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filterfuncs.py
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import numpy as np
"""
"""
def minmod(a1,a2,a3):
Ng = a1.shape[0]
s = (1.0/3.0)*(np.sign(a1)+np.sign(a2)+np.sign(a3))
flagS = np.isclose(np.absolute(s),1.0)
minimum = s*np.minimum(np.abs(a1),np.abs(a2),np.abs(a3))
minmodFunction = np.zeros((Ng))
minmodFunction[np.where(flagS)] = minimum[np.where(flagS)]
return minmodFunction
def limiter1(u,umin,umax,Vand,invVand,Dr,x,xm,dx):
#TODO truncate matrices to avoid unnecessary products
uLimited = np.zeros((u.shape))
uhat = np.zeros((u.shape))
ubar = np.zeros((u.shape))
uave = np.zeros((u.shape[1],3))
uhat = np.matmul(invVand,u)
uhat[2:,:] = 0.0
utilde = np.matmul(Vand,uhat)
ubar = np.matmul(invVand,u)
ubar[1:,:] = 0.0
uave[ :,1] = np.matmul(Vand,ubar)[0,:]
uave[0:-1,2] = uave[ 1:,1]
uave[ -1,2] = uave[ -1,1]
uave[ 1:,0] = uave[0:-1,1]
uave[ 0,0] = uave[ 0,1]
a1 = 2.0/dx*np.matmul(Dr,utilde)[0,:]
a2 = 1.0/dx*(uave[:,1] - uave[:,0])
a3 = 1.0/dx*(uave[:,2] - uave[:,1])
uLimited = uave[:,1] + (x-xm)*minmod(a1,a2,a3)
return uLimited
def limiter2(u,umin,umax,Vand,invVand,Dr,x,xm,dx):
#TODO truncate matrices to avoid unnecessary products
uLimited = np.zeros((u.shape))
uhat = np.zeros((u.shape))
ubar = np.zeros((u.shape))
uave = np.zeros((u.shape[1],3))
ue0 = u[ 0,:]
ueN = u[-1,:]
uhat = np.matmul(invVand,u)
uhat[1:,:] = 0.0
uave[ :,1] = np.matmul(Vand,uhat)[0,:]
uave[0:-1,2] = uave[ 1:,1]
uave[ -1,2] = uave[ -1,1]
uave[ 1:,0] = uave[0:-1,1]
uave[ 0,0] = uave[ 0,1]
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#minmod input
a1 = uave[:,1] - ue0
a2 = uave[:,1] - uave[:,0]
a3 = uave[:,2] - uave[:,1]
ve1 = uave[:,1] - minmod(0.5*a1,a2,a3) #- ue0
flag1 = np.where(np.abs(ve1) >= 1e-7, True, False)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#minmod input
a1 = ueN - uave[:,1]
a2 = uave[:,1] - uave[:,0]
a3 = uave[:,2] - uave[:,1]
ve2 = uave[:,1] + minmod(0.5*a1,a2,a3) #- ueN
flag2 = np.where(np.abs(ve2) >= 1e-7, True, False)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
flagE = np.logical_or(flag1,flag2)
a1 = ueN - ue0
a2 = uave[:,1] - uave[:,0]
a3 = uave[:,2] - uave[:,1]
#slope limiting
uLimited[:,:] = np.where(flagE,
uave[:,1] + (x-xm)*minmod(a1,a2,a3)/dx,
u[:,:])
return uLimited
def limiterN(u,umin,umax,Vand,invVand,Dr,x,xm,dx):
#TODO truncate matrices to avoid unnecessary products
uLimited = np.zeros((u.shape))
uhat = np.zeros((u.shape))
ubar = np.zeros((u.shape))
uave = np.zeros((u.shape[1],3))
ue0 = u[ 0,:]
ueN = u[-1,:]
uhat = np.matmul(invVand,u)
uhat[1:,:] = 0.0
uave[ :,1] = np.matmul(Vand,uhat)[0,:]
uave[0:-1,2] = uave[ 1:,1]
uave[ -1,2] = uave[ -1,1]
uave[ 1:,0] = uave[0:-1,1]
uave[ 0,0] = uave[ 0,1]
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#minmod input
a1 = uave[:,1] - ue0
a2 = uave[:,1] - uave[:,0]
a3 = uave[:,2] - uave[:,1]
# a1 = uave[:,1] - ue0
# a2 = ue0 - uave[:,0]
# a3 = uave[:,2] - ueN
ve1 = uave[:,1] - minmod(a1,a2,a3) - ue0
flag1 = np.where(np.abs(ve1) >= 1e-7, True, False)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#minmod input
a1 = ueN - uave[:,1]
a2 = uave[:,1] - uave[:,0]
