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BROADCAST_cgns.py
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BROADCAST_cgns.py
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# This Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0. If a copy of the MPL was not distributed with this file, You can obtain one at https://mozilla.org/MPL/2.0/.
#!/usr/bin/env python
'''
File: Toy2D.py
Created on 21 january 2021
@author: Cedric Content
@contact: [email protected]
@organization: ONERA - DAAA
@summary: This file is the main file of the program. It contains the
routine "main" and other related routines.
'''
import srcfv.f_geom as f_geom
import srcfv.f_bnd as f_bnd
import srcfv.f_sch as f_sch
import srcfv.f_lhs as f_lhs
import srcfv.f_lin as f_lin
# import srcfv.f_adj as f_adj
import srcfv.f_norm as f_norm
# FROM A.POULAIN Thesis
import misc.f_misc as f_misc
import misc.PETSc_func as pet
import resolvent_all as resol
import SIM
import SIM.BLprofiles_implicit as blsim
import f_init
import meshBL as mesh
import numpy as _np
import matplotlib.pyplot as plt
import os
import sys
import timeit
import Converter.Internal as I
import Converter.PyTree as C
# import CGNS.MAP as cgm
######################### Private functions ####################
def __writestate_node(filename, im, jm, w, x0, y0, gh) :
# print 'write file'
f_out = open(filename , 'w')
f_out.write('TITLE="state"\n')
f_out.write('VARIABLES= "X" "Y" "ro" "rou" "rov" "row" "roe" \n')
f_out.write('ZONE I = ' + str(im) + ', J = ' + str(jm) + '\n')
for j in range(gh,jm+gh):
for i in range(gh,im+gh):
ro = 0.25*(w[i-1,j-1,0] + w[i,j-1,0] + w[i-1,j,0] + w[i,j,0])
rou = 0.25*(w[i-1,j-1,1] + w[i,j-1,1] + w[i-1,j,1] + w[i,j,1])
rov = 0.25*(w[i-1,j-1,2] + w[i,j-1,2] + w[i-1,j,2] + w[i,j,2])
row = 0.25*(w[i-1,j-1,3] + w[i,j-1,3] + w[i-1,j,3] + w[i,j,3])
roe = 0.25*(w[i-1,j-1,4] + w[i,j-1,4] + w[i-1,j,4] + w[i,j,4])
f_out.write(str(x0[i,j]) + ' ' + str(y0[i,j]) + ' ' +
str(ro) + ' ' + str(rou) + ' ' +
str(rov) + ' ' + str(row) + ' ' +
str(roe) + '\n')
f_out.close()
def __writestate_center(filename, im, jm, w, xc, yc, gh) :
# print 'write file'
f_out = open(filename , 'w')
f_out.write('TITLE="state"\n')
f_out.write('VARIABLES= "X" "Y" "ro" "rou" "rov" "row" "roe" \n')
f_out.write('ZONE I = ' + str(im) + ', J = ' + str(jm) + '\n')
for j in range(gh,jm+gh):
for i in range(gh,im+gh):
ro = w[i,j,0]
rou = w[i,j,1]
rov = w[i,j,2]
row = w[i,j,3]
roe = w[i,j,4]
f_out.write(str(xc[i,j]) + ' ' + str(yc[i,j]) + ' ' +
str(ro) + ' ' + str(rou) + ' ' +
str(rov) + ' ' + str(row) + ' ' +
str(roe) + '\n')
f_out.close()
def __writestate_center_gh(filename, imloc, jmloc, w, xc, yc) :
# print 'write file'
f_out = open(filename , 'w')
f_out.write('TITLE="state"\n')
f_out.write('VARIABLES= "X" "Y" "ro" "rou" "rov" "row" "roe" \n')
f_out.write('ZONE I = ' + str(imloc) + ', J = ' + str(jmloc) + '\n')
for j in range(jmloc):
for i in range(imloc):
ro = w[i,j,0]
rou = w[i,j,1]
rov = w[i,j,2]
row = w[i,j,3]
roe = w[i,j,4]
f_out.write(str(xc[i,j]) + ' ' + str(yc[i,j]) + ' ' +
str(ro) + ' ' + str(rou) + ' ' +
str(rov) + ' ' + str(row) + ' ' +
str(roe) + '\n')
f_out.close()
def __writeline(filename, imloc, w, xc,jloc) :
# print 'write file'
f_out = open(filename , 'w')
f_out.write('TITLE="state"\n')
f_out.write('VARIABLES= "X" "ro" "rou" "rov" "row" "roe" \n')
f_out.write('ZONE I = ' + str(imloc) + '\n')
for i in range(imloc):
ro = w[i,0]
rou = w[i,1]
rov = w[i,2]
row = w[i,3]
roe = w[i,4]
f_out.write(str(xc[i,jloc]) + ' ' +
str(ro) + ' ' + str(rou) + ' ' +
str(rov) + ' ' + str(row) + ' ' +
str(roe) + '\n')
f_out.close()
def __comp_Sutherland(propref, Ts, Cs, T):
'''Dynamical viscosity / thermal conductivity from sutherland law'''
return propref*_np.sqrt(T/Ts)*((1.+Cs/Ts)/(1.+Cs/T))
def __compute_tot_energy_inf(R_pg, gamma, t_inf, v_inf):
'''Total energy E = R/(gamma-1)*Tinf+(uinf**2)/2'''
return R_pg/(gamma-1.)*t_inf+0.5*v_inf*v_inf
def remove_zero_jac(IA, JA, Jac, mini=2.e-16):
''' Remove the zero components from the Jac list in order not to store any zero in the sparse matrix '''
to_keep = _np.absolute(Jac) > mini
Jac = Jac[to_keep,...]
IA = IA[to_keep,...]
