public static XdgTimesteppingTestControl AggDbg()
{
XdgTimesteppingTestControl R = new XdgTimesteppingTestControl();
R.ProjectName = "XdgMassMatrixEvolution/AgglomDebuch";
R.savetodb = false;
R.FieldOptions.Add("Phi", new FieldOpts()
{
Degree = 3,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("u", new FieldOpts()
{
Degree = 1,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Vx", new FieldOpts()
{
Degree = 1,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Vy", new FieldOpts()
{
Degree = 1,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.GridFunc = delegate() {
var grd = Grid2D.Cartesian2DGrid(new double[] { -4, -2, 0, 2, 4 }, GenericBlas.Linspace(-1, 1, 2));
grd.AddPredefinedPartitioning("For2", (double[] X) => (Math.Sign(X[0]) + 1) / 2);
return(grd);
};
R.GridPartType = GridPartType.Predefined;
R.GridPartOptions = "For2";
const double S = 0.3;
R.S = ((double[] X, double t) => S);
R.Phi = ((double[] X, double t) => X[0] - S * t);
// set the level-set
R.InitialValues_Evaluators.Add("Phi", X => R.Phi(X, 0.0));
R.InitialValues_Evaluators.Add("Vx", X => 0.3);
R.InitialValues_Evaluators.Add("Vy", X => 0.0);
R.InitialValues_Evaluators.Add("u#A", X => 0.8);
R.InitialValues_Evaluators.Add("u#B", X => 1.66);
//R.InitialValues_Evaluators.Add("u#A", X => X[0] < 0 ? 0.8 : 1.66);
//R.InitialValues_Evaluators.Add("u#B", X => X[0] < 0 ? 0.8 : 1.66);
R.dtFixed = 0.18;
return(R);
}
public static void TestConvection_MovingInterface_MultiinitHighOrder(
[Values(1, 2, 3)] int PolyOrder,
[Values(0.2, 0.23)] double TimestepSize
)
{
// set up
// ------------------------------------------
TimeSteppingScheme tsc;
switch (PolyOrder)
{
case 0: tsc = TimeSteppingScheme.ImplicitEuler; break;
case 1: tsc = TimeSteppingScheme.BDF2; break;
case 2: tsc = TimeSteppingScheme.BDF3; break;
case 3: tsc = TimeSteppingScheme.BDF4; break;
default: throw new ArgumentOutOfRangeException();
}
XdgTimesteppingTestControl ctrl = HardCodedControl.Gerade(angle: 0, degree: PolyOrder, GridResolutionFactor: 1);
ctrl.NoOfTimesteps = 8;
ctrl.dtFixed = TimestepSize;
ctrl.Endtime = ctrl.dtFixed * ctrl.NoOfTimesteps;
ctrl.MultiStepInit = true;
ctrl.TimeSteppingScheme = tsc;
ctrl.InterfaceMode = InterfaceMode.MovingInterface;
// run
// ------------------------------------------
XdgTimesteppingMain p = new XdgTimesteppingMain();
p.Init(ctrl);
p.RunSolverMode();
// evaluate/check
// ------------------------------------------
double thres = 5.0e-11;
double uA_Err = (double)p.QueryHandler.QueryResults["uA_Err"];
double uB_Err = (double)p.QueryHandler.QueryResults["uB_Err"];
double JmpL2Err = (double)p.QueryHandler.QueryResults["uJmp_Err"];
Console.WriteLine("L2 Error of solution (A/B/jmp): {0}/{1}/{2} (threshold is {3}).", uA_Err, uB_Err, JmpL2Err, thres);
Assert.LessOrEqual(uA_Err, thres);
Assert.LessOrEqual(uB_Err, thres);
Assert.LessOrEqual(JmpL2Err, thres);
}
public static void TestConvection_Splitting_LowOrder(
[Values(TimeSteppingScheme.ExplicitEuler, TimeSteppingScheme.CrankNicolson, TimeSteppingScheme.ImplicitEuler,
TimeSteppingScheme.BDF2, TimeSteppingScheme.BDF3, TimeSteppingScheme.BDF4,
TimeSteppingScheme.RK1, TimeSteppingScheme.RK1u1, TimeSteppingScheme.RK3, TimeSteppingScheme.RK4,
TimeSteppingScheme.RK_ImplicitEuler, TimeSteppingScheme.RK_CrankNic, TimeSteppingScheme.RK_IMEX3)] TimeSteppingScheme tsc,
[Values(0.2, 0.23)] double TimestepSize,
[Values(8)] int NoOfTs,
[Values(0.0)] double TimeOffest
)
{
// set up
// ------------------------------------------
