/*
* Advect vortons using velocity field
*
* timeStep - amount of time by which to advance simulation
*
*/
void AdvectVortons(float timeStep)
{
int numVortons = mVortons.Count;
for (int offset = 0; offset < numVortons; ++offset)
{ // For each vorton...
Vorton rVorton = mVortons[offset];
Vector3 velocity = ((Vector)mVelGrid.Interpolate(rVorton.position)).v;
mVortons[offset].position += velocity * timeStep;
mVortons[offset].velocity = velocity; // Cache this for use in collisions with rigid bodies.
}
}
/*
* 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;
}
}