JA = JA[to_keep,...]
return IA, JA, Jac
def centers_array(A):
''' Compute the values of an array A at the centers'''
return 0.25 * ( A[:-1,:-1] + A[1:,:-1] + A[:-1,1:] + A[1:,1:] )
def writeCGNS(filename, im, jm, gh, w, x0, y0, vol, volf, nx, ny, xc, yc, field, wbd, res, sch, k2, k4, interf1, interf2, interf3, interf4, lf, cp, cv, gam, cs, tref, muref, rgaz, mach, prandtl, pinf=None):
''' Write the data in a CGNS tree '''
I.__FlowSolutionCenters__ = 'FlowSolution#Centers'
w0 = _np.array(w, copy=True)
res0 = _np.array(res, copy=True)
t=I.newCGNSTree()
b=I.newCGNSBase(name='Base',parent=t)
# z=I.newZone(name="Zone1",parent=b,zsize=[[(im+1)*(jm+1),im*jm, 0]])
z=I.newZone(name="Zone1",parent=b,zsize=[[(im+1)*(jm+1),im*jm,0]])
Gc=I.newGridCoordinates(parent=z)
I.newDataArray(name="CoordinateX",value=x0[:,:],parent=Gc)
I.newDataArray(name="CoordinateY",value=y0[:,:],parent=Gc)
# I.newDataArray(name="CoordinateZ",value=y0*0,parent=Gc)
Geom = I.newDiscreteData(name="Geometry", parent=z)
I.newDataArray(name="Volume",value=vol,parent=Geom)
I.newDataArray(name="VolumeInv",value=volf,parent=Geom)
I.newDataArray(name="NormalX",value=nx,parent=Geom)
I.newDataArray(name="NormalY",value=ny,parent=Geom)
I.newDataArray(name="DimX",value=im,parent=Geom)
I.newDataArray(name="DimY",value=jm,parent=Geom)
I.newDataArray(name="GhostCell",value=gh,parent=Geom)
I.newDataArray(name="CoordinateCenterX",value=xc[:,:],parent=Geom)
I.newDataArray(name="CoordinateCenterY",value=yc[:,:],parent=Geom)
# Fs=I.newFlowSolution(name="FlowSolution#Init", gridLocation='CellCenter', parent=z)
# # I.newGridLocation(value='CellCenter', parent=Fs)
# I.newDataArray(name="Density",value=w0[gh:-gh,gh:-gh,0],parent=Fs)
# I.newDataArray(name="MomentumX",value=w0[gh:-gh,gh:-gh,1],parent=Fs)
# I.newDataArray(name="MomentumY",value=w0[gh:-gh,gh:-gh,2],parent=Fs)
# I.newDataArray(name="MomentumZ",value=w0[gh:-gh,gh:-gh,3],parent=Fs)
# I.newDataArray(name="EnergyStagnationDensity",value=w0[gh:-gh,gh:-gh,4],parent=Fs)
# Res = I.newDiscreteData(name="Residual#Init", parent=z)
# I.newGridLocation(value='CellCenter', parent=Res)
# I.newDataArray(name="ResidualDensity",value=res0[gh:-gh,gh:-gh,0],parent=Res)
# I.newDataArray(name="ResidualMomentumX",value=res0[gh:-gh,gh:-gh,1],parent=Res)
# I.newDataArray(name="ResidualMomentumY",value=res0[gh:-gh,gh:-gh,2],parent=Res)
# I.newDataArray(name="ResidualMomentumZ",value=res0[gh:-gh,gh:-gh,3],parent=Res)
# I.newDataArray(name="ResidualEnergyStagnationDensity",value=res0[gh:-gh,gh:-gh,4],parent=Res)
## With Ghost cells
Fs=I.newFlowSolution(name="FlowSolution#Init", gridLocation='CellCenter', parent=z)
# I.newGridLocation(value='CellCenter', parent=Fs)
I.newDataArray(name="Density",value=w0[:,:,0],parent=Fs)
I.newDataArray(name="MomentumX",value=w0[:,:,1],parent=Fs)
I.newDataArray(name="MomentumY",value=w0[:,:,2],parent=Fs)
I.newDataArray(name="MomentumZ",value=w0[:,:,3],parent=Fs)
I.newDataArray(name="EnergyStagnationDensity",value=w0[:,:,4],parent=Fs)
Res = I.newDiscreteData(name="Residual#Init", parent=z)
I.newGridLocation(value='CellCenter', parent=Res)
I.newDataArray(name="ResidualDensity",value=res0[:,:,0],parent=Res)
I.newDataArray(name="ResidualMomentumX",value=res0[:,:,1],parent=Res)
I.newDataArray(name="ResidualMomentumY",value=res0[:,:,2],parent=Res)
I.newDataArray(name="ResidualMomentumZ",value=res0[:,:,3],parent=Res)
I.newDataArray(name="ResidualEnergyStagnationDensity",value=res0[:,:,4],parent=Res)
routinein = lf[0]
routineout = lf[1]
routinenr = lf[2]
routinew = lf[3]
routinesch = lf[4]
libbnd = lf[5]
libsch = lf[6]
BC = I.newZoneBC(parent=z)
BCin = I.newBC(name="Inflow",parent=BC, btype="FamilySpecified", family=libbnd + "." + routinein)
I.newGridLocation(value='CellCenter', parent=BCin)
I.newPointRange(name="PointRange",value=[interf1[0,0], interf1[1,0], interf1[0,1], interf1[1,1]],parent=BCin)
I.newDataArray(name="Field",value=field,parent=BCin)
BCout = I.newBC(name="Outflow",parent=BC, btype="FamilySpecified", family=libbnd + "." + routineout)
I.newGridLocation(value='CellCenter', parent=BCout)
I.newPointRange(name="PointRange",value=[interf2[0,0], interf2[1,0], interf2[0,1], interf2[1,1]],parent=BCout)
I.newDataArray(name="Pref",value=pinf,parent=BCout)
BCwall = I.newBC(name="Wall",parent=BC, btype="FamilySpecified", family=libbnd + "." + routinew)
