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Helper class to model a hyperbolic PDE in first-order conservative formulation. More...

Inheritance diagram for exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation:

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Collaboration diagram for exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation:

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Public Member Functions
	__init__ (self, unknowns, auxiliary_variables, dimensions)

	__str__ (self)

	LaTeX (self)

	substitute_expression (self, expression, new_expression)
	Usually used to set a symbolic variable (expression) to a value (new_expression).

	implementation_of_flux (self, invoke_evalf_before_output=False)
	Return implementation for flux along one coordinate axis (d) as C code.

	implementation_of_ncp (self, invoke_evalf_before_output=False)
	Return implementation for nonconservative product (ncp) along one coordinate axis (d) as C code.

	implementation_of_eigenvalues (self, invoke_evalf_before_output=False)
	Return eigenvalues.

	implementation_of_max_eigenvalue (self, invoke_evalf_before_output=False, use_absolute_values=True)
	Return maximum eigenvalue.

	implementation_of_sources (self, invoke_evalf_before_output=False)
	Return implementation for sources as C code.

Public Member Functions inherited from exahype2.symhype.PDE.PDE
	unknown_identifier_for_plotter (self)
	Returns identifier for the unknowns.

	name_Q_entry (self, offset_in_Q, name)
	Q covers both unknowns plus auxiliary variables.

	name_auxiliary_variable (self, number, name)

	name_Q_entries (self, offset_in_Q, cardinality, name)

	grad (self, Q)

	implementation_of_homogeneous_Neumann_BC (self)

	implementation_of_boundary_conditions (self, invoke_evalf_before_output=False)
	invoke_evalf_before_output: boolean If your expression is a symbolic expression (default) then we use evalf before we pipe it into the output.

	implementation_of_initial_conditions (self, invoke_evalf_before_output=False)
	invoke_evalf_before_output: boolean If your expression is a symbolic expression (default) then we use evalf before we pipe it into the output.

Data Fields
	F

	ncp

	eigenvalues

	sources

	unknowns

	dimensions

Data Fields inherited from exahype2.symhype.PDE.PDE
	unknowns

	auxiliary_variables

	dimensions

	Q

	delta_Q

	initial_values

	boundary_values

	x

	h

Additional Inherited Members
Protected Member Functions inherited from exahype2.symhype.PDE.PDE
	_implementation_of_mapping_onto_named_quantities (self, is_cell_mapping=True, is_boundary=False, has_delta=False)
	Return the C code that maps the quantities from Q onto properly labelled quantities.

Detailed Description

Helper class to model a hyperbolic PDE in first-order conservative formulation.

To model your PDE, you typically run through a couple of single steps. First, include this package plus sympy. Next, create a new instance of this class to which you pass the number of equations in your PDE system, i.e., the number of unknowns you want to develop, plus the dimension.

As a consequence, the solver holds an equation pde which describes the PDE's right-hand side in the representation

\partial Q(t) + div_x F(Q)

Most people prefer not to work with a vector Q but with some symbolic names. Feel free to derive them from Q via constructs similar to

rho = euler.Q[0] j = sympy.Array(euler.Q[1:4]) E = euler.Q[4]

Definition at line 9 of file FirstOrderConservativePDEFormulation.py.

Constructor & Destructor Documentation

◆ init()

exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.__init__	(	self,
		unknowns,
		auxiliary_variables,
		dimensions )

Reimplemented from exahype2.symhype.PDE.PDE.

Definition at line 33 of file FirstOrderConservativePDEFormulation.py.

Member Function Documentation

◆ str()

exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.__str__ ( self )

Definition at line 41 of file FirstOrderConservativePDEFormulation.py.

Referenced by peano4.toolbox.particles.postprocessing.ParticleVTUReader.VTUParticleSet.__repr__().

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◆ implementation_of_eigenvalues()

exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.implementation_of_eigenvalues	(		self,
			invoke_evalf_before_output = False )

Return eigenvalues.

This yields a set of eigenvalues, i.e., one per unknown. For many solvers such as Rusanov, you need only one.

d: int The axis along which we wanna have the eigenvalues

invoke_evalf_before_output: boolean If your expression is a symbolic expression (default) then we use evalf before we pipe it into the output. If your expression is something numeric, then evalf will fail (as it is not defined for scalar quantities).

Definition at line 178 of file FirstOrderConservativePDEFormulation.py.