XdgTimesteppingTestControl ctrl = HardCodedControl.Gerade(angle: 0, degree: 0, GridResolutionFactor: 1);
ctrl.NoOfTimesteps = NoOfTs;
ctrl.dtFixed = TimestepSize;
ctrl.Endtime = ctrl.dtFixed * ctrl.NoOfTimesteps;
ctrl.MultiStepInit = false;
ctrl.TimeSteppingScheme = tsc;
ctrl.InterfaceMode = InterfaceMode.Splitting;
// run
// ------------------------------------------
XdgTimesteppingMain p = new XdgTimesteppingMain();
p.Init(ctrl);
p.RunSolverMode();
// evaluate/check
// ------------------------------------------
double thres = 5.0e-13;
double uA_Err = (double)p.QueryHandler.QueryResults["uA_Err"];
double uB_Err = (double)p.QueryHandler.QueryResults["uB_Err"];
double JmpL2Err = (double)p.QueryHandler.QueryResults["uJmp_Err"];
Console.WriteLine("L2 Error of solution (A/B/jmp): {0}/{1}/{2} (threshold is {3}).", uA_Err, uB_Err, JmpL2Err, thres);
Assert.LessOrEqual(uA_Err, thres);
double uB_Min = (double)p.QueryHandler.QueryResults["uB_Min"];
double uB_Max = (double)p.QueryHandler.QueryResults["uB_Max"];
Console.WriteLine("Min/Max of uB: {0} / {1}", uB_Min, uB_Max);
Assert.GreaterOrEqual(uB_Min, ctrl.uA_Ex(new double[2], 0) * 0.99999);
Assert.LessOrEqual(uB_Max, ctrl.uB_Ex(new double[2], 0) * 1.00001);
//Assert.LessOrEqual(uB_Err, thres);
//Assert.LessOrEqual(JmpL2Err, thres);
}
public static void TestConvection_MovingInterface_SingleInitLowOrder(
[Values(TimeSteppingScheme.ExplicitEuler, TimeSteppingScheme.CrankNicolson, TimeSteppingScheme.ImplicitEuler,
TimeSteppingScheme.BDF2, TimeSteppingScheme.BDF3, TimeSteppingScheme.BDF4,
TimeSteppingScheme.RK1, TimeSteppingScheme.RK1u1, TimeSteppingScheme.RK3, TimeSteppingScheme.RK4,
TimeSteppingScheme.RK_ImplicitEuler, TimeSteppingScheme.RK_CrankNic, TimeSteppingScheme.RK_IMEX3)] TimeSteppingScheme tsc,
[Values(0.2, 0.23)] double TimestepSize,
[Values(8)] int NoOfTs
)
{
// set up
// ------------------------------------------
XdgTimesteppingTestControl ctrl = HardCodedControl.Gerade(angle: 0, degree: 0, GridResolutionFactor: 1);
ctrl.NoOfTimesteps = NoOfTs;
ctrl.dtFixed = TimestepSize;
ctrl.Endtime = ctrl.dtFixed * ctrl.NoOfTimesteps;
ctrl.MultiStepInit = false;
ctrl.TimeSteppingScheme = tsc;
ctrl.InterfaceMode = InterfaceMode.MovingInterface;
BoSSS.Solution.Application <XdgTimesteppingTestControl> .CommandLineOptions ops = null;
//Console.WriteLine("remove me VVVV");
//ops = new BoSSS.Solution.Application<XdgTimesteppingTestControl>.CommandLineOptions() {
// delPlt = true,
// ImmediatePlotPeriod = 1,
// SuperSampling = 5
//};
// run
// ------------------------------------------
XdgTimesteppingMain p = new XdgTimesteppingMain();
p.Init(ctrl, ops);
p.RunSolverMode();
// evaluate/check
// ------------------------------------------
double thres = 5.0e-13;
double uA_Err = (double)p.QueryHandler.QueryResults["uA_Err"];
double uB_Err = (double)p.QueryHandler.QueryResults["uB_Err"];
double JmpL2Err = (double)p.QueryHandler.QueryResults["uJmp_Err"];
Console.WriteLine("L2 Error of solution (A/B/jmp): {0}/{1}/{2} (threshold is {3}).", uA_Err, uB_Err, JmpL2Err, thres);
Assert.LessOrEqual(uA_Err, thres);
Assert.LessOrEqual(uB_Err, thres);
Assert.LessOrEqual(JmpL2Err, thres);
}
/// <summary>
/// Tests the <see cref="BoSSS.Solution.XdgTimestepping.XdgBDFTimestepping"/>
/// as well as the <see cref="BoSSS.Solution.XdgTimestepping.XdgRKTimestepping"/> time-stepper at
/// polynomial order 0 with single-value init, see <see cref="BoSSS.Solution.XdgTimestepping.XdgBDFTimestepping.SingleInit"/>.