I.newGridLocation(value='CellCenter', parent=BCwall)
I.newPointRange(name="PointRange",value=[interf3[0,0], interf3[1,0], interf3[0,1], interf3[1,1]],parent=BCwall)
BCtop = I.newBC(name="NoRef",parent=BC, btype="FamilySpecified", family=libbnd + "." + routinenr)
I.newGridLocation(value='CellCenter', parent=BCtop)
I.newPointRange(name="PointRange",value=[interf4[0,0], interf4[1,0], interf4[0,1], interf4[1,1]],parent=BCtop)
I.newDataArray(name="Wbd",value=wbd,parent=BCtop)
Num = I.newIntegralData(name="NumericalScheme", parent=b)
I.newDataArray(name="SchemeType",value=sch,parent=Num)
I.newDataArray(name="Scheme",value=libsch + "." + routinesch,parent=Num)
# I.newFamily(name=libsch + "." + routinesch,parent=Num)
I.newDataArray(name="k2",value=k2,parent=Num)
I.newDataArray(name="k4",value=k4,parent=Num)
C._addState(b, 'Mach', mach)
C._addState(b, 'Prandtl', prandtl)
C._addState(b, 'Rgaz', rgaz)
C._addState(b, 'Cp', cp)
C._addState(b, 'Cv', cv)
C._addState(b, 'Gamma', gam)
C._addState(b, 'TemperatureSutherland', cs)
C._addState(b, 'TemperatureRefSutherland', tref)
C._addState(b, 'ViscosityRefSutherland', muref)
C.convertPyTree2File(t, filename+'.hdf')
return t
def fillCGNS(filename, t, w, res, IA, JA, Jacvol, gh):
''' fill a given CGNS tree with current solution, residual and the lists (IA,JA,Aij) to build the Jacobian'''
# I.__FlowSolutionCenters__ = 'FlowSolution#EndOfRun'
z=I.getZones(t)[0]
# Fs2=I.newFlowSolution(name="FlowSolution#EndOfRun", gridLocation='CellCenter', parent=z)
# # I.newGridLocation(value='CellCenter', parent=Fs2)
# I.newDataArray(name="Density",value=w[gh:-gh,gh:-gh,0],parent=Fs2)
# I.newDataArray(name="MomentumX",value=w[gh:-gh,gh:-gh,1],parent=Fs2)
# I.newDataArray(name="MomentumY",value=w[gh:-gh,gh:-gh,2],parent=Fs2)
# I.newDataArray(name="MomentumZ",value=w[gh:-gh,gh:-gh,3],parent=Fs2)
# I.newDataArray(name="EnergyStagnationDensity",value=w[gh:-gh,gh:-gh,4],parent=Fs2)
# Res2 = I.newDiscreteData(name="Residual#EndOfRun", parent=z)
# I.newGridLocation(value='CellCenter', parent=Res2)
# I.newDataArray(name="ResidualDensity",value=res[gh:-gh,gh:-gh,0],parent=Res2)
# I.newDataArray(name="ResidualMomentumX",value=res[gh:-gh,gh:-gh,1],parent=Res2)
# I.newDataArray(name="ResidualMomentumY",value=res[gh:-gh,gh:-gh,2],parent=Res2)
# I.newDataArray(name="ResidualMomentumZ",value=res[gh:-gh,gh:-gh,3],parent=Res2)
# I.newDataArray(name="ResidualEnergyStagnationDensity",value=res[gh:-gh,gh:-gh,4],parent=Res2)
## With Ghost cells
Fs2=I.newFlowSolution(name="FlowSolution#EndOfRun", gridLocation='CellCenter', parent=z)
# I.newGridLocation(value='CellCenter', parent=Fs2)
I.newDataArray(name="Density",value=w[:,:,0],parent=Fs2)
I.newDataArray(name="MomentumX",value=w[:,:,1],parent=Fs2)
I.newDataArray(name="MomentumY",value=w[:,:,2],parent=Fs2)
I.newDataArray(name="MomentumZ",value=w[:,:,3],parent=Fs2)
I.newDataArray(name="EnergyStagnationDensity",value=w[:,:,4],parent=Fs2)
Res2 = I.newDiscreteData(name="Residual#EndOfRun", parent=z)
I.newGridLocation(value='CellCenter', parent=Res2)
I.newDataArray(name="ResidualDensity",value=res[:,:,0],parent=Res2)
I.newDataArray(name="ResidualMomentumX",value=res[:,:,1],parent=Res2)
I.newDataArray(name="ResidualMomentumY",value=res[:,:,2],parent=Res2)
I.newDataArray(name="ResidualMomentumZ",value=res[:,:,3],parent=Res2)
I.newDataArray(name="ResidualEnergyStagnationDensity",value=res[:,:,4],parent=Res2)
Jac = I.newDiscreteData(name="JacobianListsCSR", parent=z)
I.newGridLocation(value='CellCenter', parent=Jac)
I.newDataArray(name="IA",value=IA,parent=Jac)
I.newDataArray(name="JA",value=JA,parent=Jac)
I.newDataArray(name="Aij",value=Jacvol,parent=Jac)
C.convertPyTree2File(t, filename+'.hdf')
def readCGNStree(filename):
''' read a CGNS tree made to run BROADCAST code '''
# T = cgm.load(filename+'.hdf')
# treeBroadcast, cgnslinks, cgnspaths = T[0], T[1], T[2]
treeBroadcast = C.convertFile2PyTree(filename+'.hdf')
vol = I.getValue(I.getNodeFromName(treeBroadcast, "Volume"))
volf = I.getValue(I.getNodeFromName(treeBroadcast, "VolumeInv"))
nx = I.getValue(I.getNodeFromName(treeBroadcast, "NormalX"))
ny = I.getValue(I.getNodeFromName(treeBroadcast, "NormalY"))
im = I.getValue(I.getNodeFromName(treeBroadcast, "DimX"))
jm = I.getValue(I.getNodeFromName(treeBroadcast, "DimY"))
gh = I.getValue(I.getNodeFromName(treeBroadcast, "GhostCell"))
