/*
* Stretch and tilt vortons using velocity field
* timeStep - amount of time by which to advance simulation
* uFrame - frame counter
*
* see J. T. Beale, A convergent three-dimensional vortex method with
* grid-free stretching, Math. Comp. 46 (1986), 401-24, April.
*
* This routine assumes CreateInfluenceTree has already executed.
*
*/
void StretchAndTiltVortons(float timeStep)
{
if ((0.0f == mVelGrid.GetExtent().x) ||
(0.0f == mVelGrid.GetExtent().y) ||
(0.0f == mVelGrid.GetExtent().z))
{ // Domain is 2D, so stretching & tilting does not occur.
return;
}
// Compute all gradients of all components of velocity.
UniformGrid <Matrix3x3> velocityJacobianGrid = new UniformGrid <Matrix3x3>(mVelGrid);
velocityJacobianGrid.Init();
UniformGridMath.ComputeJacobian(ref velocityJacobianGrid, mVelGrid);
int numVortons = mVortons.Count;
for (int offset = 0; offset < numVortons; ++offset)
{ // For each vorton...
Matrix3x3 velJac = (Matrix3x3)velocityJacobianGrid.Interpolate(mVortons[offset].position);
Vector3 stretchTilt = mVortons[offset].vorticity * velJac; // Usual way to compute stretching & tilting
mVortons[offset].vorticity += /* fudge factor for stability */ 0.5f * stretchTilt * timeStep;
}
}
public void DebugDrawInfluenceGrid()
{
if (mInfluenceTree != null && mInfluenceTree.mLayers.Count != 0)
{
for (int u = 0; u < mInfluenceTree.mLayers.Count; ++u)
{
//if (u != 0) continue;
UniformGrid <Vorton> grid = mInfluenceTree.mLayers[u];
//Gizmos.color = new Vector4(1, 1 - 1 / ((float)u + 1), 1 - 1 / ((float)u + 1), 1.1f - 1 / ((float)u + 1));
Vector3 cellExtent = grid.GetCellExtent();
Vector3 gridExtent = grid.GetExtent();
Vector3 numCells = new Vector3(grid.GetNumCells(0), grid.GetNumCells(1), grid.GetNumCells(2));
Vector3 gridOrigin = grid.GetMinCorner();
for (int i = 0; i < numCells.x; ++i)
{
for (int j = 0; j < numCells.y; ++j)
{
for (int k = 0; k < numCells.z; ++k)
{
if (mInfluenceTree[0][0] == null)
{
break;
}
uint[] indices = { (uint)i, (uint)j, (uint)k };
uint offset = mInfluenceTree[(uint)u].OffsetFromIndices(indices);
float vorticity = mInfluenceTree[(uint)u][offset].vorticity.magnitude;
Gizmos.color = new Vector4(vorticity, u / mInfluenceTree.mLayers.Count, u / mInfluenceTree.mLayers.Count, vorticity);
Gizmos.DrawWireCube(gridOrigin + new Vector3(cellExtent.x * i + cellExtent.x / 2, cellExtent.y * j + cellExtent.y / 2, cellExtent.z * k + cellExtent.z / 2), cellExtent);
}
}
}
}
}
}