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FiniteVolumeSchemes.py
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FiniteVolumeSchemes.py
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# -*- coding: utf-8 -*-
"""
Created on Fri Jun 7 18:49:22 2019
@author: ben91
"""
from SimulationClasses import *
import numpy as np
def Hook5():
def scheme(u):
fl = 1/30*u[:,0]-13/60*u[:,1]+47/60*u[:,2]+9/20*u[:,3]-1/20*u[:,4]
return fl
FVM = FiniteVolumeMethod(5, scheme)
return FVM
def WENO5():
def scheme(u):
ep = 1E-6
#compute fluxes on sub stencils
f1 = 1/3*u[:,0]-7/6*u[:,1]+11/6*u[:,2]
f2 = -1/6*u[:,1]+5/6*u[:,2]+1/3*u[:,3]
f3 = 1/3*u[:,2]+5/6*u[:,3]-1/6*u[:,4]
#compute smoothness indicators
B1 = 13/12*np.power(u[:,0]-2*u[:,1]+u[:,2],2) + 1/4*np.power(u[:,0]-4*u[:,1]+3*u[:,2],2)
B2 = 13/12*np.power(u[:,1]-2*u[:,2]+u[:,3],2) + 1/4*np.power(u[:,1]-u[:,3],2)
B3 = 13/12*np.power(u[:,2]-2*u[:,3]+u[:,4],2) + 1/4*np.power(3*u[:,2]-4*u[:,3]+u[:,4],2)
#assign linear weights
g1 = 1/10
g2 = 3/5
g3 = 3/10
#compute the unscaled nonlinear weights
wt1 = g1/np.power(ep+B1,2)
wt2 = g2/np.power(ep+B2,2)
wt3 = g3/np.power(ep+B3,2)
wts = wt1 + wt2 + wt3
#scale the nonlinear weights
w1 = wt1/wts
w2 = wt2/wts
w3 = wt3/wts
#compute the flux
fl = f1*w1+f2*w2+f3*w3
return fl
FVM = FiniteVolumeMethod(5, scheme)
return FVM
def ENO3():
def scheme(u):
ep = 1E-6
f1 =-1/2*u[:,0]+3/2*u[:,1]
f2 = 1/2*u[:,1]+1/2*u[:,2]
B1 = (u[:,0]-u[:,1])**2
B2 = (u[:,1]-u[:,2])**2
#WENO3 stuff
g1 = 1/3
g2 = 2/3
wt1 = g1/(ep+B1**2)
wt2 = g2/(ep+B2**2)
wts = wt1 + wt2
w1 = wt1/wts
w2 = wt2/wts
fl = f1*w1+f2*w2
#return fl
fl = np.zeros_like(f1)
for i in range(0,len(fl)):
if(B1[i]>B2[i]):
fl[i] = f2[i]
else:
fl[i] = f1[i]
#fl[B1>B2] = f2[B1>B2]
#fl[B1<=B2] = f1[B1<=B2]
return fl
FVM = FiniteVolumeMethod(3, scheme)
return FVM
def upwind():
def scheme(u):
return u[:,2]
FVM = FiniteVolumeMethod(5, scheme)
return FVM
def NNWENO5():
def scheme(u):
min_u = np.amin(u,1)
max_u = np.amax(u,1)
const_n = min_u==max_u
#print('u: ', u)
u_tmp = np.zeros_like(u[:,2])
u_tmp[:] = u[:,2]
for i in range(0,5):
u[:,i] = (u[:,i]-min_u)/(max_u-min_u)
ep = 1E-6
#compute fluxes on sub stencils
f1 = 1/3*u[:,0]-7/6*u[:,1]+11/6*u[:,2]
f2 = -1/6*u[:,1]+5/6*u[:,2]+1/3*u[:,3]
f3 = 1/3*u[:,2]+5/6*u[:,3]-1/6*u[:,4]
#compute smoothness indicators
B1 = 13/12*np.power(u[:,0]-2*u[:,1]+u[:,2],2) + 1/4*np.power(u[:,0]-4*u[:,1]+3*u[:,2],2)
B2 = 13/12*np.power(u[:,1]-2*u[:,2]+u[:,3],2) + 1/4*np.power(u[:,1]-u[:,3],2)
B3 = 13/12*np.power(u[:,2]-2*u[:,3]+u[:,4],2) + 1/4*np.power(3*u[:,2]-4*u[:,3]+u[:,4],2)
#assign linear weights
g1 = 1/10
g2 = 3/5
g3 = 3/10
#compute the unscaled nonlinear weights
wt1 = g1/np.power(ep+B1,2)
wt2 = g2/np.power(ep+B2,2)
