FiniteVolumeEquation<Vector2D> laplacian(Scalar gamma, VectorFiniteVolumeField &phi, Scalar theta)
{
FiniteVolumeEquation<Vector2D> eqn(phi);
const VectorFiniteVolumeField &phi0 = phi.oldField(0);
for (const Cell &cell: phi.cells())
{
for (const InteriorLink &nb: cell.neighbours())
{
Scalar coeff = gamma * dot(nb.rCellVec(), nb.outwardNorm()) / nb.rCellVec().magSqr();
eqn.add(cell, nb.cell(), theta * coeff);
eqn.add(cell, cell, theta * -coeff);
eqn.addSource(cell, (1. - theta) * coeff * (phi0(nb.cell()) - phi0(cell)));
}
for (const BoundaryLink &bd: cell.boundaries())
{
Scalar coeff = gamma * dot(bd.rFaceVec(), bd.outwardNorm()) / bd.rFaceVec().magSqr();
switch (phi.boundaryType(bd.face()))
{
case VectorFiniteVolumeField::FIXED:
eqn.add(cell, cell, theta * -coeff);
eqn.addSource(cell, theta * coeff * phi(bd.face()));
eqn.addSource(cell, (1. - theta) * coeff * (phi0(bd.face()) - phi0(cell)));
break;
case VectorFiniteVolumeField::NORMAL_GRADIENT:
break;
case VectorFiniteVolumeField::SYMMETRY:
{
Vector2D tw = bd.outwardNorm().tangentVec().unitVec();
eqn.add(cell, cell, theta * -coeff);
eqn.add(cell, cell, theta * coeff * outer(tw, tw));
eqn.addSource(cell, (1. - theta) * coeff * (dot(phi0(cell), tw) * tw - phi0(cell)));
}
break;
case VectorFiniteVolumeField::PARTIAL_SLIP:
{
Vector2D tw = bd.outwardNorm().tangentVec().unitVec();
Scalar lambda = phi.boundaryRefValue(bd.face()).x;
Scalar a = lambda != 0. ? lambda * coeff / (lambda * coeff - 1.) : 0.;
eqn.add(cell, cell, theta * -coeff);
eqn.add(cell, cell, theta * a * coeff * outer(tw, tw));
eqn.addSource(cell, (1. - theta) * coeff * (a * dot(phi0(cell), tw) * tw - phi0(cell)));
}
default:
throw Exception("fv", "laplacian<Vector2D>", "unrecognized or unspecified boundary type.");
}
}
}
return eqn;
}
int
main(int argc,char **argv) {
progname = basename(argv[0]);
eqnexit(eqn(argc, argv));
/*NOTREACHED*/
return 0;
}
int main(int argc, char** argv) {
// Initialize Tempest
TempestInitialize(&argc, &argv);
try {
// Model cap.
double dZtop;
// Earth radius scaling parameter.
double dEarthScaling;
// Deactivate physics
bool fNoPhysics;
// Bryan Boundary Layer
bool fBryanPBL;
// Reed-Jablonowksi precipitation
bool fReedJablonowskiPrecip;
// Parse the command line
BeginTempestCommandLine("TropicalCycloneTest");
SetDefaultResolution(20);
SetDefaultLevels(30);
SetDefaultOutputDeltaT("1h");
SetDefaultDeltaT("200s");
SetDefaultEndTime("10d");
SetDefaultHorizontalOrder(4);
SetDefaultVerticalOrder(1);
CommandLineDouble(dZtop, "ztop", 30000.0);
CommandLineDouble(dEarthScaling, "X", 1.0);
CommandLineBool(fNoPhysics, "nophys");
CommandLineBool(fBryanPBL, "bryanpbl");
CommandLineBool(fReedJablonowskiPrecip, "rjprecip");
ParseCommandLine(argc, argv);
EndTempestCommandLine(argv)
// Setup the Model
AnnounceBanner("MODEL SETUP");
