/
tilb.py
1211 lines (894 loc) · 29.9 KB
/
tilb.py
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# vim: set expandtab:
import taichi as ti
import time
################################################################################
#
# Data types
#
DataType = ti.f32
DataSize = 4
def setDataType (dataType):
global DataType
global DataSize
if ("f32" == dataType):
DataType = ti.f32
DataSize = 4
elif ("f64" == dataType):
DataType = ti.f64
DataSize = 8
else:
raise Exception (f"Unsupported dataType {dataType}")
print (f"DataType = \"{dataType}\", DataSize = {DataSize}")
################################################################################
#
# Data layouts.
#
def setResolution (x, y):
global nx
global ny
nx = x
ny = y
def defineHelperFields():
global nodeType
global vel
global rho
global bcVel
global bcRho
nodeType = ti. field ( dtype = ti.u16)
vel = ti.Vector.field (2, dtype = DataType)
rho = ti. field ( dtype = DataType)
bcVel = ti.Vector.field (2, dtype = DataType)
bcRho = ti. field ( dtype = DataType)
def allocateHelperFields():
global nodeType
global vel
global rho
global bcVel
global bcRho
defineHelperFields()
ti.root.dense (ti.ij, (nx, ny)).place (nodeType)
ti.root.dense (ti.ij, (nx, ny)).place (vel)
ti.root.dense (ti.ij, (nx, ny)).place (rho)
ti.root.dense (ti.ij, (nx, ny)).place (bcVel)
ti.root.dense (ti.ij, (nx, ny)).place (bcRho)
layout = "dense"
def setLayout (newLayout):
if ( "dense" == newLayout
or "bitmask_node" == newLayout
or "tile" == newLayout
or "pointer_tile" == newLayout
):
global layout
layout = newLayout
else:
raise Exception (f"Unsupported layout \"{newLayout}\"")
# Use these for Vector fields.
#
@ti.func
def getFVec (F, i,j,k):
val = ti.cast (0.0, DataType)
if (0 == k):
val = F [i,j][0]
elif (1 == k):
val = F [i,j][1]
elif (2 == k):
val = F [i,j][2]
elif (3 == k):
val = F [i,j][3]
elif (4 == k):
val = F [i,j][4]
elif (5 == k):
val = F [i,j][5]
elif (6 == k):
val = F [i,j][6]
elif (7 == k):
val = F [i,j][7]
elif (8 == k):
val = F [i,j][8]
return val
@ti.func
def setFVec (F, i,j,k, val):
if (0 == k):
F [i,j][0] = val
elif (1 == k):
F [i,j][1] = val
elif (2 == k):
F [i,j][2] = val
elif (3 == k):
F [i,j][3] = val
elif (4 == k):
F [i,j][4] = val
elif (5 == k):
F [i,j][5] = val
elif (6 == k):
F [i,j][6] = val
elif (7 == k):
F [i,j][7] = val
elif (8 == k):
F [i,j][8] = val
# Use these for dense fields.
#
@ti.func
def getFScalar (F, i,j,k):
return F [i,j,k]
@ti.func
def setFScalar (F, i,j,k, val):
F [i,j,k] = val
def defineVectorFields():
global f_old
global f_new
global getF
global setF
f_old = ti.Vector.field (9, dtype = DataType)
f_new = ti.Vector.field (9, dtype = DataType)
getF = getFVec
setF = setFVec
def allocateFDense():
global f_new
global f_old
ti.root.dense (ti.ij, (nx, ny)).place (f_new(0))
ti.root.dense (ti.ij, (nx, ny)).place (f_new(1))
ti.root.dense (ti.ij, (nx, ny)).place (f_new(2))
ti.root.dense (ti.ij, (nx, ny)).place (f_new(3))
ti.root.dense (ti.ij, (nx, ny)).place (f_new(4))
ti.root.dense (ti.ij, (nx, ny)).place (f_new(5))
ti.root.dense (ti.ij, (nx, ny)).place (f_new(6))
ti.root.dense (ti.ij, (nx, ny)).place (f_new(7))
ti.root.dense (ti.ij, (nx, ny)).place (f_new(8))
ti.root.dense (ti.ij, (nx, ny)).place (f_old(0))
ti.root.dense (ti.ij, (nx, ny)).place (f_old(1))
ti.root.dense (ti.ij, (nx, ny)).place (f_old(2))
ti.root.dense (ti.ij, (nx, ny)).place (f_old(3))
ti.root.dense (ti.ij, (nx, ny)).place (f_old(4))
ti.root.dense (ti.ij, (nx, ny)).place (f_old(5))
ti.root.dense (ti.ij, (nx, ny)).place (f_old(6))
ti.root.dense (ti.ij, (nx, ny)).place (f_old(7))
ti.root.dense (ti.ij, (nx, ny)).place (f_old(8))
def allocateMemoryVectorSeparate():
defineVectorFields()
allocateFDense()
allocateHelperFields()
def allocateMemoryBitmaskedSingleNodeOnlyType():
defineVectorFields()
global nodeType
global vel
global rho
global bcVel
global bcRho
defineHelperFields()
ti.root.bitmasked (ti.ij, (nx,ny)).place (nodeType)
ti.root.dense (ti.ij, (nx, ny)).place (vel)
ti.root.dense (ti.ij, (nx, ny)).place (rho)
ti.root.dense (ti.ij, (nx, ny)).place (bcVel)
ti.root.dense (ti.ij, (nx, ny)).place (bcRho)
allocateFDense()
def allocateMemoryTiled():