wt3 = g3/np.power(ep+B3,2)
wts = wt1 + wt2 + wt3
#scale the nonlinear weights
w1 = wt1/wts
w2 = wt2/wts
w3 = wt3/wts
#compute the coefficients
c1 = np.transpose(np.array([1/3*w1,-7/6*w1-1/6*w2,11/6*w1+5/6*w2+1/3*w3,1/3*w2+5/6*w3,-1/6*w3]))
A1 = np.array([[-0.94130915, -0.32270527, -0.06769955],
[-0.37087336, -0.05059665, 0.55401474],
[ 0.40815187, -0.5602299 , -0.01871526],
[ 0.56200236, -0.5348897 , -0.04091108],
[-0.6982639 , -0.49512517, 0.52821904]])
b1 = np.array([-0.04064859, 0. , 0. ])
c2 = np.maximum(np.matmul(c1,A1)+b1,0)
A2 = np.array([[ 0.07149544, 0.9637294 , 0.41981453],
[ 0.75602794, -0.0222342 , -0.95690656],
[ 0.07406807, -0.41880417, -0.4687035 ]])
b2 = np.array([-0.0836111 , -0.00330033, -0.01930024])
c3 = np.maximum(np.matmul(c2,A2)+b2,0)
A3 = np.array([[ 0.8568574 , -0.5809458 , 0.04762125],
[-0.26066098, -0.23142155, -0.6449008 ],
[ 0.7623346 , 0.81388015, -0.03217626]])
b3 = np.array([-0.0133561 , -0.05374921, 0. ])
c4 = np.maximum(np.matmul(c3,A3)+b3,0)
A4 = np.array([[-0.2891752 , -0.53783405, -0.17556567, -0.7775279 , 0.69957024],
[-0.12895434, 0.13607207, 0.12294354, 0.29842544, -0.00198237],
[ 0.5356503 , 0.09317833, 0.5135357 , -0.32794708, 0.13765627]])
b4 = np.array([ 0.00881096, 0.01138764, 0.00464343, 0.0070305 , -0.01644066])
dc = np.matmul(c4,A4)+b4
ct = c1 - dc
Ac = np.array([[-0.2, -0.2, -0.2, -0.2, -0.2],
[-0.2, -0.2, -0.2, -0.2, -0.2],
[-0.2, -0.2, -0.2, -0.2, -0.2],
[-0.2, -0.2, -0.2, -0.2, -0.2],
[-0.2, -0.2, -0.2, -0.2, -0.2]])
bc = np.array([0.2, 0.2, 0.2, 0.2, 0.2])
dc2 = np.matmul(ct,Ac)+bc
C = ct + dc2
fl = u[:,0]*C[:,0] + u[:,1]*C[:,1] + u[:,2]*C[:,2] + u[:,3]*C[:,3] + u[:,4]*C[:,4]
fl = fl.flatten()
fl = np.multiply(fl,(max_u-min_u))+min_u
fl[const_n] = u_tmp[const_n]#if const across stencil, set to that value
return fl
FVM = FiniteVolumeMethod(5, scheme)
return FVM
def NNWENO5dx(dx):
def scheme(u):
min_u = np.amin(u,1)
max_u = np.amax(u,1)
const_n = min_u==max_u
#print('u: ', u)
u_tmp = np.zeros_like(u[:,2])
u_tmp[:] = u[:,2]
for i in range(0,5):
u[:,i] = (u[:,i]-min_u)/(max_u-min_u)
ep = 1E-6
#compute fluxes on sub stencils
f1 = 1/3*u[:,0]-7/6*u[:,1]+11/6*u[:,2]
f2 = -1/6*u[:,1]+5/6*u[:,2]+1/3*u[:,3]
f3 = 1/3*u[:,2]+5/6*u[:,3]-1/6*u[:,4]
#compute smoothness indicators
B1 = 13/12*np.power(u[:,0]-2*u[:,1]+u[:,2],2) + 1/4*np.power(u[:,0]-4*u[:,1]+3*u[:,2],2)
B2 = 13/12*np.power(u[:,1]-2*u[:,2]+u[:,3],2) + 1/4*np.power(u[:,1]-u[:,3],2)
B3 = 13/12*np.power(u[:,2]-2*u[:,3]+u[:,4],2) + 1/4*np.power(3*u[:,2]-4*u[:,3]+u[:,4],2)
#assign linear weights
g1 = 1/10
g2 = 3/5
g3 = 3/10
#compute the unscaled nonlinear weights
wt1 = g1/np.power(ep+B1,2)
wt2 = g2/np.power(ep+B2,2)
wt3 = g3/np.power(ep+B3,2)
