/// <summary>
/// Calculating the level set gradient using the specified scheme in a narrow band around the zero level set, therein the calculions are performed
/// </summary>
/// <param name="LS"> The level set function </param>
/// <param name="LSG"> Gradient of the level set function </param>
/// <param name="f"> Specifying the method of flux calculation </param>
/// <param name="Restriction"> The narrow band around the zero level set wherein the calculations are performed </param>
void CalculateLevelSetGradient(LevelSet LS, VectorField <SinglePhaseField> LSG, string f, SubGrid Restriction)
{
SpatialOperator SO;
CoordinateMapping CoDom;
if (m_ctx.SpatialDimension == 2)
{
SO = new SpatialOperator(1, 2, QuadOrderFunc.Linear(), new string[] { "LS", "LSG[0]", "LSG[1]" });
SO.EquationComponents["LSG[0]"].Add(CreateFlux(m_ctx, f, 0));
SO.EquationComponents["LSG[1]"].Add(CreateFlux(m_ctx, f, 1));
SO.Commit();
CoDom = new CoordinateMapping(LSG[0], LSG[1]);
}
else if (m_ctx.SpatialDimension == 3)
{
SO = new SpatialOperator(1, 3, QuadOrderFunc.Linear(), new string[] { "LS", "LSG[0]", "LSG[1]", "LSG[2]" });
SO.EquationComponents["LSG[0]"].Add(CreateFlux(m_ctx, f, 0));
SO.EquationComponents["LSG[1]"].Add(CreateFlux(m_ctx, f, 1));
SO.EquationComponents["LSG[2]"].Add(CreateFlux(m_ctx, f, 2));
SO.Commit();
CoDom = new CoordinateMapping(LSG[0], LSG[1], LSG[2]);
}
else
{
throw new NotSupportedException();
}
SO.Evaluate(1.0, 0.0, LS.Mapping, null, CoDom, sgrd: Restriction, bndMode: SubGridBoundaryModes.OpenBoundary);
}
/// <summary>
/// Obtaining the time integrated spatial discretization of the reinitialization equation in a narrow band around the zero level set, based on a Godunov's numerical Hamiltonian calculation
/// </summary>
/// <param name="LS"> The level set function </param>
/// <param name="Restriction"> The narrow band around the zero level set </param>
/// <param name="NumberOfTimesteps">
/// maximum number of pseudo-timesteps
/// </param>
/// <param name="thickness">
/// The smoothing width of the signum function.
/// This is the main stabilization parameter for re-initialization.
/// It should be set to approximately 3 cells.
/// </param>
/// <param name="TimestepSize">
/// size of the pseudo-timestep
/// </param>
public void ReInitialize(LevelSet LS, SubGrid Restriction, double thickness, double TimestepSize, int NumberOfTimesteps)
{
using (var tr = new FuncTrace()) {
// log parameters:
tr.Info("thickness: " + thickness.ToString(NumberFormatInfo.InvariantInfo));
tr.Info("TimestepSize: " + TimestepSize.ToString(NumberFormatInfo.InvariantInfo));
tr.Info("NumberOfTimesteps: " + NumberOfTimesteps);
ExplicitEuler TimeIntegrator;
SpatialOperator SO;
Func <int[], int[], int[], int> QuadratureOrder = QuadOrderFunc.NonLinear(3);
if (m_ctx.SpatialDimension == 2)
{
SO = new SpatialOperator(1, 5, 1, QuadratureOrder, new string[] { "LS", "LSCGV", "LSDG[0]", "LSUG[0]", "LSDG[1]", "LSUG[1]", "Result" });
SO.EquationComponents["Result"].Add(new GodunovHamiltonian(m_ctx, thickness));
SO.Commit();
TimeIntegrator = new RungeKutta(m_Scheme, SO, new CoordinateMapping(LS), new CoordinateMapping(LSCGV, LSDG[0], LSUG[0], LSDG[1], LSUG[1]), sgrd: Restriction);
}
else
{
SO = new SpatialOperator(1, 7, 1, QuadratureOrder, new string[] { "LS", "LSCGV", "LSDG[0]", "LSUG[0]", "LSDG[1]", "LSUG[1]", "LSDG[2]", "LSUG[2]", "Result" });
SO.EquationComponents["Result"].Add(new GodunovHamiltonian(m_ctx, thickness));
SO.Commit();
TimeIntegrator = new RungeKutta(m_Scheme, SO, new CoordinateMapping(LS), new CoordinateMapping(LSCGV, LSDG[0], LSUG[0], LSDG[1], LSUG[1], LSDG[2], LSUG[2]), sgrd: Restriction);
}
// Calculating the gradients in each sub-stage of a Runge-Kutta integration procedure
ExplicitEuler.ChangeRateCallback EvalGradients = delegate(double t1, double t2) {
LSUG.Clear();
CalculateLevelSetGradient(LS, LSUG, "Upwind", Restriction);
LSDG.Clear();
CalculateLevelSetGradient(LS, LSDG, "Downwind", Restriction);
LSCG.Clear();
CalculateLevelSetGradient(LS, LSCG, "Central", Restriction);
LSCGV.Clear();
var VolMask = (Restriction != null) ? Restriction.VolumeMask : null;
LSCGV.ProjectAbs(1.0, VolMask, LSCG.ToArray());
};
TimeIntegrator.OnBeforeComputeChangeRate += EvalGradients;
{
EvalGradients(0, 0);
var GodunovResi = new SinglePhaseField(LS.Basis, "Residual");
SO.Evaluate(1.0, 0.0, LS.Mapping, TimeIntegrator.ParameterMapping.Fields, GodunovResi.Mapping, Restriction);
//Tecplot.Tecplot.PlotFields(ArrayTools.Cat<DGField>( LSUG, LSDG, LS, GodunovResi), "Residual", 0, 3);
}
// pseudo-timestepping
// ===================
double factor = 1.0;
double time = 0;
LevelSet prevLevSet = new LevelSet(LS.Basis, "prevLevSet");
CellMask RestrictionMask = (Restriction == null) ? null : Restriction.VolumeMask;
for (int i = 0; (i < NumberOfTimesteps); i++)
{
tr.Info("Level set reinitialization pseudo-timestepping, timestep " + i);
// backup old Levelset
// -------------------
prevLevSet.Clear();
prevLevSet.Acc(1.0, LS, RestrictionMask);
// time integration
// ----------------
double dt = TimestepSize * factor;
tr.Info("dt = " + dt.ToString(NumberFormatInfo.InvariantInfo) + " (factor = " + factor.ToString(NumberFormatInfo.InvariantInfo) + ")");
TimeIntegrator.Perform(dt);
time += dt;
// change norm
// ------
prevLevSet.Acc(-1.0, LS, RestrictionMask);
double ChangeNorm = prevLevSet.L2Norm(RestrictionMask);
Console.WriteLine("Reinit: PseudoTime: {0} - Changenorm: {1}", i, ChangeNorm);
//Tecplot.Tecplot.PlotFields(new SinglePhaseField[] { LS }, m_ctx, "Reinit-" + i, "Reinit-" + i, i, 3);
}
//*/
}
}