Commit 27d8ae65 authored by Gianmarco Mengaldo's avatar Gianmarco Mengaldo

Regression tests added for both ADRSolver (diffusion operator) and...

Regression tests added for both ADRSolver (diffusion operator) and CompressibleFlowSolver (NS). Solved a bug in LDG (Vn instead of m_traceNormals into the Upwind method).
parent 13aa1f16
......@@ -61,6 +61,7 @@ namespace Nektar
const Array<OneD, Array<OneD, NekDouble> > &inarray,
Array<OneD, Array<OneD, NekDouble> > &outarray)
{
//cout<<setprecision(16);
int i, j, k;
int nDim = fields[0]->GetCoordim(0);
int nPts = fields[0]->GetTotPoints();
......@@ -168,6 +169,13 @@ namespace Nektar
}
fields[0]->GetTrace()->GetNormals(m_traceNormals);
// Get the normal velocity Vn
for(i = 0; i < nDim; ++i)
{
Vmath::Svtvp(nTracePts, 1.0, m_traceNormals[i], 1,
Vn, 1, Vn, 1);
}
// Get the sign of (v \cdot n), v = an arbitrary vector
// Evaluate upwind flux:
// uflux = \hat{u} \phi \cdot u = u^{(+,-)} n
......@@ -186,7 +194,7 @@ namespace Nektar
// edge::eForward, if V*n<0 <=> V*n_F<0, pick uflux = uBwd
// edge::eBackward, if V*n<0 <=> V*n_B>=0, pick uflux = uBwd
fields[i]->GetTrace()->Upwind(m_traceNormals[j],
fields[i]->GetTrace()->Upwind(/*m_traceNormals[j]*/Vn,
Fwd, Bwd, fluxtemp);
// Imposing weak boundary condition with flux
......@@ -315,6 +323,13 @@ namespace Nektar
}
fields[0]->GetTrace()->GetNormals(m_traceNormals);
// Get the normal velocity Vn
for(i = 0; i < nDim; ++i)
{
Vmath::Svtvp(nTracePts, 1.0, m_traceNormals[i], 1,
Vn, 1, Vn, 1);
}
// Evaulate upwind flux:
// qflux = \hat{q} \cdot u = q \cdot n - C_(11)*(u^+ - u^-)
for (i = 0; i < nvariables; ++i)
......@@ -337,7 +352,7 @@ namespace Nektar
// edge::eBackward, if V*n<0 <=> V*n_B>=0, pick
// qflux = qFwd = q+
fields[i]->GetTrace()->Upwind(m_traceNormals[j],
fields[i]->GetTrace()->Upwind(/*m_traceNormals[j]*/Vn,
qBwd, qFwd,
qfluxtemp);
......
......@@ -84,7 +84,7 @@ namespace Nektar
const Array<OneD, Array<OneD, NekDouble> > &inarray,
Array<OneD, Array<OneD, NekDouble> > &outarray)
{
cout<<setprecision(16);
//cout<<setprecision(16);
int i, j;
int nDim = fields[0]->GetCoordim(0);
int nScalars = inarray.num_elements();
......
......@@ -35,6 +35,7 @@
#include <SolverUtils/Diffusion/DiffusionLFR.h>
#include <LibUtilities/Polylib/Polylib.h>
#include <boost/math/special_functions/gamma.hpp>
#include <iostream>
#include <iomanip>
......@@ -768,9 +769,9 @@ namespace Nektar
const Array<OneD, Array<OneD, NekDouble> > &inarray,
Array<OneD, Array<OneD, NekDouble> > &outarray)
{
//cout<<setprecision(16);
int i, j, n, z;
int nLocalSolutionPts, phys_offset;
Array<TwoD, const NekDouble> gmat;
Array<OneD, const NekDouble> jac;
Array<OneD, NekDouble> auxArray1, auxArray2, auxArray3;
......@@ -802,10 +803,10 @@ namespace Nektar
iuFluxO1[i][j] = Array<OneD, NekDouble>(nTracePts, 0.0);
}
}
// Compute interface numerical fluxes for inarray in physical space
v_NumFluxforScalar(fields, inarray, iuFluxO1);
switch(nDim)
{
// 1D problems
......