defineVectorFields()
defineHelperFields()
global nodeType
global vel
global rho
global bcVel
global bcRho
ti.root.dense (ti.ij, (nx, ny)).place (vel)
ti.root.dense (ti.ij, (nx, ny)).place (rho)
ti.root.dense (ti.ij, (nx, ny)).place (bcVel)
ti.root.dense (ti.ij, (nx, ny)).place (bcRho)
tileEdge = 16
tnx = nx // tileEdge
tny = ny // tileEdge
if (0 != (nx % tileEdge)):
tnx += 1
if (0 != (ny % tileEdge)):
tny += 1
tileLayout = ti.root.dense (ti.ij, (tnx, tny))
tileLayout.dense (ti.ij, (tileEdge,tileEdge)).place (nodeType)
# Reduced uncoalesced memory transactions, but it seems that
# taichi 0.7.26 does not change order of indices.
#
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_new (0))
tileLayout.dense (ti.ji, (tileEdge, tileEdge)).place (f_new (1))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_new (2))
tileLayout.dense (ti.ji, (tileEdge, tileEdge)).place (f_new (3))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_new (4))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_new (5))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_new (6))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_new (7))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_new (8))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_old (0))
tileLayout.dense (ti.ji, (tileEdge, tileEdge)).place (f_old (1))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_old (2))
tileLayout.dense (ti.ji, (tileEdge, tileEdge)).place (f_old (3))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_old (4))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_old (5))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_old (6))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_old (7))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_old (8))
def allocateMemoryPointerTiled():
defineVectorFields()
defineHelperFields()
global nodeType
global vel
global rho
global bcVel
global bcRho
ti.root.dense (ti.ij, (nx, ny)).place (vel)
ti.root.dense (ti.ij, (nx, ny)).place (rho)
ti.root.dense (ti.ij, (nx, ny)).place (bcVel)
ti.root.dense (ti.ij, (nx, ny)).place (bcRho)
tileEdge = 16
tnx = nx // tileEdge
tny = ny // tileEdge
if (0 != (nx % tileEdge)):
tnx += 1
if (0 != (ny % tileEdge)):
tny += 1
# One level of pointers.
tileLayout = ti.root.pointer (ti.ij, (tnx, tny))
# Two levels of pointers.
#t2 = 8
#tnx2 = tnx // t2
#tny2 = tny // t2
#if (0 != (tnx % t2)):
# tnx2 += 1
#if (0 != (tny % t2)):
# tny2 += 1
#
#tileLayout = ti.root.pointer (ti.ij, (tnx2, tny2)).pointer (ti.ij, (t2, t2))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (nodeType)
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_new (0))
tileLayout.dense (ti.ji, (tileEdge, tileEdge)).place (f_new (1))
tileLayout.dense (ti.ji, (tileEdge, tileEdge)).place (f_new (2))
tileLayout.dense (ti.ji, (tileEdge, tileEdge)).place (f_new (3))
tileLayout.dense (ti.ji, (tileEdge, tileEdge)).place (f_new (4))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_new (5))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_new (6))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_new (7))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_new (8))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_old (0))
tileLayout.dense (ti.ji, (tileEdge, tileEdge)).place (f_old (1))
tileLayout.dense (ti.ji, (tileEdge, tileEdge)).place (f_old (2))
tileLayout.dense (ti.ji, (tileEdge, tileEdge)).place (f_old (3))
tileLayout.dense (ti.ji, (tileEdge, tileEdge)).place (f_old (4))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_old (5))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_old (6))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_old (7))
tileLayout.dense (ti.ij, (tileEdge, tileEdge)).place (f_old (8))
def allocate():
print (f"layout = \"{layout}\"")
if ("dense" == layout):
allocateMemoryVectorSeparate()
elif ("bitmask_node" == layout):
allocateMemoryBitmaskedSingleNodeOnlyType()
elif ("tile" == layout):
allocateMemoryTiled()
elif ("pointer_tile" == layout):
allocateMemoryPointerTiled()
else:
raise Exception (f"Unsupported layout \"{layout}\"")
ti.root.place (nFluidNodesField, nComputationalNodesField, nBounceBackNodesField)
