/// <summary>
/// Returns thermodynamic pressure as function of inital mass and temperature.
/// </summary>
/// <param name="InitialMass"></param>
/// <param name="Temperature"></param>
/// <returns></returns>
public double GetMassDeterminedThermodynamicPressure(double InitialMass, SinglePhaseField Temperature)
{
SinglePhaseField OneOverTemperature = new SinglePhaseField(Temperature.Basis);
OneOverTemperature.ProjectPow(1.0, Temperature, -1.0);
return(InitialMass / OneOverTemperature.IntegralOver(null));
}
/// <summary>
/// Approximation of the signum function of the level set field
/// </summary>
/// <param name="Output"></param>
/// <param name="gridParameter"></param>
/// <param name="optionalCellMask"></param>
public void ApproximateSignFunction(
SinglePhaseField Output, double gridParameter, CellMask optionalCellMask)
{
SinglePhaseField quot = new SinglePhaseField(m_Basis, "quot");
SinglePhaseField sqrt = new SinglePhaseField(m_Basis, "sqrt");
sqrt.ProjectProduct(1.0, this, this, optionalCellMask);
sqrt.AccConstant(gridParameter * gridParameter, optionalCellMask);
quot.ProjectPow(1.0, sqrt, 0.5, optionalCellMask);
//Output.ProjectQuotient (1.0, this, quot,false);
Output.ProjectQuotient(1.0, this, quot, optionalCellMask, false);
}
/// <summary>
/// In this method, the vector normal to the surface as well as certain derivatives
/// of it that we intend to use are set up
/// </summary>
protected void NormalVec(double deltax)
{
wx = new SinglePhaseField(m_gradBasis, "wx");
wy = new SinglePhaseField(m_gradBasis, "wy");
if (m_Context.Grid.SpatialDimension == 2)
{
m_Gradw = new VectorField <SinglePhaseField>(wx, wy);
}
else if (m_Context.Grid.SpatialDimension == 3)
{
wz = new SinglePhaseField(m_gradBasis, "wz");
m_Gradw = new VectorField <SinglePhaseField>(wx, wy, wz);
}
else
{
throw new NotSupportedException("only spatial dimension 2 and 3 are supported.");
}
SinglePhaseField absval = new SinglePhaseField(m_gradBasis);
m_Gradw[0].Derivative(1.0, m_Field, 0);
m_Gradw[1].Derivative(1.0, m_Field, 1);
if (m_Context.Grid.SpatialDimension == 3)
{
m_Gradw[2].Derivative(1.0, m_Field, 2);
}
/*
* Normalization of the gradient vector
* Might be better implemented using a
* Function
*/
absval.ProjectAbs(1.0, m_Gradw);
m_Gradw[0].ProjectQuotient(1.0, m_Gradw[0], absval, null, false);
m_Gradw[1].ProjectQuotient(1.0, m_Gradw[1], absval, null, false);
if (m_Context.Grid.SpatialDimension == 3)
{
m_Gradw[2].ProjectQuotient(1.0, m_Gradw[2], absval, null, false);
}
SinglePhaseField n1x = new SinglePhaseField(m_derivsBasis, "n1x");
SinglePhaseField n2x = new SinglePhaseField(m_derivsBasis, "n2x");
SinglePhaseField n1y = new SinglePhaseField(m_derivsBasis, "n1y");
SinglePhaseField n2y = new SinglePhaseField(m_derivsBasis, "n2y");
if (m_Context.Grid.SpatialDimension == 3)
{
SinglePhaseField n3x = new SinglePhaseField(m_derivsBasis, "n3x");
SinglePhaseField n3y = new SinglePhaseField(m_derivsBasis, "n3y");
SinglePhaseField n1z = new SinglePhaseField(m_derivsBasis, "n1z");
SinglePhaseField n2z = new SinglePhaseField(m_derivsBasis, "n2z");
SinglePhaseField n3z = new SinglePhaseField(m_derivsBasis, "n3z");
m_normderivs = new VectorField <SinglePhaseField>(n1x, n2x, n3x, n1y, n2y, n3y, n1z, n2z, n3z);
/* Partial derivatives of the normal vector.
* These quantities are used in the product rule applied to the surface projection
* and to compute the mean curvature
*/
m_normderivs[0].Derivative(1.0, m_Gradw[0], 0);
m_normderivs[1].Derivative(1.0, m_Gradw[1], 0);
m_normderivs[2].Derivative(1.0, m_Gradw[2], 0);
m_normderivs[3].Derivative(1.0, m_Gradw[0], 1);
m_normderivs[4].Derivative(1.0, m_Gradw[1], 1);
m_normderivs[5].Derivative(1.0, m_Gradw[2], 1);
m_normderivs[6].Derivative(1.0, m_Gradw[0], 2);
m_normderivs[7].Derivative(1.0, m_Gradw[1], 2);
m_normderivs[8].Derivative(1.0, m_Gradw[2], 2);
}
else
{
m_normderivs = new VectorField <SinglePhaseField>(n1x, n2x, n1y, n2y);
/* Partial derivatives of the normal vector.
* These quantities are used in the product rule applied to the surface projection
* and to compute the mean curvature
*/
m_normderivs[0].Derivative(1.0, m_Gradw[0], 0);
m_normderivs[1].Derivative(1.0, m_Gradw[1], 0);
m_normderivs[2].Derivative(1.0, m_Gradw[0], 1);
m_normderivs[3].Derivative(1.0, m_Gradw[1], 1);
}
/*
* Divergence of the surface normal vector yields the total curvature
* which is twice the mean curvature
* ATTENTION: here with inverse sign!!!!!
*/
m_Curvature = new SinglePhaseField(m_derivsBasis);
m_Curvature.Acc(1.0, m_normderivs[0]);
m_Curvature.Acc(1.0, m_normderivs[4]);
if (m_Context.Grid.SpatialDimension == 3)
{
m_Curvature.Acc(1.0, m_normderivs[8]);
}
m_sign = new SinglePhaseField(m_Basis, "sign");
SinglePhaseField quot = new SinglePhaseField(m_Basis, "quot");
SinglePhaseField sqrt = new SinglePhaseField(m_Basis, "sqrt");
sqrt.ProjectProduct(1.0, m_Field, m_Field);
sqrt.AccConstant(0.01);
quot.ProjectPow(1.0, sqrt, deltax * deltax);
m_sign.ProjectQuotient(1.0, m_Field, quot);
}