......@@ -74,8 +74,21 @@ IF( NEKTAR_SOLVER_ADR )
ADD_NEKTAR_TEST(Advection_m12_Order2)
ADD_NEKTAR_TEST(Advection_m14_DG_Order4)
ADD_NEKTAR_TEST(Advection_m14_Order4)
ADD_NEKTAR_TEST(ExDiffusion_m3)
ADD_NEKTAR_TEST(ExDiffusion_m8)
ADD_NEKTAR_TEST(ExDiffusion_1D_LDG)
ADD_NEKTAR_TEST(ExDiffusion_1D_LFRDG)
ADD_NEKTAR_TEST(ExDiffusion_1D_LFRHU)
ADD_NEKTAR_TEST(ExDiffusion_1D_LFRSD)
ADD_NEKTAR_TEST(ExDiffusion_2D_LDG_hybrid_m3)
ADD_NEKTAR_TEST(ExDiffusion_2D_LDG_hybrid_m8)
ADD_NEKTAR_TEST(ExDiffusion_2D_LDG_regular_Neumann)
ADD_NEKTAR_TEST(ExDiffusion_2D_LFRDG_regular_Neumann)
ADD_NEKTAR_TEST(ExDiffusion_2D_LFRHU_regular_Neumann)
ADD_NEKTAR_TEST(ExDiffusion_2D_LFRSD_regular_Neumann)
ADD_NEKTAR_TEST(ExDiffusion_2D_LDG_deformed)
ADD_NEKTAR_TEST(ExDiffusion_2D_LFRDG_deformed)
ADD_NEKTAR_TEST(ExDiffusion_2D_LFRHU_deformed)
ADD_NEKTAR_TEST(ExDiffusion_2D_LFRSD_deformed)
ADD_NEKTAR_TEST(Helmholtz1D_8modes_DG)
ADD_NEKTAR_TEST(Helmholtz1D_8modes)
ADD_NEKTAR_TEST(Helmholtz1D_8nodes)
......
<?xml version="1.0" encoding="utf-8"?>
<test>
<description>2D unsteady DG explicit diffusion, order 4, P=8</description>
<description>1D unsteady LDG explicit diffusion, order 3, P=2</description>
<executable>ADRSolver</executable>
<parameters>ExDiffusion_m8.xml</parameters>
<parameters>ExDiffusion_1D_LDG.xml</parameters>
<files>
<file description="Session File">ExDiffusion_m8.xml</file>
<file description="Session File">ExDiffusion_1D_LDG.xml</file>
</files>
<metrics>
<metric type="L2" id="1">
<value variable="u" tolerance="1e-12">0.000337147</value>
<value variable="u" tolerance="1e-12">0.00196469</value>
</metric>
<metric type="Linf" id="2">
<value variable="u" tolerance="1e-12">0.00279079</value>
<value variable="u" tolerance="1e-12">0.00925869</value>
</metric>
</metrics>
</test>
<?xml version="1.0" encoding="utf-8" ?>
<NEKTAR>
<GEOMETRY DIM="1" SPACE="1">
<VERTEX>
<V ID="0"> -1.0 0.0 0.0</V>
<V ID="1"> -0.8 0.0 0.0</V>
<V ID="2"> -0.6 0.0 0.0</V>
<V ID="3"> -0.4 0.0 0.0</V>
<V ID="4"> -0.2 0.0 0.0</V>
<V ID="5"> 0.0 0.0 0.0</V>
<V ID="6"> 0.2 0.0 0.0</V>
<V ID="7"> 0.4 0.0 0.0</V>
<V ID="8"> 0.6 0.0 0.0</V>
<V ID="9"> 0.8 0.0 0.0</V>
<V ID="10"> 1.0 0.0 0.0</V>
</VERTEX>
<ELEMENT>
<S ID="0"> 0 1 </S>
<S ID="1"> 1 2 </S>
<S ID="2"> 2 3 </S>
<S ID="3"> 3 4 </S>
<S ID="4"> 4 5 </S>
<S ID="5"> 5 6 </S>
<S ID="6"> 6 7 </S>