################################################################################
#
# LBM computations.
#
def setNu (newNu):
global nu
global tau
global omega
nu = newNu
tau = 3.0 * nu + 0.5
omega = 1.0 / tau
print (f"nu = {nu}, tau = {tau}, omega = {omega}")
SOLID = 0
FLUID = 1
BOUNDARY_BB = 2
BOUNDARY_VEL_NEQN_NORTH = 3
BOUNDARY_VEL_NEQN_SOUTH = 4
BOUNDARY_VEL_NEQN_EAST = 5
BOUNDARY_VEL_NEQN_WEST = 6
BOUNDARY_P_WEST = 7
BOUNDARY_P_EAST = 8
@ti.pyfunc
def isBoundaryVel (boundaryType):
result = False
if ( BOUNDARY_VEL_NEQN_NORTH == boundaryType or
BOUNDARY_VEL_NEQN_SOUTH == boundaryType or
BOUNDARY_VEL_NEQN_EAST == boundaryType or
BOUNDARY_VEL_NEQN_WEST == boundaryType ):
result = True
return result
@ti.pyfunc
def isBoundaryP (boundaryType):
result = False
if ( BOUNDARY_P_EAST == boundaryType or
BOUNDARY_P_WEST == boundaryType ):
result = True
return result
#
# 6 2 5
# \ | /
# \ | /
# 3 ---- 0 ---- 1
# / | \
# / | \
# 7 4 8
#
inv_k = [0, 3,4,1,2,7,8,5,6]
ec = [[0, 0], [1, 0], [0, 1], [-1, 0], [0, -1], [1, 1], [-1, 1], [-1, -1], [1, -1]]
wc = [ 4.0 / 9.0, 1.0 / 9.0, 1.0 / 9.0, 1.0 / 9.0, 1.0 / 9.0, 1.0 / 36.0,
1.0 / 36.0, 1.0 / 36.0, 1.0 / 36.0]
NaN = float('nan')
@ti.func
def getNodeType (i, j):
nType = ti.cast (nodeType [i,j], ti.u32)
return nType & 0x0F
@ti.func
def setNodeType (i, j, nType):
tmp = ti.cast (nodeType [i,j], ti.u32)
nodeType [i,j] = ti.cast ((tmp & 0xF0) | (nType & 0x0F), ti.u16)
@ti.func
def getPackedNeighborMap (i, j):
nType = ti.cast (nodeType [i,j], ti.u32)
return nType >> 8
@ti.func
def setPackedNeighborMap (i, j, neighborMap):
tmp = ti.cast (nodeType [i,j], ti.u32)
nodeType [i,j] = (tmp & 0x0F) | (neighborMap << 8)
@ti.func
def hasNeighborInMask (neighborMask, k):
nghbrBit = 1 << (k - 1)
bitMask = neighborMask & nghbrBit
return (0 != bitMask)
@ti.func
def hasNeighbor (i, j, k):
return hasNeighborInMask (ti.cast (getPackedNeighborMap (i,j), ti.u32), k)
@ti.func
def f_eq (vel, rho, e, w):
eu = e[0] * vel [0] + e[1] * vel [1]
uv = vel [0]**2.0 + vel [1]**2.0
return w * rho * (1.0 + 3.0 * eu + 4.5 * eu**2 - 1.5 * uv)
def initializeAtEquilibrium (rho0, vx0, vy0):
@ti.kernel
def initializeAtEquilibriumKernel (rho0 : DataType,
vx0 : DataType,
vy0 : DataType):
for i, j in nodeType:
node = getNodeType (i, j)
if (SOLID != node):
vel [i, j][0] = vx0
vel [i, j][1] = vy0
if (isBoundaryVel (node)):
vel [i,j] = bcVel [i,j]
rho [i, j] = rho0