x0 = I.getValue(I.getNodeFromName(treeBroadcast, "CoordinateX"))
y0 = I.getValue(I.getNodeFromName(treeBroadcast, "CoordinateY"))
xc = I.getValue(I.getNodeFromName(treeBroadcast, "CoordinateCenterX"))
yc = I.getValue(I.getNodeFromName(treeBroadcast, "CoordinateCenterY"))
wbd = I.getValue(I.getNodeFromName(treeBroadcast, "Wbd"))
field = I.getValue(I.getNodeFromName(treeBroadcast, "Field"))
pinf = I.getValue(I.getNodeFromName(treeBroadcast, "Pref"))
sch = I.getValue(I.getNodeFromName(treeBroadcast, "SchemeType"))
k2 = I.getValue(I.getNodeFromName(treeBroadcast, "k2"))
k4 = I.getValue(I.getNodeFromName(treeBroadcast, "k4"))
cp = I.getValue(I.getNodeFromName(treeBroadcast, "Cp"))
cv = I.getValue(I.getNodeFromName(treeBroadcast, "Cv"))
gam = I.getValue(I.getNodeFromName(treeBroadcast, "Gamma"))
rgaz = I.getValue(I.getNodeFromName(treeBroadcast, "Rgaz"))
cs = I.getValue(I.getNodeFromName(treeBroadcast, "TemperatureSutherland"))
tref = I.getValue(I.getNodeFromName(treeBroadcast, "TemperatureRefSutherland"))
muref = I.getValue(I.getNodeFromName(treeBroadcast, "ViscosityRefSutherland"))
mach = I.getValue(I.getNodeFromName(treeBroadcast, "Mach"))
prandtl = I.getValue(I.getNodeFromName(treeBroadcast, "Prandtl"))
pathBCInflow = I.getPathsFromName(treeBroadcast,"Inflow", pyCGNSLike=True)[0]
interf1 = _np.reshape(I.getValue(I.getNodeFromPath(treeBroadcast, pathBCInflow + "/PointRange")), (2,2), order='F')
pathBCOutflow = I.getPathsFromName(treeBroadcast,"Outflow", pyCGNSLike=True)[0]
interf2 = _np.reshape(I.getValue(I.getNodeFromPath(treeBroadcast, pathBCOutflow + "/PointRange")), (2,2), order='F')
pathBCWall = I.getPathsFromName(treeBroadcast,"Wall", pyCGNSLike=True)[0]
interf3 = _np.reshape(I.getValue(I.getNodeFromPath(treeBroadcast, pathBCWall + "/PointRange")), (2,2), order='F')
pathBCNoRef = I.getPathsFromName(treeBroadcast,"NoRef", pyCGNSLike=True)[0]
interf4 = _np.reshape(I.getValue(I.getNodeFromPath(treeBroadcast, pathBCNoRef + "/PointRange")), (2,2), order='F')
libsch, routinesch = I.getValue(I.getNodeFromName(treeBroadcast, "Scheme")).split('.')
libbnd, routinein = I.getValue(I.getNodeFromPath(treeBroadcast, pathBCInflow + "/FamilyName")).split('.')
libbnd, routineout = I.getValue(I.getNodeFromPath(treeBroadcast, pathBCOutflow + "/FamilyName")).split('.')
libbnd, routinew = I.getValue(I.getNodeFromPath(treeBroadcast, pathBCWall + "/FamilyName")).split('.')
libbnd, routinenr = I.getValue(I.getNodeFromPath(treeBroadcast, pathBCNoRef + "/FamilyName")).split('.')
w = _np.zeros((im + 2*gh , jm + 2*gh , 5), order='F')
res = _np.zeros((im + 2*gh , jm + 2*gh , 5), order='F')
if I.getPathsFromName(treeBroadcast,"FlowSolution#EndOfRun", pyCGNSLike=True) == []:
pathw = I.getPathsFromName(treeBroadcast,"FlowSolution#Init", pyCGNSLike=True)[0]
pathres = I.getPathsFromName(treeBroadcast,"Residual#Init", pyCGNSLike=True)[0]
else:
pathw = I.getPathsFromName(treeBroadcast,"FlowSolution#EndOfRun", pyCGNSLike=True)[0]
pathres = I.getPathsFromName(treeBroadcast,"Residual#EndOfRun", pyCGNSLike=True)[0]
w[:,:,0] = I.getValue(I.getNodeFromPath(treeBroadcast, pathw + "/Density"))
w[:,:,1] = I.getValue(I.getNodeFromPath(treeBroadcast, pathw + "/MomentumX"))
w[:,:,2] = I.getValue(I.getNodeFromPath(treeBroadcast, pathw + "/MomentumY"))
w[:,:,3] = I.getValue(I.getNodeFromPath(treeBroadcast, pathw + "/MomentumZ"))
w[:,:,4] = I.getValue(I.getNodeFromPath(treeBroadcast, pathw + "/EnergyStagnationDensity"))
res[:,:,0] = I.getValue(I.getNodeFromPath(treeBroadcast, pathres + "/ResidualDensity"))
res[:,:,1] = I.getValue(I.getNodeFromPath(treeBroadcast, pathres + "/ResidualMomentumX"))
res[:,:,2] = I.getValue(I.getNodeFromPath(treeBroadcast, pathres + "/ResidualMomentumY"))
res[:,:,3] = I.getValue(I.getNodeFromPath(treeBroadcast, pathres + "/ResidualMomentumZ"))
res[:,:,4] = I.getValue(I.getNodeFromPath(treeBroadcast, pathres + "/ResidualEnergyStagnationDensity"))
lf = [routinein, routineout, routinenr, routinew, routinesch, libbnd, libsch]
# return treeBroadcast, im, jm, gh, w, x0, y0, vol, volf, nx, ny, xc, yc, field, wbd, res, sch, k2, k4, interf1, interf2, interf3, interf4, lf, cp, cv, gam, cs, tref, muref, rgaz, mach, prandtl
return treeBroadcast, im, jm, gh, w, x0, y0, vol, volf, nx, ny, xc, yc, field, wbd, res, sch, k2, k4, interf1, interf2, interf3, interf4, lf, cp, cv, gam, cs, tref, muref, rgaz, mach, prandtl, pinf