EquationSet eqn(EquationSet::PrimitiveNonhydrostaticEquations);
eqn.InsertTracer("RhoQv", "RhoQv");
eqn.InsertTracer("RhoQc", "RhoQc");
eqn.InsertTracer("RhoQr", "RhoQr");
UserDataMeta metaUserData;
metaUserData.InsertDataItem2D("PRECT");
Model model(eqn, metaUserData);
TempestSetupCubedSphereModel(model);
// Set the test case for the model
AnnounceStartBlock("Initializing test case");
model.SetTestCase(
new TropicalCycloneTest(
dZtop,
dEarthScaling));
AnnounceEndBlock("Done");
// Add DCMIP physics
if (!fNoPhysics) {
model.AttachWorkflowProcess(
new DCMIPPhysics(
model,
model.GetDeltaT(),
2,
(fBryanPBL)?(1):(0),
(fReedJablonowskiPrecip)?(1):(0)));
}
// Begin execution
AnnounceBanner("SIMULATION");
model.Go();
// Compute error norms
AnnounceBanner("RESULTS");
model.ComputeErrorNorms();
AnnounceBanner();
} catch(Exception & e) {
std::cout << e.ToString() << std::endl;
}
// Deinitialize Tempest
TempestDeinitialize();
}
void
sdis(char a1, char a2)
{
int c1, c2;
int eqnf;
int lct;
if(a1 == 'P'){
while(C1 == ' ')
;
if(c == '<') {
SKIP1;
return;
}
}
lct = 0;
eqnf = 1;
if(c != '\n')
SKIP1;
for(;;) {
while(C1 != '.')
if(c == '\n')
continue;
else
SKIP1;
if((c1=C1) == '\n')
continue;
if((c2=C1) == '\n') {
if(a1 == 'f' && (c1 == 'P' || c1 == 'H'))
return;
continue;
}
if(c1==a1 && c2 == a2) {
SKIP1;
if(lct != 0){
lct--;
continue;
}
if(eqnf)
Bprint(&(bout.Biobufhdr), " .");
Bputc(&(bout.Biobufhdr), '\n');
return;
} else
if(a1 == 'L' && c2 == 'L') {
lct++;
SKIP1;
} else
if(a1 == 'D' && c1 == 'E' && c2 == 'Q') {
eqn();
eqnf = 0;
} else
if(a1 == 'f') {
if((mac == MS && c2 == 'P') ||
(mac == MM && c1 == 'H' && c2 == 'U')){
SKIP1;
return;
}
SKIP1;
}
else
SKIP1;
}
}
void
comline(void)
{
long c1, c2;
while(C==' ' || c=='\t')
;
comx:
if((c1=c) == '\n')
return;
c2 = C;
if(c1=='.' && c2!='.')
inmacro = NO;
if(msflag && c1 == '['){
refer(c2);
return;
}
if(c2 == '\n')
return;
if(c1 == '\\' && c2 == '\"')
SKIP;
else
if (filesp==files && c1=='E' && c2=='Q')
eqn();
else
if(filesp==files && c1=='T' && (c2=='S' || c2=='C' || c2=='&')) {
if(msflag)
stbl();
else
tbl();
}
else
if(c1=='T' && c2=='E')
intable = NO;
else if (!inmacro &&
((c1 == 'd' && c2 == 'e') ||
(c1 == 'i' && c2 == 'g') ||
(c1 == 'a' && c2 == 'm')))
macro();
else
if(c1=='s' && c2=='o') {
if(iflag)
SKIP;
else {
getfname();
if(fname[0]) {
if(infile = opn(fname))
*++filesp = infile;
else infile = *filesp;
}
}
}
else
if(c1=='n' && c2=='x')
if(iflag)
SKIP;
else {
getfname();
if(fname[0] == '\0')
exits(0);
if(Bfildes(&(infile->Biobufhdr)) != 0)
Bterm(&(infile->Biobufhdr));
infile = *filesp = opn(fname);
}
else
if(c1 == 't' && c2 == 'm')
SKIP;
else
if(c1=='h' && c2=='w')
SKIP;
else
if(msflag && c1 == 'T' && c2 == 'L') {
SKIP_TO_COM;
goto comx;
}
else
if(msflag && c1=='N' && c2 == 'R')
SKIP;
else
if(msflag && c1 == 'A' && (c2 == 'U' || c2 == 'I')){
if(mac==MM)SKIP;
else {