if (isBoundaryP (node)):
rho [i,j] = bcRho [i,j]
if (SOLID == node):
for k in ti.static (range (9)):
setF (f_new, i,j, ti.static (k), NaN)
setF (f_old, i,j, ti.static (k), NaN)
else:
for k in ti.static (range (9)):
lfeq = f_eq (vel [i,j], rho [i,j], ec[k], wc[k])
setF (f_old, i,j, ti.static (k), lfeq)
if (BOUNDARY_BB == node):
setF (f_new, i,j, ti.static (k), lfeq)
else:
setF (f_new, i,j, ti.static (k), NaN)
initializeAtEquilibriumKernel (rho0, vx0, vy0)
@ti.func
def rhoV (f ,i, j):
lrho = ti.cast (0.0, DataType)
lvel0 = ti.cast (0.0, DataType)
lvel1 = ti.cast (0.0, DataType)
for k in ti.static(range(9)):
lf = getF (f, i,j,k)
lrho += lf
lvel0 += (ti.cast (ec [k][0], DataType) * lf)
lvel1 += (ti.cast (ec [k][1], DataType) * lf)
lvel0 /= lrho
lvel1 /= lrho
return lrho, lvel0, lvel1
def computeRhoV (f):
@ti.kernel
def computeRhoVKernel():
for i, j in nodeType:
nType = getNodeType (i,j)
if (isBoundaryVel (nType)):
rho [i,j] = NaN
vel [i,j][0] = bcVel [i,j][0]
vel [i,j][1] = bcVel [i,j][1]
else:
rho [i,j], vel[i,j][0], vel[i,j][1] = rhoV (f, i, j)
computeRhoVKernel()
@ti.func
def gatherFull (f, i,j,k, ei,ej, enable, nodeType):
# When no neighbor, load current value of PDF - used for bounce-back nodes
ni = i
nj = j
if (True == enable):
ni = i - ei
nj = j - ej
elif (BOUNDARY_BB == nodeType):
# Gather missing PDFs for bounce-back nodes. Needed, because after processing
# of boundary nodes ALL PDF are stored as fA. Without the below code, fA
# values for bounce-back nodes were uncorrectly set to 0.
ni = i
nj = j
return getF (f, ni, nj, k)
@ti.func
def streamCollideFunc (fA, fB, i, j, omega):
# Overlaps with load of bType - all indices for f0 do not change.
# However, may generate unnecessary loads for solid nodes.
f0 = ti.cast (0.0, DataType)
f0 = getF (fB, i,j,0)
localF = ti.cast (0.0, DataType)
nType = ti.cast (getNodeType (i,j), ti.u32)
neighborMask = ti.cast (getPackedNeighborMap (i,j), ti.u32)
lrho = ti.cast (0.0, DataType)
lvel0 = ti.cast (0.0, DataType)
lvel1 = ti.cast (0.0, DataType)
lvel = [lvel0, lvel1]
lrho = f0
f1 = ti.cast (0.0, DataType)
f2 = ti.cast (0.0, DataType)
f3 = ti.cast (0.0, DataType)
f4 = ti.cast (0.0, DataType)
f5 = ti.cast (0.0, DataType)
f6 = ti.cast (0.0, DataType)
f7 = ti.cast (0.0, DataType)
f8 = ti.cast (0.0, DataType)
if ( FLUID == nType
or BOUNDARY_BB == nType
or isBoundaryVel (nType)
or isBoundaryP (nType)
):