wts = wt1 + wt2 + wt3
#scale the nonlinear weights
w1 = wt1/wts
w2 = wt2/wts
w3 = wt3/wts
#compute the coefficients
c1 = np.transpose(np.array([1/3*w1,-7/6*w1-1/6*w2,11/6*w1+5/6*w2+1/3*w3,1/3*w2+5/6*w3,-1/6*w3]))
A1 = np.array([[-0.94130915, -0.32270527, -0.06769955],
[-0.37087336, -0.05059665, 0.55401474],
[ 0.40815187, -0.5602299 , -0.01871526],
[ 0.56200236, -0.5348897 , -0.04091108],
[-0.6982639 , -0.49512517, 0.52821904]])
b1 = np.array([-0.04064859, 0. , 0. ])
c2 = np.maximum(np.matmul(c1,A1)+b1,0)
A2 = np.array([[ 0.07149544, 0.9637294 , 0.41981453],
[ 0.75602794, -0.0222342 , -0.95690656],
[ 0.07406807, -0.41880417, -0.4687035 ]])
b2 = np.array([-0.0836111 , -0.00330033, -0.01930024])
c3 = np.maximum(np.matmul(c2,A2)+b2,0)
A3 = np.array([[ 0.8568574 , -0.5809458 , 0.04762125],
[-0.26066098, -0.23142155, -0.6449008 ],
[ 0.7623346 , 0.81388015, -0.03217626]])
b3 = np.array([-0.0133561 , -0.05374921, 0. ])
c4 = np.maximum(np.matmul(c3,A3)+b3,0)
A4 = np.array([[-0.2891752 , -0.53783405, -0.17556567, -0.7775279 , 0.69957024],
[-0.12895434, 0.13607207, 0.12294354, 0.29842544, -0.00198237],
[ 0.5356503 , 0.09317833, 0.5135357 , -0.32794708, 0.13765627]])
b4 = np.array([ 0.00881096, 0.01138764, 0.00464343, 0.0070305 , -0.01644066])
dc = np.matmul(c4,A4)+b4
ct = c1 - dc
Ac = np.array([[-0.2, -0.2, -0.2, -0.2, -0.2],
[-0.2, -0.2, -0.2, -0.2, -0.2],
[-0.2, -0.2, -0.2, -0.2, -0.2],
[-0.2, -0.2, -0.2, -0.2, -0.2],
[-0.2, -0.2, -0.2, -0.2, -0.2]])
bc = np.array([0.2, 0.2, 0.2, 0.2, 0.2])
dc2 = np.matmul(ct,Ac)+bc
C = ct + dc2
fl = u[:,0]*C[:,0] + u[:,1]*C[:,1] + u[:,2]*C[:,2] + u[:,3]*C[:,3] + u[:,4]*C[:,4]
fl = fl.flatten()
fl = np.multiply(fl,(max_u-min_u))+min_u
fl[const_n] = u_tmp[const_n]#if const across stencil, set to that value
return fl
FVM = FiniteVolumeMethod(5, scheme)
return FVM
def NNWENO5_NoScale():
def scheme(u):
min_u = np.amin(u,1)
max_u = np.amax(u,1)
const_n = min_u==max_u
u_tmp = np.zeros_like(u[:,2])
u_tmp[:] = u[:,2]
u_str = np.zeros_like(u)
for i in range(0,5):
u_str[:,i] = u[:,i]
#u[:,i] = (u[:,i]-min_u)/(max_u-min_u)
ep = 1E-6
#compute fluxes on sub stencils
#f1 = 1/3*u[:,0]-7/6*u[:,1]+11/6*u[:,2]
#f2 = -1/6*u[:,1]+5/6*u[:,2]+1/3*u[:,3]
#f3 = 1/3*u[:,2]+5/6*u[:,3]-1/6*u[:,4]
#compute smoothness indicators
B1 = 13/12*np.power(u[:,0]-2*u[:,1]+u[:,2],2) + 1/4*np.power(u[:,0]-4*u[:,1]+3*u[:,2],2)
B2 = 13/12*np.power(u[:,1]-2*u[:,2]+u[:,3],2) + 1/4*np.power(u[:,1]-u[:,3],2)
B3 = 13/12*np.power(u[:,2]-2*u[:,3]+u[:,4],2) + 1/4*np.power(3*u[:,2]-4*u[:,3]+u[:,4],2)
#assign linear weights
g1 = 1/10
g2 = 3/5
g3 = 3/10
#compute the unscaled nonlinear weights
wt1 = g1/np.power(ep+B1,2)
wt2 = g2/np.power(ep+B2,2)
wt3 = g3/np.power(ep+B3,2)
wts = wt1 + wt2 + wt3