SKIP_TO_COM;
goto comx;
}
} else
if(msflag && c1=='F' && c2=='S') {
SKIP_TO_COM;
goto comx;
}
else
if(msflag && (c1=='S' || c1=='N') && c2=='H') {
SKIP_TO_COM;
goto comx;
} else
if(c1 == 'U' && c2 == 'X') {
if(wordflag)
Bprint(&(bout.Biobufhdr), "UNIX\n");
else
Bprint(&(bout.Biobufhdr), "UNIX ");
} else
if(msflag && c1=='O' && c2=='K') {
SKIP_TO_COM;
goto comx;
} else
if(msflag && c1=='N' && c2=='D')
SKIP;
else
if(msflag && mac==MM && c1=='H' && (c2==' '||c2=='U'))
SKIP;
else
if(msflag && mac==MM && c2=='L') {
if(disp || c1=='R')
sdis('L', 'E');
else {
SKIP;
Bprint(&(bout.Biobufhdr), " .");
}
} else
if(!msflag && c1=='P' && c2=='S') {
inpic();
} else
if(msflag && (c1=='D' || c1=='N' || c1=='K'|| c1=='P') && c2=='S') {
sdis(c1, 'E');
} else
if(msflag && (c1 == 'K' && c2 == 'F')) {
sdis(c1,'E');
} else
if(msflag && c1=='n' && c2=='f')
sdis('f','i');
else
if(msflag && c1=='c' && c2=='e')
sce();
else {
if(c1=='.' && c2=='.') {
if(msflag) {
SKIP;
return;
}
while(C == '.')
;
}
inmacro++;
if(c1 <= 'Z' && msflag)
regline(YES,ONE);
else {
if(wordflag)
C;
regline(YES,TWO);
}
inmacro--;
}
}
bool BlockStochPoissonTest1D()
{
/* We will do our linear algebra using Epetra */
VectorType<double> vecType = new EpetraVectorType();
/* Read a mesh */
MeshType meshType = new BasicSimplicialMeshType();
int nx = 32;
MeshSource mesher = new PartitionedLineMesher(0.0, 1.0, nx,
meshType);
Mesh mesh = mesher.getMesh();
/* Create a cell filter that will identify the maximal cells
* in the interior of the domain */
CellFilter interior = new MaximalCellFilter();
CellFilter pts = new DimensionalCellFilter(0);
CellFilter left = pts.subset(new CoordinateValueCellPredicate(0,0.0));
CellFilter right = pts.subset(new CoordinateValueCellPredicate(0,1.0));
Expr x = new CoordExpr(0);
/* Create the stochastic coefficients */
int nDim = 1;
int order = 6;
#ifdef HAVE_SUNDANCE_STOKHOS
Out::root() << "using Stokhos hermite basis" << std::endl;
SpectralBasis pcBasis = new Stokhos::HermiteBasis<int,double>(order);
#else
Out::root() << "using George's hermite basis" << std::endl;
SpectralBasis pcBasis = new HermiteSpectralBasis(nDim, order);
#endif
Array<Expr> q(pcBasis.nterms());
Array<Expr> kappa(pcBasis.nterms());
Array<Expr> uEx(pcBasis.nterms());
double a = 0.1;
q[0] = -2 + pow(a,2)*(4 - 9*x)*x - 2*pow(a,3)*(-1 + x)*(1 + 3*x*(-3 + 4*x));
q[1] = -(a*(-3 + 10*x + 2*a*(-1 + x*(8 - 9*x +
a*(-4 + 3*(5 - 4*x)*x + 12*a*(-1 + x)*(1 + 5*(-1 + x)*x))))));
q[2] = a*(-4 + 6*x + a*(1 - x*(2 + 3*x) + a*(4 - 28*x + 30*pow(x,2))));
q[3] = -(pow(a,2)*(-3 + x*(20 - 21*x +
a*(-4 + 3*(5 - 4*x)*x + 24*a*(-1 + x)*(1 + 5*(-1 + x)*x)))));
q[4] = pow(a,3)*(1 + x*(-6 + x*(3 + 4*x)));
q[5] = -4*pow(a,4)*(-1 + x)*x*(1 + 5*(-1 + x)*x);
q[6] = 0.0;
uEx[0] = -((-1 + x)*x);
uEx[1] = -(a*(-1 + x)*pow(x,2));
uEx[2] = a*pow(-1 + x,2)*x;