# Compute velocity in-fly. For bounce-back and velocity boundary this is not needed,
# but does not hurt.
k = ti.static (1)
f = gatherFull (fB, i,j,k, ec [k][0], ec [k][1], hasNeighborInMask (neighborMask, k), nType)
lvel0 += (ti.cast (ec [k][0], DataType) * f)
lvel1 += (ti.cast (ec [k][1], DataType) * f)
lrho += f
f1 = f
k = ti.static (2)
f = gatherFull (fB, i,j,k, ec [k][0], ec [k][1], hasNeighborInMask (neighborMask, k), nType)
lvel0 += (ti.cast (ec [k][0], DataType) * f)
lvel1 += (ti.cast (ec [k][1], DataType) * f)
lrho += f
f2 = f
k = ti.static (3)
f = gatherFull (fB, i,j,k, ec [k][0], ec [k][1], hasNeighborInMask (neighborMask, k), nType)
lvel0 += (ti.cast (ec [k][0], DataType) * f)
lvel1 += (ti.cast (ec [k][1], DataType) * f)
lrho += f
f3 = f
k = ti.static (4)
f = gatherFull (fB, i,j,k, ec [k][0], ec [k][1], hasNeighborInMask (neighborMask, k), nType)
lvel0 += (ti.cast (ec [k][0], DataType) * f)
lvel1 += (ti.cast (ec [k][1], DataType) * f)
lrho += f
f4 = f
k = ti.static (5)
f = gatherFull (fB, i,j,k, ec [k][0], ec [k][1], hasNeighborInMask (neighborMask, k), nType)
lvel0 += (ti.cast (ec [k][0], DataType) * f)
lvel1 += (ti.cast (ec [k][1], DataType) * f)
lrho += f
f5 = f
k = ti.static (6)
f = gatherFull (fB, i,j,k, ec [k][0], ec [k][1], hasNeighborInMask (neighborMask, k), nType)
lvel0 += (ti.cast (ec [k][0], DataType) * f)
lvel1 += (ti.cast (ec [k][1], DataType) * f)
lrho += f
f6 = f
k = ti.static (7)
f = gatherFull (fB, i,j,k, ec [k][0], ec [k][1], hasNeighborInMask (neighborMask, k), nType)
lvel0 += (ti.cast (ec [k][0], DataType) * f)
lvel1 += (ti.cast (ec [k][1], DataType) * f)
lrho += f
f7 = f
k = ti.static (8)
f = gatherFull (fB, i,j,k, ec [k][0], ec [k][1], hasNeighborInMask (neighborMask, k), nType)
lvel0 += (ti.cast (ec [k][0], DataType) * f)
lvel1 += (ti.cast (ec [k][1], DataType) * f)
lrho += f
f8 = f
if (FLUID == nType):
lvel [0] = lvel0 / lrho
lvel [1] = lvel1 / lrho
elif (isBoundaryVel (nType)):
lvel [0] = bcVel [i,j][0]
lvel [1] = bcVel [i,j][1]
ux = lvel [0]
uy = lvel [1]
if (BOUNDARY_VEL_NEQN_NORTH == nType):
# Load missing values.
# TODO: Use better way of handling corner nodes.
k = ti.static (1)
if (not hasNeighborInMask (neighborMask, k)):
f1 = getF (fB, i - ec[k][0], j - ec[k][1], k)
k = ti.static (2)
if (not hasNeighborInMask (neighborMask, k)):
f2 = getF (fB, i - ec[k][0], j - ec[k][1], k)
k = ti.static (3)
if (not hasNeighborInMask (neighborMask, k)):
f3 = getF (fB, i - ec[k][0], j - ec[k][1], k)
k = ti.static (5)
if (not hasNeighborInMask (neighborMask, k)):
f5 = getF (fB, i - ec[k][0], j - ec[k][1], k)
k = ti.static (6)
if (not hasNeighborInMask (neighborMask, k)):
f6 = getF (fB, i - ec[k][0], j - ec[k][1], k)
lrho = (f0 + f1 + f3 + 2.0 * (f2 + f5 + f6)) / (1 + uy)
rho_y = lrho * uy * (1.0 / 6.0)
rho_x = lrho * ux * 0.5
f3_f1 = (f3 - f1) * 0.5
term = rho_x + f3_f1
f4 = f2 - 4.0 * rho_y
f7 = f5 - term - rho_y
f8 = f6 + term - rho_y
elif (BOUNDARY_VEL_NEQN_SOUTH == nType):