/// </summary>
public static void TestConvection_MovingInterface_SingleInitLowOrder(
TimeSteppingScheme tsc,
double TimestepSize,
int NoOfTs
)
{
// set up
// ------------------------------------------
XdgTimesteppingTestControl ctrl = HardCodedControl.Gerade(angle: 0, degree: 0, GridResolutionFactor: 1);
ctrl.NoOfTimesteps = NoOfTs;
ctrl.dtFixed = TimestepSize;
ctrl.Endtime = ctrl.dtFixed * ctrl.NoOfTimesteps;
ctrl.MultiStepInit = false;
ctrl.TimeSteppingScheme = tsc;
ctrl.InterfaceMode = InterfaceMode.MovingInterface;
// run
// ------------------------------------------
XdgTimesteppingMain p = new XdgTimesteppingMain();
p.Init(ctrl);
p.RunSolverMode();
// evaluate/check
// ------------------------------------------
double thres = 5.0e-13;
double uA_Err = (double)p.QueryHandler.QueryResults["uA_Err"];
double uB_Err = (double)p.QueryHandler.QueryResults["uB_Err"];
double JmpL2Err = (double)p.QueryHandler.QueryResults["uJmp_Err"];
Console.WriteLine("L2 Error of solution (A/B/jmp): {0}/{1}/{2} (threshold is {3}).", uA_Err, uB_Err, JmpL2Err, thres);
Assert.LessOrEqual(uA_Err, thres);
Assert.LessOrEqual(uB_Err, thres);
Assert.LessOrEqual(JmpL2Err, thres);
}
public static void TestBurgers_HighOrder(
[Values(0, 1, 2, 3, 0, 1)] int PolyOrder,
[Values(0.08, 0.08, 0.08, 0.08, 0.08, 0.08)] double TimestepSize,
[Values("bdf", "bdf", "bdf", "bdf", "rk", "rk")] string Timestepper,
[Values(8, 8, 8, 8, 8, 8)] int NoOfTs
)
{
// set up
// ------------------------------------------
XdgTimesteppingTestControl ctrl = HardCodedControl.Burgers(angle: 0, degree: PolyOrder, GridResolutionFactor: 1, tsm: InterfaceMode.MovingInterface);
if (Timestepper == "bdf")
{
switch (PolyOrder)
{
case 0: ctrl.TimeSteppingScheme = TimeSteppingScheme.ImplicitEuler; break;
case 1: ctrl.TimeSteppingScheme = TimeSteppingScheme.CrankNicolson; break;
case 2: ctrl.TimeSteppingScheme = TimeSteppingScheme.BDF3; break;
case 3: ctrl.TimeSteppingScheme = TimeSteppingScheme.BDF4; break;
default: throw new ArgumentOutOfRangeException();
}
ctrl.MultiStepInit = true;
}
else if (Timestepper == "rk")
{
switch (PolyOrder)
{
case 0: ctrl.TimeSteppingScheme = TimeSteppingScheme.ImplicitEuler; break;
case 1: ctrl.TimeSteppingScheme = TimeSteppingScheme.CrankNicolson; break;
//case 2: ctrl.TimeSteppingScheme = TimeSteppingScheme.RK4; break;
//case 3: ctrl.TimeSteppingScheme = TimeSteppingScheme.RK4; break;
default: throw new ArgumentOutOfRangeException();
}
ctrl.MultiStepInit = false;
}
else
{
throw new ArgumentOutOfRangeException();
}
Console.WriteLine("Polyorder = {0}, timestepper = {1}", PolyOrder, ctrl.TimeSteppingScheme);
ctrl.NoOfTimesteps = NoOfTs;
ctrl.dtFixed = TimestepSize;
ctrl.Endtime = ctrl.dtFixed * ctrl.NoOfTimesteps;
// run
// ------------------------------------------
XdgTimesteppingMain p = new XdgTimesteppingMain();
p.Init(ctrl);
p.RunSolverMode();
// evaluate/check
// ------------------------------------------
double thres = 5.0e-7;
double uA_Err = (double)p.QueryHandler.QueryResults["uA_Err"];
double uB_Err = (double)p.QueryHandler.QueryResults["uB_Err"];
double JmpL2Err = (double)p.QueryHandler.QueryResults["uJmp_Err"];
Console.WriteLine("L2 Error of solution (A/B/jmp): {0}/{1}/{2} (threshold is {3}).", uA_Err, uB_Err, JmpL2Err, thres);
Assert.LessOrEqual(uA_Err, thres);
Assert.LessOrEqual(uB_Err, thres);
Assert.LessOrEqual(JmpL2Err, thres);
}
public static XdgTimesteppingTestControl Burgers(int degree = 1,
int NoOfTimesteps = 40,
InterfaceMode tsm = InterfaceMode.MovingInterface,
int GridResolutionFactor = 2)
{