######################### Private functions ####################
# solve monoblock Boundary Layer
def bl2d_prepro(dgeom = dict(), dphys = dict(), dnum = dict(), compmode = 'direct', lf = list(), lflin = list(), out_dir = 'totodir', treename='tree', isresol= False):
'''
exemple of monoblock use of 2DTOY
to simulate 2D laminar Boundary Layer flow
'''
os.system('mkdir -p %s' % out_dir)
# Create mesh
im = dgeom['im']
jm = dgeom['jm']
L = dgeom['length']
high = dgeom['high']
xini = dgeom['xini']
ite = dnum['ite']
cfl = dnum['cfl']
k2 = dnum['k2']
k4 = dnum['k4']
sch = dnum['sch']
order = dnum['order']
freqres = dnum['freqres']
freqsort = dnum['freqsort']
# Set ghost cells dimension
if sch == 'dnc':
gh = (order+1) // 2
else:
gh = (order-1) // 2 + 1 # +1 to avoid grad exchanges in multiblock configurations
# gh = gh+2
if compmode == 'direct':
rkcoefs = dnum['rkcoefs']
elif compmode == 'fixed_point':
lasolver = dnum['lasolver']
if lasolver == 'gmres':
tol = dnum['tol']
x = _np.linspace(xini, xini+L , im+1)
## MESH v2
Ny_in = 80*jm//100 #80%
deltaBL = high/4 #high/4
percent = 0.02
Ny_out = jm - Ny_in
Nend = high/deltaBL
y_int = mesh.bigeom_stretch_in(Ny_in, deltaBL, percent)
y_out = mesh.exp_stretch_out(Ny_out, deltaBL, percent, Nend)
y = _np.concatenate((y_int, y_out))
# y = mesh.bigeom_stretch_in(Ny_in, deltaBL, percent)
# Initialize all cfd fields
x0 = _np.zeros((im + 2*gh + 1, jm + 2*gh + 1 ), order='F')
y0 = _np.zeros((im + 2*gh + 1, jm + 2*gh + 1 ), order='F')
xc = _np.zeros((im + 2*gh , jm + 2*gh ), order='F')
yc = _np.zeros((im + 2*gh , jm + 2*gh ), order='F')
nx = _np.zeros((im + 2*gh + 1, jm + 2*gh + 1, 2), order='F')
ny = _np.zeros((im + 2*gh + 1, jm + 2*gh + 1, 2), order='F')
vol = _np.zeros((im + 2*gh , jm + 2*gh ), order='F')
volf= _np.zeros((im + 2*gh , jm + 2*gh , 2), order='F')
w = _np.zeros((im + 2*gh , jm + 2*gh , 5), order='F')
res = _np.zeros((im + 2*gh , jm + 2*gh , 5), order='F')
# get physical constants
gam = dphys['gam']
cs = dphys['cs']
tref = dphys['Ts']
muref = dphys['musuth']
rgaz = dphys['rgaz']
prandtl = dphys['Prandtl']
mach = dphys['Mach']
tinf = dphys['T0']
Lref = dphys['Lref']
StateRef = dphys['stateref']
muinf = __comp_Sutherland(muref, tref, cs, tinf)
sound = _np.sqrt(gam*rgaz*tinf)
uinf = mach * sound
einf = __compute_tot_energy_inf(rgaz, gam, tinf, uinf)
dx = L/((im-1)*Lref) # adim done after muinf A.Poulain
dy = (y[1]-y[0])/Lref
sound = 1./dphys['Mach']
dt = cfl * min(dy,dx) / (sound+1.)
dtm1 = 1./dt
print("============setup===============")
print('scheme = ', sch)
print('order(or nb pts) = ', order)
print('dt = ', dt)
print('StateRef = ', StateRef)
print("gam = ", dphys['gam'])
print("Ts = ", dphys['Ts'])
print("cs = ", dphys['cs'])
print("musuth = ", dphys['musuth'])
print("rgaz = ", dphys['rgaz'])
print("Prandtl = ", dphys['Prandtl'])
print("Mach = ", dphys['Mach'])
print("T0 = ", dphys['T0'])
print("Runit = ", dphys['Runit'])
print("Lref = ", dphys['Lref'])
print("============setup===============")
print(" ")
print(" ")
#for similitude sol
dphys['mu0'] = muinf
if StateRef == 'm0_p0_t0':
pinf = dphys['P0']
rhoinf = pinf/(rgaz*tinf)
runit = rhoinf * uinf/muinf
dphys['Runit'] = runit
elif StateRef == 'm0_runit_t0':
runit = dphys['Runit']
rhoinf = runit*muinf/uinf
pinf = rhoinf*rgaz*tinf
print('mu_inf = ', muinf)
print('u_inf = ', uinf)
print('nu_inf = ', muinf/rhoinf)
# Reynolds ------------------------------------------------------------
rey = runit * L
cp = gam * rgaz /(gam-1.)
cv = rgaz /(gam-1.)
# StateRef
stateref = _np.zeros(5)
stateref[0] = rhoinf
stateref[1] = rhoinf * uinf
stateref[2] = 0.
stateref[3] = 0.
stateref[4] = rhoinf * einf
# Adim (by RVT = rho, velo et temperature)
Roref = rhoinf
Vref = uinf
Tref = tinf
# Roref = 1.
# Vref = 1.
# Tref = 1.
# Lref = 1.
Pref = Roref*Vref**2
Cvref = Vref**2/Tref
Eref = Vref**2
Rgpref = Cvref
## Adim with ref length
# Lref = 8.e-2 #8.e-2
# Muref = Roref*Vref*Lref
## OR Adim with unit Reynolds
Muref = muinf
Lref = Muref/(Roref*Vref)
uinf = uinf/Vref
tinf = tinf/Tref
rhoinf = rhoinf/Roref
# sound = sound/Vref
pinf = pinf/Pref
cp = cp/Cvref
cv = cv/Cvref
rgaz = rgaz/Rgpref
einf = einf/Eref
# sutherland
tref = tref/Tref
muref = muref/Muref
cs = cs/Tref
muinf = muinf/Muref
# StateAdim
state_adim = _np.zeros(5)
state_adim[0] = rhoinf
state_adim[1] = rhoinf * uinf
state_adim[2] = 0.