<S ID="7"> 7 8 </S>
<S ID="8"> 8 9 </S>
<S ID="9"> 9 10 </S>
</ELEMENT>
<COMPOSITE>
<C ID="0"> S[0-9] </C>
<C ID="1"> V[0] </C>
<C ID="2"> V[10] </C>
</COMPOSITE>
<DOMAIN> C[0] </DOMAIN>
</GEOMETRY>
<EXPANSIONS>
<E COMPOSITE="C[0]" FIELDS="u" TYPE="GLL_LAGRANGE_SEM" NUMMODES="3"/>
</EXPANSIONS>
<CONDITIONS>
<PARAMETERS>
<P> TimeStep = 0.000001 </P>
<P> NumSteps = 100 </P>
<P> FinTime = TimeStep * NumSteps </P>
<P> IO_CheckSteps = 100000 </P>
<P> IO_InfoSteps = 100000 </P>
</PARAMETERS>
<SOLVERINFO>
<I PROPERTY="EQTYPE" VALUE="UnsteadyDiffusion" />
<I PROPERTY="Projection" VALUE="DisContinuous" />
<I PROPERTY="DiffusionType" VALUE="LDG" />
<I PROPERTY="DiffusionAdvancement" VALUE="Explicit" />
<I PROPERTY="TimeIntegrationMethod" VALUE="ClassicalRungeKutta4"/>
</SOLVERINFO>
<VARIABLES>
<V ID="0"> u </V>
</VARIABLES>
<BOUNDARYREGIONS>
<B ID="0"> C[1] </B>
<B ID="1"> C[2] </B>
</BOUNDARYREGIONS>
<BOUNDARYCONDITIONS>
<REGION REF="0">
<D VAR="u" USERDEFINEDTYPE="TimeDependent"
VALUE="exp(-2.0*PI*PI*t)*sin(PI*x)" />
</REGION>
<REGION REF="1">
<D VAR="u" USERDEFINEDTYPE="TimeDependent"
VALUE="exp(-2.0*PI*PI*t)*sin(PI*x)" />
</REGION>
</BOUNDARYCONDITIONS>
<FUNCTION NAME="InitialConditions">
<E VAR="u" VALUE="sin(PI*x)" />
</FUNCTION>
<FUNCTION NAME="ExactSolution">
<E VAR="u" VALUE="exp(-2.0*PI*PI*FinTime)*sin(PI*x)" />
</FUNCTION>
</CONDITIONS>
</NEKTAR>
<?xml version="1.0" encoding="utf-8"?>
<test>
<description>1D unsteady LFRDG explicit diffusion, order 3, P=2</description>
<executable>ADRSolver</executable>
<parameters>ExDiffusion_1D_LFRDG.xml</parameters>
<files>
<file description="Session File">ExDiffusion_1D_LFRDG.xml</file>
</files>
<metrics>
<metric type="L2" id="1">
<value variable="u" tolerance="1e-12">0.00295</value>
</metric>
<metric type="Linf" id="2">
<value variable="u" tolerance="1e-12">0.0137468</value>
</metric>
</metrics>
</test>
<?xml version="1.0" encoding="utf-8" ?>
<NEKTAR>
<GEOMETRY DIM="1" SPACE="1">
<VERTEX>
<V ID="0"> -1.0 0.0 0.0</V>
<V ID="1"> -0.8 0.0 0.0</V>
<V ID="2"> -0.6 0.0 0.0</V>
<V ID="3"> -0.4 0.0 0.0</V>
<V ID="4"> -0.2 0.0 0.0</V>
<V ID="5"> 0.0 0.0 0.0</V>
<V ID="6"> 0.2 0.0 0.0</V>
<V ID="7"> 0.4 0.0 0.0</V>
<V ID="8"> 0.6 0.0 0.0</V>
<V ID="9"> 0.8 0.0 0.0</V>
<V ID="10"> 1.0 0.0 0.0</V>
</VERTEX>
<ELEMENT>
<S ID="0"> 0 1 </S>
<S ID="1"> 1 2 </S>
<S ID="2"> 2 3 </S>