XdgTimesteppingTestControl R = new XdgTimesteppingTestControl();
R.ProjectName = "XdgMassMatrixEvolution/Burgers";
R.savetodb = false;
R.DbPath = null; //@"\\fdyprime\userspace\kummer\BoSSS-db-XNSE";
// DG config
// =========
R.FieldOptions.Add("Phi", new FieldOpts()
{
Degree = 2,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("u", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Vx", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Vy", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
// grid
// ====
R.GridFunc = delegate() {
double[] Xnodes = GenericBlas.Linspace(-2, 2, 7 * GridResolutionFactor + 1);
double[] Ynodes = GenericBlas.Linspace(-2, 2, 7 * GridResolutionFactor + 1);
var grd = Grid2D.Cartesian2DGrid(Xnodes, Ynodes);
grd.EdgeTagNames.Add(1, "Dirichlet");
grd.EdgeTagNames.Add(2, "Neumann");
grd.DefineEdgeTags(delegate(double[] X) {
byte ret;
if (Math.Abs(X[0] - (-1)) <= 1.0e-8 || Math.Abs(X[0] - (+1)) <= 1.0e-8)
{
ret = 1;
}
else
{
ret = 2;
}
return(ret);
});
return(grd);
};
// exact solution
// ==============
double TimeOffset = 0.1;
double angle = 45 * Math.PI / 180.0;
//double angle = 0.0;
double Nx = Math.Cos(angle);
double Ny = Math.Sin(angle);
R.BurgersDirection = new Platform.LinAlg.Vector(Nx, Ny);
const double S = 0.5 * (2 + 1);
R.S = ((double[] X, double t) => S);
R.Phi = ((double[] X, double t) => (X[0] - Nx * S * (t + TimeOffset)) * Nx + (X[1] - Ny * S * (t + TimeOffset)) * Ny);
Func <double[], double> projCoord = X => X[0] * Nx + X[1] * Ny;
// initial value for x < 0
Func <double, double> uA0 = x => Math.Exp(-x.Pow2()) + 1.0;
// We will need Newtons alg. to find the origin of a characteristic;
// for a decent initial value of Newton, we sample the initial value at certain points
double[] xTrial = GenericBlas.Linspace(-10, 10, 1000);
double[] u0Tril = xTrial.Select(x => uA0(x)).ToArray();
Func <double, double, double> uAEx = delegate(double t, double xi) {
double ret = 0;
t += TimeOffset;
if (t < 0)
{
throw new ArgumentOutOfRangeException();
}
if (t == 0)
{
return(uA0(xi));
}
// find low ang high bound for Newton
int I = xTrial.Length;
int iMinDist_lo = -1;
double MinDist_lo = double.MaxValue;
int iMinDist_hi = -1;
double MinDist_hi = double.MaxValue;
for (int i = 0; i < I; i++)
{
double x0 = xTrial[i];
double u0Atx0 = u0Tril[i];
double x1 = x0 + u0Atx0 * t; // x1 is position of the characteristic, which originates from x0, at time t
double dist = Math.Abs(x1 - xi);
if (dist < MinDist_lo && x1 < xi)
{
iMinDist_lo = i;
MinDist_lo = dist;
}
if (dist < MinDist_hi && x1 > xi)
{
iMinDist_hi = i;
MinDist_hi = dist;
}
}
double xi_lo = xTrial[iMinDist_lo];
double xi_hi = xTrial[iMinDist_hi];
Func <double, double> func = (xi0 => (uA0(xi0) * t + xi0 - xi));
Func <double, double> dfunc = (xi0 => (1.0 - 2.0 * t * Math.Exp(-(xi0.Pow2()))));
double xi0i = rtsave(func, dfunc, xi_lo, xi_hi, 1e-12);
// Probe
//if (!converged)
// throw new ArithmeticException();
// return value at origin of characteristic
ret = uA0(xi0i);
return(ret);
};
{
// test for uAEx
double x0 = -0.5;
double u_at_x0 = uA0(x0);
double dt = -0.02;
double x = x0 + u_at_x0 * (dt + TimeOffset); // characteristic through x0, at time dt
double u_at = uAEx(dt, x);
if (Math.Abs(u_at - u_at_x0) > 1.0e-8)
{
throw new ArithmeticException();
}
}
/*
* Func<double, double, double> uAEx = delegate (double t, double xi) {
* return 2.0;
* };
*/
R.uA_Ex = ((X, t) => uAEx(t, projCoord(X)));
R.uB_Ex = ((X, t) => 1.0);
R.Eq = Equation.Burgers;
R.InitialValues_Evaluators.Add("Phi", X => R.Phi(X, 0.0));
R.InitialValues_Evaluators.Add("u#A", X => R.uA_Ex(X, 0.0));
