void GridFractionalBoundaryConditionSolver3::constrainVelocity(
FaceCenteredGrid3* velocity,
unsigned int extrapolationDepth) {
Size3 size = velocity->resolution();
if (_colliderSdf == nullptr || _colliderSdf->resolution() != size) {
updateCollider(
collider(),
size,
velocity->gridSpacing(),
velocity->origin());
}
auto u = velocity->uAccessor();
auto v = velocity->vAccessor();
auto w = velocity->wAccessor();
auto uPos = velocity->uPosition();
auto vPos = velocity->vPosition();
auto wPos = velocity->wPosition();
Array3<double> uTemp(u.size());
Array3<double> vTemp(v.size());
Array3<double> wTemp(w.size());
Array3<char> uMarker(u.size(), 1);
Array3<char> vMarker(v.size(), 1);
Array3<char> wMarker(w.size(), 1);
Vector3D h = velocity->gridSpacing();
// Assign collider's velocity first and initialize markers
velocity->parallelForEachUIndex([&](size_t i, size_t j, size_t k) {
Vector3D pt = uPos(i, j, k);
double phi0 = _colliderSdf->sample(pt - Vector3D(0.5 * h.x, 0.0, 0.0));
double phi1 = _colliderSdf->sample(pt + Vector3D(0.5 * h.x, 0.0, 0.0));
double frac = fractionInsideSdf(phi0, phi1);
frac = 1.0 - clamp(frac, 0.0, 1.0);
if (frac > 0.0) {
uMarker(i, j, k) = 1;
} else {
Vector3D colliderVel = collider()->velocityAt(pt);
u(i, j, k) = colliderVel.x;
uMarker(i, j, k) = 0;
}
});
velocity->parallelForEachVIndex([&](size_t i, size_t j, size_t k) {
Vector3D pt = vPos(i, j, k);
double phi0 = _colliderSdf->sample(pt - Vector3D(0.0, 0.5 * h.y, 0.0));
double phi1 = _colliderSdf->sample(pt + Vector3D(0.0, 0.5 * h.y, 0.0));
double frac = fractionInsideSdf(phi0, phi1);
frac = 1.0 - clamp(frac, 0.0, 1.0);
if (frac > 0.0) {
vMarker(i, j, k) = 1;
} else {
Vector3D colliderVel = collider()->velocityAt(pt);
v(i, j, k) = colliderVel.y;
vMarker(i, j, k) = 0;
}
});
velocity->parallelForEachWIndex([&](size_t i, size_t j, size_t k) {
Vector3D pt = wPos(i, j, k);
double phi0 = _colliderSdf->sample(pt - Vector3D(0.0, 0.0, 0.5 * h.z));
double phi1 = _colliderSdf->sample(pt + Vector3D(0.0, 0.0, 0.5 * h.z));
double frac = fractionInsideSdf(phi0, phi1);
frac = 1.0 - clamp(frac, 0.0, 1.0);
if (frac > 0.0) {
wMarker(i, j, k) = 1;
} else {
Vector3D colliderVel = collider()->velocityAt(pt);
w(i, j, k) = colliderVel.z;
wMarker(i, j, k) = 0;
}
});
// Free-slip: Extrapolate fluid velocity into the collider
extrapolateToRegion(
velocity->uConstAccessor(), uMarker, extrapolationDepth, u);
extrapolateToRegion(
velocity->vConstAccessor(), vMarker, extrapolationDepth, v);
extrapolateToRegion(
velocity->wConstAccessor(), wMarker, extrapolationDepth, w);
// No-flux: project the extrapolated velocity to the collider's surface
// normal
velocity->parallelForEachUIndex([&](size_t i, size_t j, size_t k) {
Vector3D pt = uPos(i, j, k);
if (isInsideSdf(_colliderSdf->sample(pt))) {
Vector3D colliderVel = collider()->velocityAt(pt);
Vector3D vel = velocity->sample(pt);
Vector3D g = _colliderSdf->gradient(pt);