# Load missing values.
# TODO: Use better way of handling corner nodes.
k = ti.static (1)
if (not hasNeighborInMask (neighborMask, k)):
f1 = getF (fB, i - ec[k][0], j - ec[k][1], k)
k = ti.static (3)
if (not hasNeighborInMask (neighborMask, k)):
f3 = getF (fB, i - ec[k][0], j - ec[k][1], k)
k = ti.static (4)
if (not hasNeighborInMask (neighborMask, k)):
f4 = getF (fB, i - ec[k][0], j - ec[k][1], k)
k = ti.static (7)
if (not hasNeighborInMask (neighborMask, k)):
f7 = getF (fB, i - ec[k][0], j - ec[k][1], k)
k = ti.static (8)
if (not hasNeighborInMask (neighborMask, k)):
f8 = getF (fB, i - ec[k][0], j - ec[k][1], k)
lrho = (f0 + f1 + f3 + 2.0 * (f4 + f7 + f8)) / (1 - uy)
f2 = f4 + lrho * uy * 2.0 / 3.0
f5 = f7 - 0.5 * (f1 - f3) + 0.5 * lrho * ux + lrho * uy / 6.0
f6 = f8 + 0.5 * (f1 - f3) - 0.5 * lrho * ux + lrho * uy / 6.0
elif (BOUNDARY_VEL_NEQN_WEST == nType):
k = ti.static (1)
if (not hasNeighborInMask (neighborMask, k)):
f1 = getF (fB, i - ec[k][0], j - ec[k][1], k)
k = ti.static (2)
if (not hasNeighborInMask (neighborMask, k)):
f2 = getF (fB, i - ec[k][0], j - ec[k][1], k)
k = ti.static (4)
if (not hasNeighborInMask (neighborMask, k)):
f4 = getF (fB, i - ec[k][0], j - ec[k][1], k)
k = ti.static (5)
if (not hasNeighborInMask (neighborMask, k)):
f5 = getF (fB, i - ec[k][0], j - ec[k][1], k)
k = ti.static (8)
if (not hasNeighborInMask (neighborMask, k)):
f8 = getF (fB, i - ec[k][0], j - ec[k][1], k)
lrho = (f0 + f2 + f4 + 2.0 * (f3 + f6 + f7)) / (1 - ux)
f1 = f3 + lrho * ux * (2.0 / 3.0)
f5 = f7 - 0.5 * (f2 - f4) + 0.5 * lrho * uy + lrho * ux * (1.9 / 6.0)
f8 = f6 + 0.5 * (f2 - f4) - 0.5 * lrho * uy + lrho * ux * (1.9 / 6.0)
elif (isBoundaryP (nType)):
lrho = bcRho [i,j]
if (BOUNDARY_P_WEST == nType):
if (not hasNeighborInMask (neighborMask, 4)):
# Bottom corner
ux = 0
uy = 0
lvel [0] = ux
lvel [1] = uy
f1 = f3
f2 = f4
f5 = f7
f6 = 0.5 * (lrho - (f0 + f1 + f2 + f3 + f4 + f5 + f7))
f8 = f6
elif (not hasNeighborInMask (neighborMask, 2)):
# Top corner
ux = 0
uy = 0
lvel [0] = ux
lvel [1] = uy
f1 = f3
f4 = f2
f8 = f6
f5 = 0.5 * (lrho - (f0 + 2.0 * f2 + 2.0 * f3 + 2.0 * f6))
f7 = f5
else:
lvel [1] = 0
uy = lvel [1]
ux = 1 - (f0 + f2 + f4 + 2.0 * (f3 + f6 + f7)) / lrho
lvel [0] = ux
f1 = f3 + lrho * ux * (2.0 / 3.0)
f5 = f7 - 0.5 * (f2 - f4) + lrho * ux * (1.0 / 6.0)
f8 = f6 + 0.5 * (f2 - f4) + lrho * ux * (1.0 / 6.0)
elif (BOUNDARY_P_EAST == nType):
if (not hasNeighborInMask (neighborMask, 4)):
# Bottom corner
ux = 0
uy = 0
lvel [0] = ux
lvel [1] = uy
f3 = f1
f2 = f4
f6 = f8
f5 = 0.5 * (lrho - f0) - f1 - f4 - f8
f7 = f5
elif (not hasNeighborInMask (neighborMask, 2)):
# Top corner
ux = 0
uy = 0
lvel [0] = ux
lvel [1] = uy
f3 = f1
f4 = f2
f7 = f5
f6 = 0.5 * (lrho - f0) - f1 - f2 - f5
f8 = f6
else:
lvel [1] = 0
uy = lvel [1]
ux = (f0 + f2 + f4 + 2.0 * (f1 + f5 + f8)) / lrho - 1.0
lvel [0] = ux
f3 = f1 - lrho * ux * (2.0 / 3.0)
f6 = f8 - 0.5 * (f2 - f4) - lrho * ux * (1.0 / 6.0)
f7 = f5 + 0.5 * (f2 - f4) - lrho * ux * (1.0 / 6.0)