R.InitialValues_Evaluators.Add("u#B", X => R.uB_Ex(X, 0.0));
// anderes zeugs
// =============
R.TimeSteppingScheme = TimeSteppingScheme.RK4;
R.MultiStepInit = false;
R.InterfaceMode = tsm;
R.Endtime = 0.11;
R.NoOfTimesteps = NoOfTimesteps;
R.dtFixed = R.Endtime / R.NoOfTimesteps;
R.AgglomerationThreshold = 0.1;
// return
// ======
return(R);
}
public static XdgTimesteppingTestControl Heat1D(int degree = 1,
int NoOfTimesteps = 8,
InterfaceMode tsm = InterfaceMode.MovingInterface,
int GridResolutionFactor = 1)
{
XdgTimesteppingTestControl R = new XdgTimesteppingTestControl();
R.ProjectName = "XdgMassMatrixEvolution/Heat1D";
R.savetodb = false;
//R.DbPath = @"\\fdyprime\userspace\kummer\BoSSS-db-XNSE";
R.DbPath = null;
// DG config
// =========
R.FieldOptions.Add("Phi", new FieldOpts()
{
Degree = 2,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("u", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Vx", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Vy", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
// grid
// ====
R.GridFunc = delegate() {
double[] Xnodes = GenericBlas.Linspace(-1, 1, 18 * GridResolutionFactor + 1);
double[] Ynodes = GenericBlas.Linspace(-1, 1, 3);
var grd = Grid2D.Cartesian2DGrid(Xnodes, Ynodes);
grd.EdgeTagNames.Add(1, "Dirichlet");
grd.EdgeTagNames.Add(2, "Neumann");
grd.DefineEdgeTags(delegate(double[] X) {
byte ret;
if (Math.Abs(X[0] - (-1)) <= 1.0e-8 || Math.Abs(X[0] - (+1)) <= 1.0e-8)
{
ret = 1;
}
else
{
ret = 2;
}
return(ret);
});
return(grd);
};
// exact solution
// ==============
double muA = 1;
double muB = 10;
Func <double, double> hA = t => 1 - t - t.Pow2();
Func <double, double> hB = t => - .3125000000 * Math.Sin(.7853981635 + .7853981635 * t) * (t.Pow2() + t - 1.0) / Math.Sin(.2513274123 + .2513274123 * t);
Func <double, double> oA = t => (0.6250000000e-1 * (16.0 * Math.Cos(.7853981635 + .7853981635 * t) * t.Pow2() * Math.Sin(.2513274123 + .2513274123 * t) - 5.0 * Math.Sin(.7853981635 + .7853981635 * t) * Math.Cos(.2513274123 + .2513274123 * t) * t.Pow2() + 4.045084972 * Math.Sin(.7853981635 + .7853981635 * t) * t.Pow2() + 16.0 * Math.Cos(.7853981635 + .7853981635 * t) * t * Math.Sin(.2513274123 + .2513274123 * t) - 5.0 * Math.Sin(.7853981635 + .7853981635 * t) * Math.Cos(.2513274123 + .2513274123 * t) * t + 4.045084972 * Math.Sin(.7853981635 + .7853981635 * t) * t - 16.0 * Math.Cos(.7853981635 + .7853981635 * t) * Math.Sin(.2513274123 + .2513274123 * t) + 5.0 * Math.Sin(.7853981635 + .7853981635 * t) * Math.Cos(.2513274123 + .2513274123 * t) - 4.045084972 * Math.Sin(.7853981635 + .7853981635 * t))) / Math.Sin(.2513274123 + .2513274123 * t);
Func <double, double> oB = t => .2528178107 * Math.Sin(.7853981635 + .7853981635 * t) * (t.Pow2() + t - 1.0) / Math.Sin(.2513274123 + .2513274123 * t);
Func <double, double, double> uA_Ex = (t, x) => oA(t) + hA(t) * Math.Cos(x * Math.PI * 0.5 * 10.0 / 8.0);
Func <double, double, double> uB_Ex = (t, x) => oB(t) + hB(t) * Math.Cos(x * Math.PI / 5);
Func <double, double, double> rhsA = (t, x) => (0.6250000000e-1 * (-11.30973355 * Math.Sin(.7853981635 + .7853981635 * t) * t.Pow2() * Math.Sin(.2513274123 + .2513274123 * t) + 32.0 * Math.Cos(.7853981635 + .7853981635 * t) * t * Math.Sin(.2513274123 + .2513274123 * t) + 0.9424777962e-1 * Math.Cos(.7853981635 + .7853981635 * t) * t.Pow2() * Math.Cos(.2513274123 + .2513274123 * t) - 10.0 * Math.Sin(.7853981635 + .7853981635 * t) * Math.Cos(.2513274123 + .2513274123 * t) * t + 3.177002308 * Math.Cos(.7853981635 + .7853981635 * t) * t.Pow2() + 8.090169943 * Math.Sin(.7853981635 + .7853981635 * t) * t - 11.30973355 * Math.Sin(.7853981635 + .7853981635 * t) * t * Math.Sin(.2513274123 + .2513274123 * t) + 16.0 * Math.Cos(.7853981635 + .7853981635 * t) * Math.Sin(.2513274123 + .2513274123 * t) + 0.9424777962e-1 * Math.Cos(.7853981635 + .7853981635 * t) * t * Math.Cos(.2513274123 + .2513274123 * t) - 5.0 * Math.Sin(.7853981635 + .7853981635 * t) * Math.Cos(.2513274123 + .2513274123 * t) + 3.177002308 * Math.Cos(.7853981635 + .7853981635 * t) * t + 4.045084972 * Math.Sin(.7853981635 + .7853981635 * t) + 11.30973355 * Math.Sin(.7853981635 + .7853981635 * t) * Math.Sin(.2513274123 + .2513274123 * t) - 0.9424777962e-1 * Math.Cos(.7853981635 + .7853981635 * t) * Math.Cos(.2513274123 + .2513274123 * t) - 3.177002308 * Math.Cos(.7853981635 + .7853981635 * t))) / Math.Sin(.2513274123 + .2513274123 * t) - (0.1570796327e-1 * (16.0 * Math.Cos(.7853981635 + .7853981635 * t) * t.Pow2() * Math.Sin(.2513274123 + .2513274123 * t) - 5.0 * Math.Sin(.7853981635 + .7853981635 * t) * Math.Cos(.2513274123 + .2513274123 * t) * t.Pow2() + 4.045084972 * Math.Sin(.7853981635 + .7853981635 * t) * t.Pow2() + 16.0 * Math.Cos(.7853981635 + .7853981635 * t) * t * Math.Sin(.2513274123 + .2513274123 * t) - 5.0 * Math.Sin(.7853981635 + .7853981635 * t) * Math.Cos(.2513274123 + .2513274123 * t) * t + 4.045084972 * Math.Sin(.7853981635 + .7853981635 * t) * t - 16.0 * Math.Cos(.7853981635 + .7853981635 * t) * Math.Sin(.2513274123 + .2513274123 * t) + 5.0 * Math.Sin(.7853981635 + .7853981635 * t) * Math.Cos(.2513274123 + .2513274123 * t) - 4.045084972 * Math.Sin(.7853981635 + .7853981635 * t))) * Math.Cos(.2513274123 + .2513274123 * t) / Math.Sin(.2513274123 + .2513274123 * t).Pow2() + (-2.0 * t - 1.0) * Math.Cos(1.963495409 * x) + (3.855314220 * (-1.0 * t.Pow2() - 1.0 * t + 1.0)) * Math.Cos(1.963495409 * x);
Func <double, double, double> rhsB = (t, x) => - 0.6354004615e-1 * Math.Sin(.7853981635 + .7853981635 * t) * (t.Pow2() + t - 1.0) * Math.Cos(.2513274123 + .2513274123 * t) / Math.Sin(.2513274123 + .2513274123 * t).Pow2() + .1985626442 * Math.Cos(.7853981635 + .7853981635 * t) * (t.Pow2() + t - 1.0) / Math.Sin(.2513274123 + .2513274123 * t) + .2528178107 * Math.Sin(.7853981635 + .7853981635 * t) * (2.0 * t + 1.0) / Math.Sin(.2513274123 + .2513274123 * t) + 0.7853981635e-1 * Math.Sin(.7853981635 + .7853981635 * t) * (t.Pow2() + t - 1.0) * Math.Cos(.6283185308 * x) * Math.Cos(.2513274123 + .2513274123 * t) / Math.Sin(.2513274123 + .2513274123 * t).Pow2() - .2454369261 * Math.Cos(.7853981635 + .7853981635 * t) * (t.Pow2() + t - 1.0) * Math.Cos(.6283185308 * x) / Math.Sin(.2513274123 + .2513274123 * t) - .3125000000 * Math.Sin(.7853981635 + .7853981635 * t) * (2.0 * t + 1.0) * Math.Cos(.6283185308 * x) / Math.Sin(.2513274123 + .2513274123 * t) - 1.233700550 * Math.Sin(.7853981635 + .7853981635 * t) * (t.Pow2() + t - 1.0) * Math.Cos(.6283185308 * x) / Math.Sin(.2513274123 + .2513274123 * t);
R.uA_Ex = ((X, t) => uA_Ex(t, X[0]));
R.uB_Ex = ((X, t) => uB_Ex(t, X[0]));
R.rhsA = ((X, t) => rhsA(t, X[0]));
R.rhsB = ((X, t) => rhsB(t, X[0]));
R.Eq = Equation.HeatEq;
R.muA = muA;
R.muB = muB;
const double S = 0.4;
R.S = ((double[] X, double t) => S);
R.Phi = ((double[] X, double t) => X[0].Pow2() - (0.4 + t * S).Pow2());
R.InitialValues_Evaluators.Add("Phi", X => R.Phi(X, 0.0));
R.InitialValues_Evaluators.Add("u#A", X => R.uA_Ex(X, 0));
R.InitialValues_Evaluators.Add("u#B", X => R.uB_Ex(X, 0));
// restart
// =======
//R.RestartInfo = new Tuple<Guid, Foundation.IO.TimestepNumber>(new Guid("aff36e92-1546-4fdf-a7bc-fbeff1e67f49"), 58);