References exahype2.symhype.PDE.PDE._implementation_of_mapping_onto_named_quantities(), exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.dimensions, exahype2.symhype.PDE.PDE.dimensions, peano4.visualisation.input.PatchFileParser.UnknownAttributes.dimensions, peano4.visualisation.input.PatchFileParser.PatchFileParser.dimensions, convert::data::PatchData.dimensions, convert::data::Variable.dimensions, mghype.api.matrixgenerators.DLinear.DLinear.dimensions, mghype.api.matrixgenerators.DLinearMassIdentity.DLinearMassIdentity.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.dimensions, mghype.api.matrixgenerators.GaussLobatto.GLMatrixFree.dimensions, mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.dimensions, equations.acoustic.Acoustic.dimensions, equations.advection.Advection.dimensions, equations.elastic.Elastic.dimensions, equations.equation.Equation.dimensions, equations.euler.Euler.dimensions, equations.swe.SWE_W_Bathymetry.dimensions, equations.swe.SWE_WO_Bathymetry.dimensions, exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.eigenvalues, equations.equation.Equation.eigenvalues(), equations.acoustic.Acoustic.eigenvalues(), equations.advection.Advection.eigenvalues(), equations.elastic.Elastic.eigenvalues(), equations.euler.Euler.eigenvalues(), equations.swe.SWE_W_Bathymetry.eigenvalues(), equations.swe.SWE_WO_Bathymetry.eigenvalues(), exahype2.solvers.aderdg.ADERDG.ADERDG.unknowns(), exahype2.solvers.fv.FV.FV.unknowns(), exahype2.solvers.rkdg.RungeKuttaDG.RungeKuttaDG.unknowns(), exahype2.solvers.rkfd.CellCenteredFiniteDifferences.CellCenteredFiniteDifferences.unknowns(), exahype2.solvers.fv.FV.FV.unknowns(), exahype2.solvers.rkdg.RungeKuttaDG.RungeKuttaDG.unknowns(), exahype2.solvers.rkfd.CellCenteredFiniteDifferences.CellCenteredFiniteDifferences.unknowns(), exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.unknowns, exahype2.symhype.PDE.PDE.unknowns, peano4.visualisation.input.Patch.Patch.unknowns, peano4.visualisation.input.PatchFileParser.UnknownAttributes.unknowns, and convert::data::Variable.unknowns.

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◆ implementation_of_flux()

exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.implementation_of_flux	(		self,
			invoke_evalf_before_output = False )

Return implementation for flux along one coordinate axis (d) as C code.

Definition at line 108 of file FirstOrderConservativePDEFormulation.py.

References exahype2.symhype.PDE.PDE._implementation_of_mapping_onto_named_quantities(), exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.dimensions, exahype2.symhype.PDE.PDE.dimensions, peano4.visualisation.input.PatchFileParser.UnknownAttributes.dimensions, peano4.visualisation.input.PatchFileParser.PatchFileParser.dimensions, convert::data::PatchData.dimensions, convert::data::Variable.dimensions, mghype.api.matrixgenerators.DLinear.DLinear.dimensions, mghype.api.matrixgenerators.DLinearMassIdentity.DLinearMassIdentity.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.dimensions, mghype.api.matrixgenerators.GaussLobatto.GLMatrixFree.dimensions, mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.dimensions, equations.acoustic.Acoustic.dimensions, equations.advection.Advection.dimensions, equations.elastic.Elastic.dimensions, equations.equation.Equation.dimensions, equations.euler.Euler.dimensions, equations.swe.SWE_W_Bathymetry.dimensions, equations.swe.SWE_WO_Bathymetry.dimensions, exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.F, exahype2.solvers.aderdg.ADERDG.ADERDG.unknowns(), exahype2.solvers.fv.FV.FV.unknowns(), exahype2.solvers.rkdg.RungeKuttaDG.RungeKuttaDG.unknowns(), exahype2.solvers.rkfd.CellCenteredFiniteDifferences.CellCenteredFiniteDifferences.unknowns(), exahype2.solvers.fv.FV.FV.unknowns(), exahype2.solvers.rkdg.RungeKuttaDG.RungeKuttaDG.unknowns(), exahype2.solvers.rkfd.CellCenteredFiniteDifferences.CellCenteredFiniteDifferences.unknowns(), exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.unknowns, exahype2.symhype.PDE.PDE.unknowns, peano4.visualisation.input.Patch.Patch.unknowns, peano4.visualisation.input.PatchFileParser.UnknownAttributes.unknowns, and convert::data::Variable.unknowns.

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◆ implementation_of_max_eigenvalue()

exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.implementation_of_max_eigenvalue	(	self,
		invoke_evalf_before_output = False,
		use_absolute_values = True )

Return maximum eigenvalue.

Definition at line 220 of file FirstOrderConservativePDEFormulation.py.

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◆ implementation_of_ncp()

exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.implementation_of_ncp	(		self,
			invoke_evalf_before_output = False )

Return implementation for nonconservative product (ncp) along one coordinate axis (d) as C code.

Definition at line 144 of file FirstOrderConservativePDEFormulation.py.