#
# Collide.
#
f0_new = ti.cast (0.0, DataType)
f1_new = ti.cast (0.0, DataType)
f2_new = ti.cast (0.0, DataType)
f3_new = ti.cast (0.0, DataType)
f4_new = ti.cast (0.0, DataType)
f5_new = ti.cast (0.0, DataType)
f6_new = ti.cast (0.0, DataType)
f7_new = ti.cast (0.0, DataType)
f8_new = ti.cast (0.0, DataType)
if ( FLUID == nType
or isBoundaryVel (nType)
or isBoundaryP (nType)
):
omega_1 = 1.0 - omega
rho_9 = lrho * (1.0 / 9.0)
uv = lvel [0]**2 + lvel [1]**2
uv_3_2 = 1.5 * uv
uv_term = 1 - uv_3_2
local_feq = 4.0 * rho_9 * uv_term
new_f = omega_1 * f0 + omega * local_feq
f0_new = new_f
eu = lvel [0]
eu_term = 3.0 * eu
eu2_term = 4.5 * eu * eu
term_1 = uv_term + eu2_term
local_feq = rho_9 * (term_1 + eu_term)
new_f = omega_1 * f1 + omega * local_feq
f1_new = new_f
local_feq = rho_9 * (term_1 - eu_term)
new_f = omega_1 * f3 + omega * local_feq
f3_new = new_f
eu = lvel [1]
eu_term = 3.0 * eu
eu2_term = 4.5 * eu * eu
term_1 = uv_term + eu2_term
local_feq = rho_9 * (term_1 + eu_term)
new_f = omega_1 * f2 + omega * local_feq
f2_new = new_f
local_feq = rho_9 * (term_1 - eu_term)
new_f = omega_1 * f4 + omega * local_feq
f4_new = new_f
rho_36 = lrho * (1.0 / 36.0)
eu = lvel [0] + lvel [1]
eu_term = 3.0 * eu
eu2_term = 4.5 * eu * eu
term_1 = uv_term + eu2_term
local_feq = rho_36 * (term_1 + eu_term)
new_f = omega_1 * f5 + omega * local_feq
f5_new = new_f
local_feq = rho_36 * (term_1 - eu_term)
new_f = omega_1 * f7 + omega * local_feq
f7_new = new_f
eu = lvel [1] - lvel [0]
eu_term = 3.0 * eu
eu2_term = 4.5 * eu * eu
term_1 = uv_term + eu2_term
local_feq = rho_36 * (term_1 + eu_term)
new_f = omega_1 * f6 + omega * local_feq
f6_new = new_f
local_feq = rho_36 * (term_1 - eu_term)
new_f = omega_1 * f8 + omega * local_feq
f8_new = new_f
# Do not collide for bounce-back nodes.
elif (BOUNDARY_BB == nType):
f0_new = f0
f1_new = f3
f2_new = f4
f3_new = f1
f4_new = f2
f5_new = f7
f6_new = f8
f7_new = f5
f8_new = f6
if ( FLUID == nType
or BOUNDARY_BB == nType
or isBoundaryVel (nType)
or isBoundaryP (nType)
):
setF (fA, i,j, 0, f0_new)
setF (fA, i,j, 1, f1_new)
setF (fA, i,j, 2, f2_new)
setF (fA, i,j, 3, f3_new)
setF (fA, i,j, 4, f4_new)
setF (fA, i,j, 5, f5_new)
setF (fA, i,j, 6, f6_new)
setF (fA, i,j, 7, f7_new)
setF (fA, i,j, 8, f8_new)
@ti.kernel
def streamCollideA (omega: DataType):
fA, fB = ti.static (f_new, f_old)
ti.block_dim (512)
for i, j in nodeType:
streamCollideFunc (fA, fB, i, j, omega)
@ti.kernel
def streamCollideB (omega: DataType):
fA, fB = ti.static (f_old, f_new)
ti.block_dim (512)
for i, j in nodeType:
streamCollideFunc (fA, fB, i, j, omega)
def run (numberOfTimeSteps):
nIterations = numberOfTimeSteps // 2
for i in range (nIterations):
streamCollideA (omega)
streamCollideB (omega)
return 2 * nIterations
################################################################################
#
# Geometry.
#
@ti.kernel
def initNeighborMap():
for i, j in nodeType:
hasAllNeighbors = True
neighborBitMask = 0