<S ID="3"> 3 4 </S>
<S ID="4"> 4 5 </S>
<S ID="5"> 5 6 </S>
<S ID="6"> 6 7 </S>
<S ID="7"> 7 8 </S>
<S ID="8"> 8 9 </S>
<S ID="9"> 9 10 </S>
</ELEMENT>
<COMPOSITE>
<C ID="0"> S[0-9] </C>
<C ID="1"> V[0] </C>
<C ID="2"> V[10] </C>
</COMPOSITE>
<DOMAIN> C[0] </DOMAIN>
</GEOMETRY>
<EXPANSIONS>
<E COMPOSITE="C[0]" FIELDS="u" TYPE="GLL_LAGRANGE_SEM" NUMMODES="3"/>
</EXPANSIONS>
<CONDITIONS>
<PARAMETERS>
<P> TimeStep = 0.000001 </P>
<P> NumSteps = 100 </P>
<P> FinTime = TimeStep * NumSteps </P>
<P> IO_CheckSteps = 100000 </P>
<P> IO_InfoSteps = 100000 </P>
</PARAMETERS>
<SOLVERINFO>
<I PROPERTY="EQTYPE" VALUE="UnsteadyDiffusion" />
<I PROPERTY="Projection" VALUE="DisContinuous" />
<I PROPERTY="DiffusionType" VALUE="LFRDG" />
<I PROPERTY="DiffusionAdvancement" VALUE="Explicit" />
<I PROPERTY="TimeIntegrationMethod" VALUE="ClassicalRungeKutta4"/>
</SOLVERINFO>
<VARIABLES>
<V ID="0"> u </V>
</VARIABLES>
<BOUNDARYREGIONS>
<B ID="0"> C[1] </B>
<B ID="1"> C[2] </B>
</BOUNDARYREGIONS>
<BOUNDARYCONDITIONS>
<REGION REF="0">
<D VAR="u" USERDEFINEDTYPE="TimeDependent"
VALUE="exp(-2.0*PI*PI*t)*sin(PI*x)" />
</REGION>
<REGION REF="1">
<D VAR="u" USERDEFINEDTYPE="TimeDependent"
VALUE="exp(-2.0*PI*PI*t)*sin(PI*x)" />
</REGION>
</BOUNDARYCONDITIONS>
<FUNCTION NAME="InitialConditions">
<E VAR="u" VALUE="sin(PI*x)" />
</FUNCTION>
<FUNCTION NAME="ExactSolution">
<E VAR="u" VALUE="exp(-2.0*PI*PI*FinTime)*sin(PI*x)" />
</FUNCTION>
</CONDITIONS>
</NEKTAR>
<?xml version="1.0" encoding="utf-8"?>
<test>
<description>1D unsteady LFRHU explicit diffusion, order 3, P=2</description>
<executable>ADRSolver</executable>
<parameters>ExDiffusion_1D_LFRHU.xml</parameters>
<files>
<file description="Session File">ExDiffusion_1D_LFRHU.xml</file>
</files>
<metrics>
<metric type="L2" id="1">
<value variable="u" tolerance="1e-12">0.00196469</value>
</metric>
<metric type="Linf" id="2">
<value variable="u" tolerance="1e-12">0.00925869</value>
</metric>
</metrics>
</test>
<?xml version="1.0" encoding="utf-8" ?>
<NEKTAR>
<GEOMETRY DIM="1" SPACE="1">
<VERTEX>
<V ID="0"> -1.0 0.0 0.0</V>
<V ID="1"> -0.8 0.0 0.0</V>
<V ID="2"> -0.6 0.0 0.0</V>
<V ID="3"> -0.4 0.0 0.0</V>
<V ID="4"> -0.2 0.0 0.0</V>
<V ID="5"> 0.0 0.0 0.0</V>
<V ID="6"> 0.2 0.0 0.0</V>
<V ID="7"> 0.4 0.0 0.0</V>
<V ID="8"> 0.6 0.0 0.0</V>
<V ID="9"> 0.8 0.0 0.0</V>
<V ID="10"> 1.0 0.0 0.0</V>