#scale the nonlinear weights
w1 = wt1/wts
w2 = wt2/wts
w3 = wt3/wts
#compute the coefficients
c1 = np.transpose(np.array([1/3*w1,-7/6*w1-1/6*w2,11/6*w1+5/6*w2+1/3*w3,1/3*w2+5/6*w3,-1/6*w3]))
A1 = np.array([[-0.94130915, -0.32270527, -0.06769955],
[-0.37087336, -0.05059665, 0.55401474],
[ 0.40815187, -0.5602299 , -0.01871526],
[ 0.56200236, -0.5348897 , -0.04091108],
[-0.6982639 , -0.49512517, 0.52821904]])
b1 = np.array([-0.04064859, 0. , 0. ])
c2 = np.maximum(np.matmul(c1,A1)+b1,0)
A2 = np.array([[ 0.07149544, 0.9637294 , 0.41981453],
[ 0.75602794, -0.0222342 , -0.95690656],
[ 0.07406807, -0.41880417, -0.4687035 ]])
b2 = np.array([-0.0836111 , -0.00330033, -0.01930024])
c3 = np.maximum(np.matmul(c2,A2)+b2,0)
A3 = np.array([[ 0.8568574 , -0.5809458 , 0.04762125],
[-0.26066098, -0.23142155, -0.6449008 ],
[ 0.7623346 , 0.81388015, -0.03217626]])
b3 = np.array([-0.0133561 , -0.05374921, 0. ])
c4 = np.maximum(np.matmul(c3,A3)+b3,0)
A4 = np.array([[-0.2891752 , -0.53783405, -0.17556567, -0.7775279 , 0.69957024],
[-0.12895434, 0.13607207, 0.12294354, 0.29842544, -0.00198237],
[ 0.5356503 , 0.09317833, 0.5135357 , -0.32794708, 0.13765627]])
b4 = np.array([ 0.00881096, 0.01138764, 0.00464343, 0.0070305 , -0.01644066])
dc = np.matmul(c4,A4)+b4
ct = c1 - dc
Ac = np.array([[-0.2, -0.2, -0.2, -0.2, -0.2],
[-0.2, -0.2, -0.2, -0.2, -0.2],
[-0.2, -0.2, -0.2, -0.2, -0.2],
[-0.2, -0.2, -0.2, -0.2, -0.2],
[-0.2, -0.2, -0.2, -0.2, -0.2]])
bc = np.array([0.2, 0.2, 0.2, 0.2, 0.2])
dc2 = np.matmul(ct,Ac)+bc
C = ct + dc2
#fl = u[:,0]*C[:,0] + u[:,1]*C[:,1] + u[:,2]*C[:,2] + u[:,3]*C[:,3] + u[:,4]*C[:,4]
fl = u_str[:,0]*C[:,0] + u_str[:,1]*C[:,1] + u_str[:,2]*C[:,2] + u_str[:,3]*C[:,3] + u_str[:,4]*C[:,4]
fl = fl.flatten()
#fl = np.multiply(fl,(max_u-min_u))+min_u
fl[const_n] = u_tmp[const_n]#if const across stencil, set to that value
return fl
FVM = FiniteVolumeMethod(5, scheme)
return FVM
def NNMethod(model):
def scheme(u):
min_u = np.amin(u,1)
max_u = np.amax(u,1)
const_n = min_u==max_u
#print('u: ', u)
u_tmp = np.zeros_like(u[:,2])
u_tmp[:] = u[:,2]
for i in range(0,5):
u[:,i] = (u[:,i]-min_u)/(max_u-min_u)
fl = model.predict(u)#compute \Delta u
fl = fl.flatten()
fl = np.multiply(fl,(max_u-min_u))+min_u
fl[const_n] = u_tmp[const_n]#if const across stencil, set to that value
#print('fl: ', fl)
return fl
FVM = FiniteVolumeMethod(5, scheme)
return FVM
def NNMethod_noScale(model):
def scheme(u):
min_u = np.amin(u,1)
max_u = np.amax(u,1)
const_n = min_u==max_u
#print('u: ', u)
u_tmp = np.zeros_like(u[:,2])
u_tmp[:] = u[:,2]
#for i in range(0,5):
#u[:,i] = (u[:,i]-min_u)/(max_u-min_u)
fl = model.predict(u)#compute \Delta u
fl = fl.flatten()
#fl = np.multiply(fl,(max_u-min_u))+min_u