//R.InitialValues_Evaluators.Clear();
// anderes zeugs
// =============
R.TimeSteppingScheme = TimeSteppingScheme.BDF4;
R.InterfaceMode = tsm;
R.Endtime = 0.4;
R.NoOfTimesteps = NoOfTimesteps;
R.dtFixed = R.Endtime / R.NoOfTimesteps;
R.AgglomerationThreshold = 0.1;
// return
// ======
return(R);
}
public static XdgTimesteppingTestControl Rarefaction(int degree = 2,
int NoOfTimesteps = 20,
InterfaceMode tsm = InterfaceMode.MovingInterface,
int GridResolutionFactor = 2)
{
XdgTimesteppingTestControl R = new XdgTimesteppingTestControl();
R.ProjectName = "XdgMassMatrixEvolution/Rarefaction";
R.savetodb = false;
//R.DbPath = @"\\fdyprime\userspace\kummer\BoSSS-db-XNSE";
R.DbPath = null;
// DG config
// =========
R.FieldOptions.Add("Phi", new FieldOpts()
{
Degree = 2,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("u", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Vx", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Vy", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
// grid
// ====
R.GridFunc = delegate() {
double[] nodes = GenericBlas.Linspace(-2.7, 2.7, 18 * GridResolutionFactor + 1);
BoundingBox cutOut = new BoundingBox(new double[] { -0.3, -0.3 }, new double[] { 0.3, 0.3 });
var grd = Grid2D.Cartesian2DGrid(nodes, nodes, CutOuts: cutOut);
grd.EdgeTagNames.Add(1, "Inflow");
grd.EdgeTagNames.Add(2, "Outflow");
grd.DefineEdgeTags(delegate(double[] X) {
byte ret = 2;
if (Math.Abs(X[0]) <= 0.31 && Math.Abs(X[1]) <= 0.31)
{
ret = 1;
}
return(ret);
});
return(grd);
};
// exact solution
// ==============
R.uA_Ex = ((X, t) => 3.0 / Math.Sqrt(X[0].Pow2() + X[1].Pow2()));
R.uB_Ex = ((X, t) => 1.0 / Math.Sqrt(X[0].Pow2() + X[1].Pow2()));
// boundary condition
// ==================
R.AddBoundaryValue("Inflow", "u", R.uA_Ex);
R.AddBoundaryValue("Outflow");
// Initial values
// ==============
const double S = 1;
R.S = ((double[] X, double t) => S);
R.Phi = ((double[] X, double t) => X[0].Pow2() + X[1].Pow2() - (1.0 + t).Pow2());
R.CircleRadius = t => (1.0 + t);
R.CutCellQuadratureType = XQuadFactoryHelper.MomentFittingVariants.ExactCircle;
R.InitialValues_Evaluators.Add("Phi", X => R.Phi(X, 0.0));
R.InitialValues_Evaluators.Add("Vx", X => X[0] / Math.Sqrt(X[0].Pow2() + X[1].Pow2()));
R.InitialValues_Evaluators.Add("Vy", X => X[1] / Math.Sqrt(X[0].Pow2() + X[1].Pow2()));
R.InitialValues_Evaluators.Add("u#A", X => R.uA_Ex(X, 0.0));
R.InitialValues_Evaluators.Add("u#B", X => R.uB_Ex(X, 0.0));
// restart
// =======
//R.RestartInfo = new Tuple<Guid, Foundation.IO.TimestepNumber>(new Guid("aff36e92-1546-4fdf-a7bc-fbeff1e67f49"), 58);
//R.InitialValues_Evaluators.Clear();
// anderes zeugs
// =============
R.TimeSteppingScheme = TimeSteppingScheme.BDF4;
R.InterfaceMode = tsm;
//R.Endtime = 0.05;
R.Endtime = 0.4;
R.NoOfTimesteps = NoOfTimesteps;
R.dtFixed = R.Endtime / R.NoOfTimesteps;
R.AgglomerationThreshold = 0.1;
// return
// ======
return(R);
}
public static XdgTimesteppingTestControl Gerade(
double angle = 5 *Math.PI / 180.0, int degree = 0, int GridResolutionFactor = 1, double t_offset = 0.0)
{
XdgTimesteppingTestControl R = new XdgTimesteppingTestControl();
R.ProjectName = "XdgMassMatrixEvolution/Gerade";
R.DbPath = null;
R.savetodb = false;
// DG degree
// =========
R.FieldOptions.Add("Phi", new FieldOpts()
{
Degree = 3,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("u", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Vx", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Vy", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
// grid
// ====
R.GridFunc = delegate() {