References exahype2.symhype.PDE.PDE._implementation_of_mapping_onto_named_quantities(), exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.dimensions, exahype2.symhype.PDE.PDE.dimensions, peano4.visualisation.input.PatchFileParser.UnknownAttributes.dimensions, peano4.visualisation.input.PatchFileParser.PatchFileParser.dimensions, convert::data::PatchData.dimensions, convert::data::Variable.dimensions, mghype.api.matrixgenerators.DLinear.DLinear.dimensions, mghype.api.matrixgenerators.DLinearMassIdentity.DLinearMassIdentity.dimensions, mghype.api.matrixgenerators.GaussLobatto.GaussLobatto.dimensions, mghype.api.matrixgenerators.GaussLobatto.GLMatrixFree.dimensions, mghype.api.matrixgenerators.MatrixGenerator.MatrixGenerator.dimensions, equations.acoustic.Acoustic.dimensions, equations.advection.Advection.dimensions, equations.elastic.Elastic.dimensions, equations.equation.Equation.dimensions, equations.euler.Euler.dimensions, equations.swe.SWE_W_Bathymetry.dimensions, equations.swe.SWE_WO_Bathymetry.dimensions, exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.ncp, equations.equation.Equation.ncp(), equations.swe.SWE_W_Bathymetry.ncp(), exahype2.solvers.aderdg.ADERDG.ADERDG.unknowns(), exahype2.solvers.fv.FV.FV.unknowns(), exahype2.solvers.rkdg.RungeKuttaDG.RungeKuttaDG.unknowns(), exahype2.solvers.rkfd.CellCenteredFiniteDifferences.CellCenteredFiniteDifferences.unknowns(), exahype2.solvers.fv.FV.FV.unknowns(), exahype2.solvers.rkdg.RungeKuttaDG.RungeKuttaDG.unknowns(), exahype2.solvers.rkfd.CellCenteredFiniteDifferences.CellCenteredFiniteDifferences.unknowns(), exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.unknowns, exahype2.symhype.PDE.PDE.unknowns, peano4.visualisation.input.Patch.Patch.unknowns, peano4.visualisation.input.PatchFileParser.UnknownAttributes.unknowns, and convert::data::Variable.unknowns.

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◆ implementation_of_sources()

exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.implementation_of_sources	(		self,
			invoke_evalf_before_output = False )

Return implementation for sources as C code.

Definition at line 264 of file FirstOrderConservativePDEFormulation.py.

References exahype2.symhype.PDE.PDE._implementation_of_mapping_onto_named_quantities(), exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.sources, exahype2.solvers.aderdg.ADERDG.ADERDG.unknowns(), exahype2.solvers.fv.FV.FV.unknowns(), exahype2.solvers.rkdg.RungeKuttaDG.RungeKuttaDG.unknowns(), exahype2.solvers.rkfd.CellCenteredFiniteDifferences.CellCenteredFiniteDifferences.unknowns(), exahype2.solvers.fv.FV.FV.unknowns(), exahype2.solvers.rkdg.RungeKuttaDG.RungeKuttaDG.unknowns(), exahype2.solvers.rkfd.CellCenteredFiniteDifferences.CellCenteredFiniteDifferences.unknowns(), exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.unknowns, exahype2.symhype.PDE.PDE.unknowns, peano4.visualisation.input.Patch.Patch.unknowns, peano4.visualisation.input.PatchFileParser.UnknownAttributes.unknowns, and convert::data::Variable.unknowns.

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◆ LaTeX()

exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.LaTeX ( self )

Definition at line 61 of file FirstOrderConservativePDEFormulation.py.

References exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.eigenvalues, equations.equation.Equation.eigenvalues(), equations.acoustic.Acoustic.eigenvalues(), equations.advection.Advection.eigenvalues(), equations.elastic.Elastic.eigenvalues(), equations.euler.Euler.eigenvalues(), equations.swe.SWE_W_Bathymetry.eigenvalues(), equations.swe.SWE_WO_Bathymetry.eigenvalues(), exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.F, exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.ncp, equations.equation.Equation.ncp(), equations.swe.SWE_W_Bathymetry.ncp(), exahype2.symhype.PDE.PDE.Q, exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.sources, exahype2.solvers.aderdg.ADERDG.ADERDG.unknowns(), exahype2.solvers.fv.FV.FV.unknowns(), exahype2.solvers.rkdg.RungeKuttaDG.RungeKuttaDG.unknowns(), exahype2.solvers.rkfd.CellCenteredFiniteDifferences.CellCenteredFiniteDifferences.unknowns(), exahype2.solvers.fv.FV.FV.unknowns(), exahype2.solvers.rkdg.RungeKuttaDG.RungeKuttaDG.unknowns(), exahype2.solvers.rkfd.CellCenteredFiniteDifferences.CellCenteredFiniteDifferences.unknowns(), exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.unknowns, exahype2.symhype.PDE.PDE.unknowns, peano4.visualisation.input.Patch.Patch.unknowns, peano4.visualisation.input.PatchFileParser.UnknownAttributes.unknowns, and convert::data::Variable.unknowns.

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◆ substitute_expression()

exahype2.symhype.FirstOrderConservativePDEFormulation.FirstOrderConservativePDEFormulation.substitute_expression	(	self,
		expression,
		new_expression )