uEx[3] = pow(a,2)*pow(-1 + x,2)*pow(x,2);
uEx[4] = 0.0;
uEx[5] = 0.0;
uEx[6] = 0.0;
kappa[0] = 1.0;
kappa[1] = a*x;
kappa[2] = -(pow(a,2)*(-1 + x)*x);
kappa[3] = 1.0; // unused
kappa[4] = 1.0; // unused
kappa[5] = 1.0; // unused
kappa[6] = 1.0; // unused
Array<Expr> uBC(pcBasis.nterms());
for (int i=0; i<pcBasis.nterms(); i++) uBC[i] = 0.0;
int L = nDim+2;
int P = pcBasis.nterms();
Out::os() << "L = " << L << std::endl;
Out::os() << "P = " << P << std::endl;
/* Create the unknown and test functions. Do NOT use the spectral
* basis here */
Expr u = new UnknownFunction(new Lagrange(4), "u");
Expr v = new TestFunction(new Lagrange(4), "v");
/* Create differential operator and coordinate function */
Expr dx = new Derivative(0);
Expr grad = dx;
/* We need a quadrature rule for doing the integrations */
QuadratureFamily quad = new GaussianQuadrature(12);
/* Now we create problem objects to build each $K_j$ and $f_j$.
* There will be L matrix-vector pairs */
Array<Expr> eqn(P);
Array<Expr> bc(P);
Array<LinearProblem> prob(P);
Array<LinearOperator<double> > KBlock(L);
Array<Vector<double> > fBlock(P);
Array<Vector<double> > solnBlock;
for (int j=0; j<P; j++)
{
eqn[j] = Integral(interior, kappa[j]*(grad*v)*(grad*u) + v*q[j], quad);
bc[j] = EssentialBC(left+right, v*(u-uBC[j]), quad);
prob[j] = LinearProblem(mesh, eqn[j], bc[j], v, u, vecType);
if (j<L) KBlock[j] = prob[j].getOperator();
fBlock[j] = -1.0*prob[j].getSingleRHS();
}
/* Read the solver to be used on the diagonal blocks */
LinearSolver<double> diagSolver
= LinearSolverBuilder::createSolver("amesos.xml");
double convTol = 1.0e-12;
int maxIters = 30;
int verb = 1;
StochBlockJacobiSolver solver(diagSolver, pcBasis,
convTol, maxIters, verb);
solver.solve(KBlock, fBlock, solnBlock);
/* write the solution */
FieldWriter w = new MatlabWriter("Stoch1D");
w.addMesh(mesh);
DiscreteSpace discSpace(mesh, new Lagrange(4), vecType);
for (int i=0; i<P; i++)
{
L2Projector proj(discSpace, uEx[i]);
Expr ue_i = proj.project();
Expr df = new DiscreteFunction(discSpace, solnBlock[i]);
w.addField("u["+ Teuchos::toString(i)+"]",
new ExprFieldWrapper(df));
w.addField("uEx["+ Teuchos::toString(i)+"]",
new ExprFieldWrapper(ue_i));
}
w.write();
double totalErr2 = 0.0;
DiscreteSpace discSpace4(mesh, new Lagrange(4), vecType);
for (int i=0; i<P; i++)
{
Expr df = new DiscreteFunction(discSpace4, solnBlock[i]);
Expr errExpr = Integral(interior, pow(uEx[i]-df, 2.0), quad);
Expr scaleExpr = Integral(interior, pow(uEx[i], 2.0), quad);
double errSq = evaluateIntegral(mesh, errExpr);
double scale = evaluateIntegral(mesh, scaleExpr);
if (scale > 0.0)
Out::os() << "mode i=" << i << " error=" << sqrt(errSq/scale) << std::endl;
else
Out::os() << "mode i=" << i << " error=" << sqrt(errSq) << std::endl;
}
double tol = 1.0e-12;
return SundanceGlobal::checkTest(sqrt(totalErr2), tol);
}