var grd = Grid2D.Cartesian2DGrid(
GenericBlas.Linspace(-7, 7, 7 * GridResolutionFactor + 1),
GenericBlas.Linspace(-7, 7, 7 * GridResolutionFactor + 1)
);
grd.EdgeTagNames.Add(1, "Inflow");
grd.DefineEdgeTags(X => (byte)1);
return(grd);
};
// level-set over time
// ===================
const double S = 0.9;
R.S = ((double[] X, double t) => S);
double Nx = Math.Cos(angle);
double Ny = Math.Sin(angle);
R.Phi = ((double[] X, double t) => (X[0] - Nx * S * (t + t_offset)) * Nx + (X[1] - Ny * S * (t + t_offset)) * Ny);
// exact solution
// ==============
R.uA_Ex = ((X, t) => 0.8);
R.uB_Ex = ((X, t) => 1.66);
// Initial Values
// ==============
R.InitialValues_Evaluators.Add("Phi", X => R.Phi(X, 0.0));
R.InitialValues_Evaluators.Add("Vx", X => Nx * S);
R.InitialValues_Evaluators.Add("Vy", X => Ny * S);
R.InitialValues_Evaluators.Add("u#A", X => R.uA_Ex(X, 0.0));
R.InitialValues_Evaluators.Add("u#B", X => R.uB_Ex(X, 0.0));
// Boundary values
// ===============
R.AddBoundaryValue("Inflow", "u", (X, t) => 0.8);
// Timestepping config
// ===================
R.NoOfTimesteps = 1;
R.Endtime = 2;
R.dtFixed = R.Endtime / R.NoOfTimesteps;
R.TimeSteppingScheme = TimeSteppingScheme.ExplicitEuler;
R.InterfaceMode = InterfaceMode.MovingInterface;
R.AgglomerationThreshold = 0.1;
// return
// ======
return(R);
}
public static XdgTimesteppingTestControl Burgers(
double angle = 0.0,
int degree = 2,
int NoOfTimesteps = 80,
InterfaceMode tsm = InterfaceMode.MovingInterface,
int GridResolutionFactor = 2)
{
XdgTimesteppingTestControl R = new XdgTimesteppingTestControl();
R.ProjectName = "XdgMassMatrixEvolution/Burgers";
R.savetodb = false;
R.DbPath = null;
// DG config
// =========
R.FieldOptions.Add("Phi", new FieldOpts()
{
Degree = 2,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("u", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Vx", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
R.FieldOptions.Add("Vy", new FieldOpts()
{
Degree = degree,
SaveToDB = FieldOpts.SaveToDBOpt.TRUE
});
// grid
// ====
R.GridFunc = delegate() {
double[] Xnodes = GenericBlas.Linspace(-2, 2, 7 * GridResolutionFactor + 1);
double[] Ynodes = GenericBlas.Linspace(-2, 2, 7 * GridResolutionFactor + 1);
var grd = Grid2D.Cartesian2DGrid(Xnodes, Ynodes);
grd.EdgeTagNames.Add(1, "Dirichlet");
grd.EdgeTagNames.Add(2, "Neumann");
grd.DefineEdgeTags(delegate(double[] X) {
byte ret;
if (Math.Abs(X[0] - (-1)) <= 1.0e-8 || Math.Abs(X[0] - (+1)) <= 1.0e-8)
{
ret = 1;
}
else
{
ret = 2;
}
return(ret);
});
return(grd);
};
// exact solution
// ==============
double TimeOffset = 0.1;
double Nx = Math.Cos(angle);
double Ny = Math.Sin(angle);
R.BurgersDirection = new Platform.LinAlg.Vector(Nx, Ny);
const double S = 0.5 * (2 + 1);
R.S = ((double[] X, double t) => S);
R.Phi = ((double[] X, double t) => (X[0] - Nx * S * (t + TimeOffset)) * Nx + (X[1] - Ny * S * (t + TimeOffset)) * Ny);
Func <double[], double> projCoord = X => X[0] * Nx + X[1] * Ny;
Func <double, double, double> uAEx = delegate(double t, double xi) {
return(2.0);
};
R.uA_Ex = ((X, t) => uAEx(t, projCoord(X)));
R.uB_Ex = ((X, t) => 1.0);
R.Eq = Equation.Burgers;
R.InitialValues_Evaluators.Add("Phi", X => R.Phi(X, 0.0));
R.InitialValues_Evaluators.Add("u#A", X => R.uA_Ex(X, 0.0));
R.InitialValues_Evaluators.Add("u#B", X => R.uB_Ex(X, 0.0));
// anderes zeugs
// =============
R.TimeSteppingScheme = TimeSteppingScheme.RK4;
R.InterfaceMode = tsm;
R.Endtime = 0.2;
R.NoOfTimesteps = NoOfTimesteps;
R.dtFixed = R.Endtime / R.NoOfTimesteps;
R.AgglomerationThreshold = 0.1;
// return
// ======
return(R);
}