fl[const_n] = u_tmp[const_n]#if const across stencil, set to that value
#print('fl: ', fl)
return fl
FVM = FiniteVolumeMethod(5, scheme)
return FVM
def WENO5euler():
def scheme(f):
'''
inputs:
f: variables to WENO5 (nx3x5)
outputs:
fl: WENO5 flux
'''
ep = 1E-6
#compute fluxes on sub stencils
f1 = 1/3*f[:,:,0]-7/6*f[:,:,1]+11/6*f[:,:,2]
f2 =-1/6*f[:,:,1]+5/6*f[:,:,2]+ 1/3*f[:,:,3]
f3 = 1/3*f[:,:,2]+5/6*f[:,:,3]- 1/6*f[:,:,4]
#compute smoothness indicators
B1 = 13/12*np.power(f[:,:,0]-2*f[:,:,1]+f[:,:,2],2) + 1/4*np.power(f[:,:,0]-4*f[:,:,1]+3*f[:,:,2],2)
B2 = 13/12*np.power(f[:,:,1]-2*f[:,:,2]+f[:,:,3],2) + 1/4*np.power(f[:,:,1]-f[:,:,3],2)
B3 = 13/12*np.power(f[:,:,2]-2*f[:,:,3]+f[:,:,4],2) + 1/4*np.power(3*f[:,:,2]-4*f[:,:,3]+f[:,:,4],2)
#assign linear weights
g1 = 1/10
g2 = 3/5
g3 = 3/10
#compute the unscaled nonlinear weights
wt1 = g1/np.power(ep+B1,2)
wt2 = g2/np.power(ep+B2,2)
wt3 = g3/np.power(ep+B3,2)
wts = wt1 + wt2 + wt3
#scale the nonlinear weights
w1 = wt1/wts
w2 = wt2/wts
w3 = wt3/wts
#compute the flux
fl = f1*w1+f2*w2+f3*w3
return fl
FVM = FiniteVolumeMethodEuler(5, scheme)
return FVM
def NNWENO5euler():
def scheme(f):
'''
inputs:
f: variables to WENO5 (nx3x5)
outputs:
fl: WENO5 flux
'''
ep = 1E-6
#compute fluxes on sub stencils
f1 = 1/3*f[:,:,0]-7/6*f[:,:,1]+11/6*f[:,:,2]
f2 =-1/6*f[:,:,1]+5/6*f[:,:,2]+ 1/3*f[:,:,3]
f3 = 1/3*f[:,:,2]+5/6*f[:,:,3]- 1/6*f[:,:,4]
#compute smoothness indicators
B1 = 13/12*np.power(f[:,:,0]-2*f[:,:,1]+f[:,:,2],2) + 1/4*np.power(f[:,:,0]-4*f[:,:,1]+3*f[:,:,2],2)
B2 = 13/12*np.power(f[:,:,1]-2*f[:,:,2]+f[:,:,3],2) + 1/4*np.power(f[:,:,1]-f[:,:,3],2)
B3 = 13/12*np.power(f[:,:,2]-2*f[:,:,3]+f[:,:,4],2) + 1/4*np.power(3*f[:,:,2]-4*f[:,:,3]+f[:,:,4],2)
#assign linear weights
g1 = 1/10
g2 = 3/5
g3 = 3/10
#compute the unscaled nonlinear weights
wt1 = g1/np.power(ep+B1,2)
wt2 = g2/np.power(ep+B2,2)
wt3 = g3/np.power(ep+B3,2)
wts = wt1 + wt2 + wt3
#scale the nonlinear weights
w1 = wt1/wts
w2 = wt2/wts
w3 = wt3/wts
#compute the flux
fl = f1*w1+f2*w2+f3*w3
return fl
FVM = FiniteVolumeMethodEuler(5, scheme)
return FVM
def NNEuler(model):
def scheme(u_all):
n,m,s = np.shape(u_all)
fl = np.zeros((n,m))
u = np.zeros((n,s))
for i in range(0,m):
u[:,:] = u_all[:,i,:]
min_u = np.amin(u,1)
max_u = np.amax(u,1)
const_n = min_u==max_u
#print('u: ', u)
u_tmp = np.zeros_like(u[:,2])
u_tmp[:] = u[:,2]
for j in range(0,5):
u[:,j] = (u[:,j]-min_u)/(max_u-min_u)
fl[:,i] = model.predict(u).flatten()#compute \Delta u
#fl = fl.flatten()
fl[:,i] = np.multiply(fl[:,i],(max_u-min_u))+min_u
fl[const_n,i] = u_tmp[const_n]#if const across stencil, set to that value
#print('fl: ', fl)
return fl
FVM = FiniteVolumeMethodEuler(5, scheme)
return FVM