</VERTEX>
<ELEMENT>
<S ID="0"> 0 1 </S>
<S ID="1"> 1 2 </S>
<S ID="2"> 2 3 </S>
<S ID="3"> 3 4 </S>
<S ID="4"> 4 5 </S>
<S ID="5"> 5 6 </S>
<S ID="6"> 6 7 </S>
<S ID="7"> 7 8 </S>
<S ID="8"> 8 9 </S>
<S ID="9"> 9 10 </S>
</ELEMENT>
<COMPOSITE>
<C ID="0"> S[0-9] </C>
<C ID="1"> V[0] </C>
<C ID="2"> V[10] </C>
</COMPOSITE>
<DOMAIN> C[0] </DOMAIN>
</GEOMETRY>
<EXPANSIONS>
<E COMPOSITE="C[0]" FIELDS="u" TYPE="GLL_LAGRANGE_SEM" NUMMODES="3"/>
</EXPANSIONS>
<CONDITIONS>
<PARAMETERS>
<P> TimeStep = 0.000001 </P>
<P> NumSteps = 100 </P>
<P> FinTime = TimeStep * NumSteps </P>
<P> IO_CheckSteps = 100000 </P>
<P> IO_InfoSteps = 100000 </P>
</PARAMETERS>
<SOLVERINFO>
<I PROPERTY="EQTYPE" VALUE="UnsteadyDiffusion" />
<I PROPERTY="Projection" VALUE="DisContinuous" />
<I PROPERTY="DiffusionType" VALUE="LFRHU" />
<I PROPERTY="DiffusionAdvancement" VALUE="Explicit" />
<I PROPERTY="TimeIntegrationMethod" VALUE="ClassicalRungeKutta4"/>
</SOLVERINFO>
<VARIABLES>
<V ID="0"> u </V>
</VARIABLES>
<BOUNDARYREGIONS>
<B ID="0"> C[1] </B>
<B ID="1"> C[2] </B>
</BOUNDARYREGIONS>
<BOUNDARYCONDITIONS>
<REGION REF="0">
<D VAR="u" USERDEFINEDTYPE="TimeDependent"
VALUE="exp(-2.0*PI*PI*t)*sin(PI*x)" />
</REGION>
<REGION REF="1">
<D VAR="u" USERDEFINEDTYPE="TimeDependent"
VALUE="exp(-2.0*PI*PI*t)*sin(PI*x)" />
</REGION>
</BOUNDARYCONDITIONS>
<FUNCTION NAME="InitialConditions">
<E VAR="u" VALUE="sin(PI*x)" />
</FUNCTION>
<FUNCTION NAME="ExactSolution">
<E VAR="u" VALUE="exp(-2.0*PI*PI*FinTime)*sin(PI*x)" />
</FUNCTION>
</CONDITIONS>
</NEKTAR>
<?xml version="1.0" encoding="utf-8"?>
<test>
<description>2D unsteady DG explicit diffusion, order 4, P=3</description>
<description>1D unsteady LFRSD explicit diffusion, order 3, P=2</description>
<executable>ADRSolver</executable>
<parameters>ExDiffusion_m3.xml</parameters>
<parameters>ExDiffusion_1D_LFRSD.xml</parameters>
<files>
<file description="Session File">ExDiffusion_m3.xml</file>
<file description="Session File">ExDiffusion_1D_LFRSD.xml</file>
</files>
<metrics>
<metric type="L2" id="1">
<value variable="u" tolerance="1e-12">0.00712372</value>
<value variable="u" tolerance="1e-12">0.00225094</value>
</metric>
<metric type="Linf" id="2">
<value variable="u" tolerance="1e-12">0.0195377</value>
<value variable="u" tolerance="1e-12">0.0107938</value>
</metric>
</metrics>
</test>
......