if (g.lengthSquared() > 0.0) {
Vector3D n = g.normalized();
Vector3D velr = vel - colliderVel;
Vector3D velt = projectAndApplyFriction(
velr, n, collider()->frictionCoefficient());
Vector3D velp = velt + colliderVel;
uTemp(i, j, k) = velp.x;
} else {
uTemp(i, j, k) = colliderVel.x;
}
} else {
uTemp(i, j, k) = u(i, j, k);
}
});
velocity->parallelForEachVIndex([&](size_t i, size_t j, size_t k) {
Vector3D pt = vPos(i, j, k);
if (isInsideSdf(_colliderSdf->sample(pt))) {
Vector3D colliderVel = collider()->velocityAt(pt);
Vector3D vel = velocity->sample(pt);
Vector3D g = _colliderSdf->gradient(pt);
if (g.lengthSquared() > 0.0) {
Vector3D n = g.normalized();
Vector3D velr = vel - colliderVel;
Vector3D velt = projectAndApplyFriction(
velr, n, collider()->frictionCoefficient());
Vector3D velp = velt + colliderVel;
vTemp(i, j, k) = velp.y;
} else {
vTemp(i, j, k) = colliderVel.y;
}
} else {
vTemp(i, j, k) = v(i, j, k);
}
});
velocity->parallelForEachWIndex([&](size_t i, size_t j, size_t k) {
Vector3D pt = wPos(i, j, k);
if (isInsideSdf(_colliderSdf->sample(pt))) {
Vector3D colliderVel = collider()->velocityAt(pt);
Vector3D vel = velocity->sample(pt);
Vector3D g = _colliderSdf->gradient(pt);
if (g.lengthSquared() > 0.0) {
Vector3D n = g.normalized();
Vector3D velr = vel - colliderVel;
Vector3D velt = projectAndApplyFriction(
velr, n, collider()->frictionCoefficient());
Vector3D velp = velt + colliderVel;
wTemp(i, j, k) = velp.z;
} else {
wTemp(i, j, k) = colliderVel.z;
}
} else {
wTemp(i, j, k) = w(i, j, k);
}
});
// Transfer results
u.parallelForEachIndex([&](size_t i, size_t j, size_t k) {
u(i, j, k) = uTemp(i, j, k);
});
v.parallelForEachIndex([&](size_t i, size_t j, size_t k) {
v(i, j, k) = vTemp(i, j, k);
});
w.parallelForEachIndex([&](size_t i, size_t j, size_t k) {
w(i, j, k) = wTemp(i, j, k);
});
// No-flux: Project velocity on the domain boundary if closed
if (closedDomainBoundaryFlag() & kDirectionLeft) {
for (size_t k = 0; k < u.size().z; ++k) {
for (size_t j = 0; j < u.size().y; ++j) {
u(0, j, k) = 0;
}
}
}
if (closedDomainBoundaryFlag() & kDirectionRight) {
for (size_t k = 0; k < u.size().z; ++k) {
for (size_t j = 0; j < u.size().y; ++j) {
u(u.size().x - 1, j, k) = 0;
}
}
}
if (closedDomainBoundaryFlag() & kDirectionDown) {
for (size_t k = 0; k < v.size().z; ++k) {
for (size_t i = 0; i < v.size().x; ++i) {
v(i, 0, k) = 0;
}
}
}
if (closedDomainBoundaryFlag() & kDirectionUp) {
for (size_t k = 0; k < v.size().z; ++k) {
for (size_t i = 0; i < v.size().x; ++i) {
v(i, v.size().y - 1, k) = 0;
}
}
}
if (closedDomainBoundaryFlag() & kDirectionBack) {
for (size_t j = 0; j < w.size().y; ++j) {
for (size_t i = 0; i < w.size().x; ++i) {
w(i, j, 0) = 0;
}
}
}
if (closedDomainBoundaryFlag() & kDirectionFront) {
for (size_t j = 0; j < w.size().y; ++j) {
for (size_t i = 0; i < w.size().x; ++i) {
w(i, j, w.size().z - 1) = 0;
}
}
}
}
