eshelbian_plasticity/src/impl/EshelbianOperators.cpp, and mofem/users_modules/eshelbian_plasticity/src/impl/EshelbianPlasticity.cpp.

Definition at line 163 of file free_surface.cpp.

◆ tol

double tol = std::numeric_limits<float>::epsilon()

Definition at line 202 of file free_surface.cpp.

◆ tsPrePostProc

boost::weak_ptr<TSPrePostProc> tsPrePostProc

static

Examples: mofem/tutorials/adv-4/dynamic_first_order_con_law.cpp, and mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 794 of file free_surface.cpp.

◆ U_FIELD_DIM

constexpr int U_FIELD_DIM = SPACE_DIM

constexpr

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 105 of file free_surface.cpp.

◆ W

double W = 0.25

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 192 of file free_surface.cpp.

◆ wetting_angle

auto wetting_angle = [](double water_level) { return water_level; }

Wetting angle function (placeholder)

Parameters

water_level Current water level

Returns: Wetting angle value

Currently returns input value directly. Can be modified to implement complex wetting angle dependencies on interface position or time.

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 499 of file free_surface.cpp.

499{ return water_level; };

◆ wetting_angle_sub_stepping

auto wetting_angle_sub_stepping

Initial value:

= [](auto ts_step) {
  constexpr int sub_stepping = 16;
  return std::min(1., static_cast<double>(ts_step) / sub_stepping);
}

Wetting angle sub-stepping for gradual application.

Parameters

ts_step Current time step number

Returns: Scaling factor [0,1] for gradual wetting angle application

Gradually applies wetting angle boundary condition over first 16 steps to avoid sudden changes that could destabilize the solution.

Examples: mofem/tutorials/vec-5/free_surface.cpp.

Definition at line 236 of file free_surface.cpp.

                                                   {
  constexpr int sub_stepping = 16;
  return std::min(1., static_cast<double>(ts_step) / sub_stepping);
};

Classes

Typedefs

Enumerations

Functions

Variables

Typedef Documentation

◆ AssemblyBoundaryEleOp

◆ AssemblyDomainEleOp

◆ BoundaryEle

◆ BoundaryEleOp

◆ BoundaryNaturalBC

◆ BoundaryParentEle

◆ DomainEle

◆ DomainEleOp

◆ DomainParentEle

◆ ElementsAndOps

◆ EntData

◆ OpBoundaryAssembleScalar

◆ OpBoundaryMassL

◆ OpDomainAssembleScalar

◆ OpDomainAssembleVector

◆ OpDomainMassG

◆ OpDomainMassH

◆ OpDomainMassP

◆ OpDomainMassU

◆ OpFluidFlux

◆ OpMixScalarTimesDiv

◆ PostProcEleBdyCont

◆ PostProcEleDomain

◆ PostProcEleDomainCont

◆ SideEle

◆ SideOp

Enumeration Type Documentation

◆ FR

Function Documentation

◆ main()

Variable Documentation

◆ A

◆ a0

◆ BASE_DIM

◆ bit

◆ bubble_device

◆ capillary_tube

◆ coord_type

◆ cut_off

◆ cylindrical

◆ d_cut_off

◆ d_phase_function_h

◆ debug

◆ eps

◆ eta

◆ eta2

◆ get_current_bit

◆ get_D

◆ get_dofs_ents_all

◆ get_dofs_ents_by_field_name

◆ get_f

◆ get_f_dh

◆ get_fe_bit

◆ get_global_size

◆ get_M

◆ get_M0

◆ get_M0_dh

◆ get_M2

◆ get_M2_dh

◆ get_M3

◆ get_M3_dh

◆ get_M_dh

◆ get_projection_bit

◆ get_skin_child_bit

◆ get_skin_parent_bit

◆ get_skin_projection_bit

◆ get_start_bit

◆ h

◆ help

◆ I

◆ i

◆ init_h

◆ integration_rule

◆ j