<?xml version="1.0" encoding="utf-8" ?>
<NEKTAR>
<GEOMETRY DIM="1" SPACE="1">
<VERTEX>
<V ID="0"> -1.0 0.0 0.0</V>
<V ID="1"> -0.8 0.0 0.0</V>
<V ID="2"> -0.6 0.0 0.0</V>
<V ID="3"> -0.4 0.0 0.0</V>
<V ID="4"> -0.2 0.0 0.0</V>
<V ID="5"> 0.0 0.0 0.0</V>
<V ID="6"> 0.2 0.0 0.0</V>
<V ID="7"> 0.4 0.0 0.0</V>
<V ID="8"> 0.6 0.0 0.0</V>
<V ID="9"> 0.8 0.0 0.0</V>
<V ID="10"> 1.0 0.0 0.0</V>
</VERTEX>
<ELEMENT>
<S ID="0"> 0 1 </S>
<S ID="1"> 1 2 </S>
<S ID="2"> 2 3 </S>
<S ID="3"> 3 4 </S>
<S ID="4"> 4 5 </S>
<S ID="5"> 5 6 </S>
<S ID="6"> 6 7 </S>
<S ID="7"> 7 8 </S>
<S ID="8"> 8 9 </S>
<S ID="9"> 9 10 </S>
</ELEMENT>
<COMPOSITE>
<C ID="0"> S[0-9] </C>
<C ID="1"> V[0] </C>
<C ID="2"> V[10] </C>
</COMPOSITE>
<DOMAIN> C[0] </DOMAIN>
</GEOMETRY>
<EXPANSIONS>
<E COMPOSITE="C[0]" FIELDS="u" TYPE="GLL_LAGRANGE_SEM" NUMMODES="3"/>
</EXPANSIONS>
<CONDITIONS>
<PARAMETERS>
<P> TimeStep = 0.000001 </P>
<P> NumSteps = 100 </P>
<P> FinTime = TimeStep * NumSteps </P>
<P> IO_CheckSteps = 100000 </P>
<P> IO_InfoSteps = 100000 </P>
</PARAMETERS>
<SOLVERINFO>
<I PROPERTY="EQTYPE" VALUE="UnsteadyDiffusion" />
<I PROPERTY="Projection" VALUE="DisContinuous" />
<I PROPERTY="DiffusionType" VALUE="LFRSD" />
<I PROPERTY="DiffusionAdvancement" VALUE="Explicit" />
<I PROPERTY="TimeIntegrationMethod" VALUE="ClassicalRungeKutta4"/>
</SOLVERINFO>
<VARIABLES>
<V ID="0"> u </V>
</VARIABLES>
<BOUNDARYREGIONS>
<B ID="0"> C[1] </B>
<B ID="1"> C[2] </B>
</BOUNDARYREGIONS>
<BOUNDARYCONDITIONS>
<REGION REF="0">
<D VAR="u" USERDEFINEDTYPE="TimeDependent"
VALUE="exp(-2.0*PI*PI*t)*sin(PI*x)" />
</REGION>
<REGION REF="1">
<D VAR="u" USERDEFINEDTYPE="TimeDependent"
VALUE="exp(-2.0*PI*PI*t)*sin(PI*x)" />
</REGION>
</BOUNDARYCONDITIONS>
<FUNCTION NAME="InitialConditions">
<E VAR="u" VALUE="sin(PI*x)" />
</FUNCTION>
<FUNCTION NAME="ExactSolution">
<E VAR="u" VALUE="exp(-2.0*PI*PI*FinTime)*sin(PI*x)" />
</FUNCTION>
</CONDITIONS>
</NEKTAR>
<?xml version="1.0" encoding="utf-8"?>
<test>
<description>2D unsteady LDG explicit diffusion, deformed quads, P=3</description>