state_adim[3] = 0.
state_adim[4] = rhoinf * einf
print('======StateAdim=========')
print(' ')
print('state_adim uinf = ', uinf)
print('state_adim tinf = ', tinf)
print('state_adim rhoinf = ', rhoinf)
print('state_adim sound = ', sound)
print('state_adim pinf = ', pinf)
print('state_adim cp = ', cp)
print('state_adim cv = ', cv)
print('state_adim rgaz = ', rgaz)
print('state_adim einf = ', einf)
print('state_adim tref = ', tref)
print('state_adim muref = ', muref)
print('state_adim cs = ', cs)
print('state_adim muinf = ', muinf)
print('state_adim runit = ', runit)
print('======StateAdim=========')
print(' ')
# Compute Geometry
for i in range(im+1):
x0[i+gh,:] = x[i]
for j in range(jm+1):
y0[:,j+gh] = y[j]
# Adim Geom:
x0 *= 1./Lref
y0 *= 1./Lref
f_geom.computegeom_2d(x0,y0,nx,ny,xc,yc,vol,volf,im,jm,gh)
# Blasius for inlet
field = _np.zeros((jm, gh, 5), order = 'F') # dummy ones in place of blasius solution
wbd = _np.zeros((im+gh , 5), order = 'F') # dummy ones in place of top domain state vector
# Initialization
wbd[:, 0] = state_adim[0]
wbd[:, 1] = state_adim[1]
wbd[:, 2] = state_adim[2]
wbd[:, 3] = state_adim[3]
wbd[:, 4] = state_adim[4]
# print 'Wb shape at 2=', _np.shape(wbd)
field[:, :, 0] = state_adim[0]
field[:, :, 1] = state_adim[1]
field[:, :, 2] = state_adim[2]
field[:, :, 3] = state_adim[3]
field[:, :, 4] = state_adim[4]
# Initialize(field, w, )
w[:, :, 0] = state_adim[0]
w[:, :, 1] = state_adim[1]
w[:, :, 2] = state_adim[2]
w[:, :, 3] = state_adim[3]
w[:, :, 4] = state_adim[4]
# Initialise from A.Poulain routine
## Compressible self-similar profile
road,uad,vad,Ead = blsim.BLprofile(x0[:,:]*Lref, y0[:,gh:]*Lref,mach, dphys, isplot=False, damped=False)
## OR Incompressible blasius profile
# # import SIM.blasius_profiles as blasiussim
# # road = _np.ones((im + 2*gh , jm + gh ), order='F')
# # uad,vad = blasiussim.blasius_profiles(x0[:,:]*Lref, y0[:,gh:]*Lref,mach, dphys, isplot=False, damped=False)
road = centers_array(road)
uad = centers_array(uad)
vad = centers_array(vad)
Ead = centers_array(Ead)
w[:, gh:, 0] = road[:,:] * rhoinf
w[:, gh:, 1] = road[:,:]*uad[:,:] * rhoinf * uinf
w[:, gh:, 2] = road[:,:]*vad[:,:] * rhoinf * uinf
w[:, gh:, 4] = road[:,:]*Ead[:,:] * rhoinf * einf
# w[:, :, 2] = 0.
f_init.set_bndbl_2d(w, field, wbd, im)
######## Restart from a previous solution with exactly the same mesh
import restart_init as ri
# filet = './Wksp/dnc_5/state_atcenter_ite10.dat'
filet = '../BROADCAST/Wksp/dnc_5/state_atcenter_mesh800_y150_incompressible_RigasSipp_Mach01_shorter_pout.dat'
Xin, Yin, roin, rouin, rovin, rowin, roein = ri.read_init(filet)
# w[gh:-gh, gh:-gh, 0] = roin
# w[gh:-gh, gh:-gh, 1] = rouin
# w[gh:-gh, gh:-gh, 2] = rovin
# w[gh:-gh, gh:-gh, 3] = rowin
# w[gh:-gh, gh:-gh, 4] = roein
import interpgrid
w[gh:-gh, gh:-gh, 0] = interpgrid.interpgrid(Xin, Yin, roin, xc[gh:-gh,:], yc[:,gh:-gh])
w[gh:-gh, gh:-gh, 1] = interpgrid.interpgrid(Xin, Yin, rouin, xc[gh:-gh,:], yc[:,gh:-gh])
w[gh:-gh, gh:-gh, 2] = interpgrid.interpgrid(Xin, Yin, rovin, xc[gh:-gh,:], yc[:,gh:-gh])
w[gh:-gh, gh:-gh, 3] = interpgrid.interpgrid(Xin, Yin, rowin, xc[gh:-gh,:], yc[:,gh:-gh])
w[gh:-gh, gh:-gh, 4] = interpgrid.interpgrid(Xin, Yin, roein, xc[gh:-gh,:], yc[:,gh:-gh])
filename = out_dir + '/initialisation_gh.dat'
__writestate_center_gh(filename, im+2*gh, jm+2*gh, w, xc, yc)
#interfaces definitions (may be done at the begining)
# Ilo
interf1 = _np.zeros((2,2), order='F')
interf1[0,0] = 1 # imin
interf1[0,1] = 1 # jmin
interf1[1,0] = 1 # imax
interf1[1,1] = jm # jmax
# Ihi
interf2 = _np.zeros((2,2), order='F')
interf2[0,0] = im # imin
interf2[0,1] = 1 # jmin
interf2[1,0] = im # imax
interf2[1,1] = jm+gh # jmax
# Jlo
interf3 = _np.zeros((2,2), order='F')
interf3[0,0] = 1-gh # imin
interf3[0,1] = 1 # jmin
interf3[1,0] = im+gh # imax
interf3[1,1] = 1 # jmax
# Jhi
interf4 = _np.zeros((2,2), order='F')
interf4[0,0] = 1-gh # imin
