public static VectorFieldUnsteady CreateBowl(Vec2 center, int numCells, Vec2 dir, int numSlices, float domainR = 2)
{
Vector origin = center - new Vec2(domainR);
Vector cell = new Vec2(2 * domainR / numCells);
Index size = new Index(numCells + 1, 2);
ScalarField[] vX = new ScalarField[numSlices];
ScalarField[] vY = new ScalarField[numSlices];
for (int slice = 0; slice < numSlices; ++slice)
{
vX[slice] = ScalarField.FromAnalyticalField(BowlX, size, origin + dir * slice, cell);
vY[slice] = ScalarField.FromAnalyticalField(BowlY, size, origin + dir * slice, cell);
}
VectorFieldUnsteady field = new VectorFieldUnsteady(new ScalarFieldUnsteady[] { new ScalarFieldUnsteady(vX), new ScalarFieldUnsteady(vY) });
field.InvalidValue = float.MaxValue;
field.DoNotScale();
return field;
}
public Vec3(float a, Vec2 b)
: base(new float[] { a, b.X, b.Y })
{
}
public Vec3(Vec2 a, float b)
: base(new float[] { a.X, a.Y, b })
{
}
public Vec2(Vec2 copy)
: base(copy)
{
}
public void Eigenanalysis(out SquareMatrix eigenvalues, out SquareMatrix eigenvectors)
{
Debug.Assert(Length == 2, "Only 2D eigenanalysis implemented so far.");
eigenvectors = new SquareMatrix(2);
eigenvalues = new SquareMatrix(2);
float a = this[0][0]; float b = this[1][0]; float c = this[0][1]; float d = this[1][1];
// Computing eigenvalues.
float Th = (a + d) * 0.5f;
float D = a * d - b * c;
float root = Th * Th - D;
float complex = 0;
if (root < 0)
{
complex = -root;
root = 0;
}
root = (float)Math.Sqrt(root);
float l0 = Th + root;
float l1 = Th - root;
// Save directional information.
eigenvalues[0] = new Vec2(l0, complex);
eigenvalues[1] = new Vec2(l1, -complex);
// Computing eigenvectors.
if (c != 0)
{
eigenvectors[0] = new Vec2(l0 - d, c);
eigenvectors[1] = new Vec2(l1 - d, c);
}
else if (b != 0)
{
eigenvectors[0] = new Vec2(b, l0 - a);
eigenvectors[1] = new Vec2(b, l1 - a);
}
else
{
eigenvectors[0] = new Vec2(1, 0);
eigenvectors[1] = new Vec2(0, 1);
}
}
public static VectorFieldUnsteady CreatePathlineSpiral(int numCells, int numSlices, float domainR = 2)
{
Vector origin = new Vec2(-domainR);
Vector cell = new Vec2(2 * domainR / numCells);
Index size = new Index(numCells + 1, 2);
ScalarField[] vX = new ScalarField[numSlices];
ScalarField[] vY = new ScalarField[numSlices];
for (int slice = 0; slice < numSlices; ++slice)
{
vX[slice] = ScalarField.FromAnalyticalField(x =>(float)Math.Cos((float)slice / 3)*4, size, origin, cell);
vY[slice] = ScalarField.FromAnalyticalField(x =>(float)Math.Sin((float)slice / 3)*4, size, origin, cell);
}
return new VectorFieldUnsteady(new ScalarFieldUnsteady[] { new ScalarFieldUnsteady(vX), new ScalarFieldUnsteady(vY) });
}