<executable>ADRSolver</executable>
<parameters>ExDiffusion_2D_LDG_deformed.xml</parameters>
<files>
<file description="Session File">ExDiffusion_2D_LDG_deformed.xml</file>
</files>
<metrics>
<metric type="L2" id="1">
<value variable="u" tolerance="1e-12">0.00142525</value>
</metric>
<metric type="Linf" id="2">
<value variable="u" tolerance="1e-12">0.00922016</value>
</metric>
</metrics>
</test>
<?xml version="1.0" encoding="utf-8"?>
<NEKTAR xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xsi:noNamespaceSchemaLocation="http://www.nektar.info/schema/nektar.xsd">
<GEOMETRY DIM="2" SPACE="2">
<VERTEX>
<V ID="0"> -1.3 -1.2 0.0 </V>
<V ID="1"> 0.1 -1.2 0.0 </V>
<V ID="2"> 1.0 -1.0 0.0 </V>
<V ID="3"> -1.0 0.0 0.0 </V>
<V ID="4"> -0.4 -0.3 0.0 </V>
<V ID="5"> 1.0 0.0 0.0 </V>
<V ID="6"> -1.0 1.0 0.0 </V>
<V ID="7"> 0.3 1.2 0.0 </V>
<V ID="8"> 1.0 1.0 0.0 </V>
</VERTEX>
<EDGE>
<E ID="0"> 0 1 </E>
<E ID="1"> 1 2 </E>
<E ID="2"> 0 3 </E>
<E ID="3"> 1 4 </E>
<E ID="4"> 2 5 </E>
<E ID="5"> 3 4 </E>
<E ID="6"> 4 5 </E>
<E ID="7"> 3 6 </E>
<E ID="8"> 4 7 </E>
<E ID="9"> 5 8 </E>
<E ID="10"> 6 7 </E>
<E ID="11"> 7 8 </E>
</EDGE>
<ELEMENT>
<Q ID="0"> 2 0 3 5 </Q>
<Q ID="1"> 4 6 3 1 </Q>
<Q ID="2"> 10 7 5 8 </Q>
<Q ID="3"> 11 8 6 9 </Q>
</ELEMENT>
<COMPOSITE>
<C ID="0"> Q[0-3] </C>
<C ID="1"> E[0,1,2,4,7,9,10,11] </C>
</COMPOSITE>
<DOMAIN> C[0] </DOMAIN>
</GEOMETRY>
<EXPANSIONS>
<E COMPOSITE="C[0]" NUMMODES="4" FIELDS="u" TYPE="GLL_LAGRANGE_SEM" />
</EXPANSIONS>
<CONDITIONS>
<PARAMETERS>
<P> TimeStep = 0.000001 </P>
<P> NumSteps = 100 </P>
<P> FinTime = TimeStep*NumSteps </P>
<P> IO_CheckSteps = 100000 </P>
<P> IO_InfoSteps = 100000 </P>
</PARAMETERS>
<SOLVERINFO>
<I PROPERTY="EQTYPE" VALUE="UnsteadyDiffusion" />
<I PROPERTY="Projection" VALUE="DisContinuous" />
<I PROPERTY="DiffusionType" VALUE="LDG" />
<I PROPERTY="DiffusionAdvancement" VALUE="Explicit" />
<I PROPERTY="TimeIntegrationMethod" VALUE="ClassicalRungeKutta4"/>
</SOLVERINFO>
<VARIABLES>
<V ID="0"> u </V>
</VARIABLES>