interf4[0,1] = jm # jmin
interf4[1,0] = im # imax
interf4[1,1]= jm # jmaI
filename = out_dir + '/' + treename
tree = writeCGNS(filename, im, jm, gh, w, x0, y0, vol, volf, nx, ny, xc, yc, field, wbd, res, sch, k2, k4, interf1, interf2, interf3, interf4, lf, cp, cv, gam, cs, tref, muref, rgaz, mach, prandtl, pinf=pinf)
def bl2d_fromCGNStree(treename, ite = 10, compmode = 'fixed_point', out_dir = 'totodir', isresol= False):
filename = out_dir + '/' + treename
# tree, im, jm, gh, w, x0, y0, vol, volf, nx, ny, xc, yc, field, wbd, res, sch, k2, k4, interf1, interf2, interf3, interf4, lf, cp, cv, gam, cs, tref, muref, rgaz, mach, prandtl = readCGNStree(filename)
tree, im, jm, gh, w, x0, y0, vol, volf, nx, ny, xc, yc, field, wbd, res, sch, k2, k4, interf1, interf2, interf3, interf4, lf, cp, cv, gam, cs, tref, muref, rgaz, mach, prandtl, pinf = readCGNStree(filename)
routinein = lf[0]
routineout = lf[1]
routinenr = lf[2]
routinew = lf[3]
routinesch = lf[4]
libbnd = lf[5]
libsch = lf[6]
finflow = eval("%s.%s" % (libbnd, routinein))
foutflow = eval("%s.%s" % (libbnd, routineout))
fnoref = eval("%s.%s" % (libbnd, routinenr ))
fwall = eval("%s.%s" % (libbnd, routinew ))
fsch = eval("%s.%s" % (libsch, routinesch))
# Time Marching Loop
if compmode == 'direct':
freq = freqsort
time = 0.
wreal = w*1.
denom = im*jm*freq*len(rkcoefs)
timein0 = timeit.time.time()
for it in range(1,ite+1):
for rk in rkcoefs:
# Boundary on state vector
finflow(w,'Ilo',interf1,field,nx,ny,gam,im,jm)
# finflow(w,'Ilo', interf1, field,im,jm)
fnoref(w,wbd,'Jhi',interf4,nx,ny,gam,gh,im,jm)
foutflow(w,'Ihi', interf2, im, jm, gh)
fwall(w,'Jlo', gam, interf3, gh, im, jm)
# Compute spatial discretization
if sch == 'dnc':
# fwall needed for dissipation near bnd_wall
fsch(res, w, x0, y0, nx, ny, xc, yc, vol, volf, gh, cp, cv, prandtl, gam, rgaz, cs, muref, tref, cs, k2, k4, im, jm)
else:
fsch(res, w, x0, y0, nx, ny, xc, yc, vol, volf, gh, cp, cv, prandtl, gam, rgaz, cs, muref, tref, cs, k2, im, jm)
# advance rk
w[gh:-gh,gh:-gh,0] = wreal[gh:-gh,gh:-gh,0] + rk * dt * res[gh:-gh,gh:-gh,0] / vol[gh:-gh,gh:-gh]
w[gh:-gh,gh:-gh,1] = wreal[gh:-gh,gh:-gh,1] + rk * dt * res[gh:-gh,gh:-gh,1] / vol[gh:-gh,gh:-gh]
w[gh:-gh,gh:-gh,2] = wreal[gh:-gh,gh:-gh,2] + rk * dt * res[gh:-gh,gh:-gh,2] / vol[gh:-gh,gh:-gh]
w[gh:-gh,gh:-gh,3] = wreal[gh:-gh,gh:-gh,3] + rk * dt * res[gh:-gh,gh:-gh,3] / vol[gh:-gh,gh:-gh]
w[gh:-gh,gh:-gh,4] = wreal[gh:-gh,gh:-gh,4] + rk * dt * res[gh:-gh,gh:-gh,4] / vol[gh:-gh,gh:-gh]
#Finalize time step
if it == 1:
norm0, nmoy0 = f_norm.compute_norml2(res ,im, jm, gh)
for lala in range(5):
if (norm0[lala] <=3.e-16): norm0[lala] = 1.
time += dt
wreal = w * 1.
if it%freqres == 0:
norm, nmoy = f_norm.compute_norml2(res ,im, jm, gh)
print('ite = %i , norm2(res) = %s' % (it, norm/norm0))
# if it%freq == 0:
# timetosort = timeit.time.time()
# print 'Time in function = ', (timetosort- timein0) / denom
# norm, nmoy = f_norm.compute_norml2(res ,im, jm, gh)
# print 'ite = %i , norm2(res) = %s' % (it, norm/norm0)
# # print 'write file'
# # usefull for plotting result
# fwall(w,'Jlo', gam, interf3, gh, im, jm)
# filename = out_dir + '/state_at_ite%i.dat' % it
# __writestate_node(filename, im, jm, w, x0, y0, gh)
# filename = out_dir + '/state_atcenter_ite%i.dat' % it
# __writestate_center(filename, im, jm, w, xc, yc, gh)
# timein0 = timeit.time.time()
if it%freqsort == 0:
norm, nmoy = f_norm.compute_norml2(res ,im, jm, gh)
print('ite = %i , norm2(res) = %s' % (it, norm/norm0))
# filename = out_dir + '/state_at_ite%i.dat' % it
# __writestate_node(filename, im, jm, w, x0, y0, gh)
filename = out_dir + '/state_atcenter_ite%i.dat' % it
__writestate_center(filename, im, jm, w, xc, yc, gh)
if it == ite:
filename = out_dir + '/state_atcentergh_ite%i.dat' % it
__writestate_center_gh(filename, im, jm, w, xc, yc)
elif compmode == 'impli':
fimpli = lf[-1]
time = 0.
dtcoef = 1.