a3 = uave[:,2] - uave[:,1]
# a1 = ueN - uave[:,1]
# a2 = ue0 - uave[:,0]
# a3 = uave[:,2] - ueN
ve2 = uave[:,1] + minmod(a1,a2,a3) - ueN
flag2 = np.where(np.abs(ve2) >= 1e-7, True, False)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
flagE = np.logical_or(flag1,flag2)
#slope limiting
ubar = np.matmul(invVand,u)
ubar[2:,flagE] = 0.0
utilde = np.matmul(Vand,ubar)
#minmod input
a1 = 1.0/dx*np.matmul(Dr,utilde)[0,:]
a2 = 1.0/dx*(uave[:,1] - uave[:,0])
a3 = 1.0/dx*(uave[:,2] - uave[:,1])
# a1 = 1.0/dx*np.matmul(Dr,utilde)[0,:]
# a2 = 1.0/dx*(ue0 - uave[:,0])
# a3 = 1.0/dx*(uave[:,2] - ueN)
uLimited[:,:] = np.where(flagE,
uave[:,1] + (x-xm)*minmod(a1,a2,a3),
u[:,:])
return uLimited
def ShuLimiter(u,uMaxVal,uMinVal,Vand,invVand,Dr,x,xm,dx):
#TODO truncate matrices to avoid unnecessary products
uLimited = np.zeros((u.shape))
umax = np.zeros((u.shape[1]))
umin = np.zeros((u.shape[1]))
uave = np.zeros((u.shape[1],3))
uhat = np.matmul(invVand,u)
uhat[1:,:] = 0.0
uave[ :,1] = np.matmul(Vand,uhat)[0,:]
uave[0:-1,2] = uave[ 1:,1]
uave[ -1,2] = uave[ 0,1]
uave[ 1:,0] = uave[0:-1,1]
uave[ 0,0] = uave[ -1,1]
umin[:] = np.amin(u,axis=0)
umax[:] = np.amax(u,axis=0)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#minmod input
a1 = 1.0
a2a = (uave[:,1] - uave[:,0])/(umax - uave[:,1] + 1e-12)
a2b = (uave[:,2] - uave[:,1])/(umax - uave[:,1] + 1e-12)
a2 = np.minimum(a2a,a2b)
a3a = (uave[:,1] - uave[:,0])/(umin - uave[:,1] + 1e-12)
a3b = (uave[:,2] - uave[:,1])/(umin - uave[:,1] + 1e-12)
a3 = np.minimum(a3a,a3b)
theta = np.minimum(np.abs(a1),np.abs(a2),np.abs(a3))
uLimited[:,:] = uave[:,1] + theta*(u[:,:] - uave[:,1])
return uLimited
def ShuLimiter_bound(u,uMaxVal,uMinVal,Vand,invVand,Dr,x,xm,dx):
uLimited = np.zeros((u.shape))
umax = np.zeros((u.shape[1]))
umin = np.zeros((u.shape[1]))
uave = np.zeros((u.shape[1],3))
umin[:] = np.amin(u,axis=0)
umax[:] = np.amax(u,axis=0)
uhat = np.matmul(invVand,u)
uhat[1:,:] = 0.0
uave[ :,1] = np.matmul(Vand,uhat)[0,:]
uave[ 1:,0] = u[-1,0:-1]
uave[ 0,0] = u[-1,-1]
uave[0:-1,2] = u[ 0,1:]
uave[ -1,2] = u[ 0, 0]
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#minmod input
a1 = 1.0
a2a = (uave[:,1] - uave[:,0])/(umax - uave[:,1] + 1e-12)
a2b = (uave[:,2] - uave[:,1])/(umax - uave[:,1] + 1e-12)
a2 = np.minimum(np.abs(a2a),np.abs(a2b))
a3a = (uave[:,1] - uave[:,0])/(umin - uave[:,1] + 1e-12)
a3b = (uave[:,2] - uave[:,1])/(umin - uave[:,1] + 1e-12)
a3 = np.minimum(np.abs(a3a),np.abs(a3b))
theta = np.minimum(a1,a2,a3)
uLimited[:,:] = uave[:,1] + theta*(u[:,:] - uave[:,1])
#_theta = np.vstack((theta,theta))
return uLimited#, uave[:,0], uave[:,1], uave[:,2], _theta
################################################################################
"""
"""
def filter1D(N,Nc,s,Vand,invVand):
filterdiag = np.eye((N))
alpha = 2.0
# print(Nc,N)
if (Nc == 0):
#print(filterdiag)
return filterdiag
if (Nc >= N):
#print(filterdiag)
return filterdiag
if (Nc >= N-1):
filterdiag[-1,-1] = 0.0
#print(filterdiag)
return filterdiag
for i in range(Nc,N):
print(i)
filterdiag[i,i] = np.exp(-alpha*((i-Nc)/((N-1)-Nc))**s)
print(filterdiag)
return np.matmul(Vand,np.matmul(filterdiag,invVand))