# wreal = w*1.
dw = _np.zeros((im + 2*gh , jm + 2*gh , 5), order='F')
# Boundary on state vector
finflow(w,'Ilo',interf1,field,nx,ny,gam,im,jm)
# finflow(w,'Ilo', interf1, field,im,jm)
fnoref(w,wbd,'Jhi',interf4,nx,ny,gam,gh,im,jm)
foutflow(w,'Ihi', interf2, im, jm, gh)
fwall(w,'Jlo', gam, interf3, gh, im, jm)
filename = out_dir + '/initialisation_gh.dat'
__writestate_center_gh(filename, im+2*gh, jm+2*gh, w, xc, yc)
lmax = 10 #4
for it in range(1,ite+1):
# if it > 4000: cfl = min(0.5 + (it-4000)*0.001 ,1.)
# if it > 8000: cfl = min(3. + (it-8000)*0.001 ,10.)
# Compute spatial discretization
if sch == 'dnc':
# fwall needed for dissipation near bnd_wall
fsch(res, w, x0, y0, nx, ny, xc, yc, vol, volf, gh, cp, cv, prandtl, gam, rgaz, cs, muref, tref, cs, k2, k4, im, jm)
else:
fsch(res, w, x0, y0, nx, ny, xc, yc, vol, volf, gh, cp, cv, prandtl, gam, rgaz, cs, muref, tref, cs, k2, im, jm)
# implicit (MF)
fimpli(dw,nx,ny,w,res,vol,volf,dtcoef,cfl,gam,rgaz,prandtl,lmax,gh,cv,cs,muref,tref,cs,im,jm)
# advance BDF1
w[gh:-gh,gh:-gh,0] += dw[gh:-gh,gh:-gh,0]
w[gh:-gh,gh:-gh,1] += dw[gh:-gh,gh:-gh,1]
w[gh:-gh,gh:-gh,2] += dw[gh:-gh,gh:-gh,2]
w[gh:-gh,gh:-gh,3] += dw[gh:-gh,gh:-gh,3]
w[gh:-gh,gh:-gh,4] += dw[gh:-gh,gh:-gh,4]
# Boundary on state vector
finflow(w,'Ilo',interf1,field,nx,ny,gam,im,jm)
# finflow(w,'Ilo', interf1, field,im,jm)
fnoref(w,wbd,'Jhi',interf4,nx,ny,gam,gh,im,jm)
foutflow(w,'Ihi', interf2, im, jm, gh)
fwall(w,'Jlo', gam, interf3, gh, im, jm)
#Finalize time step
if it == 1:
norm0, nmoy0 = f_norm.compute_norml2(res ,im, jm, gh)
for lala in range(5):
if (norm0[lala] <=3.e-16): norm0[lala] = 1.
impl, impl0 = f_norm.compute_norml2(dw ,im, jm, gh)
print('ite = %i , norm2(res) = %s' % (it, norm0))
print('ite = %i , norm2(imp) = %s' % (it, impl))
if it%freqres == 0:
print('cfl = ', cfl)
norm, nmoy = f_norm.compute_norml2(res ,im, jm, gh)
print('ite = %i , norm2(res) = %s' % (it, norm/norm0))
if it%freqsort == 0:
norm, nmoy = f_norm.compute_norml2(res ,im, jm, gh)
print('ite = %i , norm2(res) = %s' % (it, norm/norm0))
# filename = out_dir + '/state_at_ite%i.dat' % it
# __writestate_node(filename, im, jm, w, x0, y0, gh)
filename = out_dir + '/state_atcenter_ite%i.dat' % it
__writestate_center(filename, im, jm, w, xc, yc, gh)
# timein0 = timeit.time.time()
if it == ite:
filename = out_dir + '/state_atcenter_ite%i.dat' % it
__writestate_center(filename, im, jm, w, xc, yc, gh)
filename = out_dir + '/state_atcentergh_ite%i.dat' % it
__writestate_center_gh(filename, im+2*gh, jm+2*gh, w, xc, yc)
elif compmode == 'fixed_point':
# get functions
# lflin = [flininflow, flinoutflow, flinnoref, flinwall, flinsch]
routinein += '_d'
routineout += '_d'
routinenr += '_d'
routinew += '_d'
routinesch += '_d'
libbnd = 'f_lin'
libsch = 'f_lin'
flinoutflow = eval("%s.%s" % (libbnd, routineout))
flininflow = eval("%s.%s" % (libbnd, routinein))
flinnoref = eval("%s.%s" % (libbnd, routinenr ))
flinwall = eval("%s.%s" % (libbnd, routinew ))
flinsch = eval("%s.%s" % (libsch, routinesch))
timeconstructjac = 0.
timeremove = 0.
timecoefdiag = 0.
timejaccsc = 0.
timejacinv = 0.
cfl = 1.e10
dt = cfl * (yc[gh,gh+1] - yc[gh,gh]) / (1./mach + 1.)
dtm1 = 1./dt
for it in range(1,ite+1):
wd = _np.zeros((im+2*gh, jm+2*gh), order='F')
resd = _np.zeros((im+2*gh, jm+2*gh), order='F')
# Boundary on state vector
# finflow(w,'Ilo', interf1, field,im,jm)
finflow(w,'Ilo',interf1,field,nx,ny,gam,im,jm)
fnoref(w,wbd,'Jhi',interf4,nx,ny,gam,gh,im,jm)
# foutflow(w,'Ihi', interf2, im, jm, gh)
foutflow(w,'Ihi',interf2,pinf,True,gam,nx,ny,im,jm,gh)
fwall(w,'Jlo', gam, interf3, gh, im, jm)
filename = out_dir + '/initialisation_gh.dat'
__writestate_center_gh(filename, im+2*gh, jm+2*gh, w, xc, yc)
# Compute spatial discretization
# if sch == 'dnc':
if 'dnc' in sch:
fsch(res, w, x0, y0, nx, ny, xc, yc, vol, volf, gh, cp, cv, prandtl, gam, rgaz, cs, muref, tref, cs, k2, k4, im, jm)
else:
fsch(res, w, x0, y0, nx, ny, xc, yc, vol, volf, gh, cp, cv, prandtl, gam, rgaz, cs, muref, tref, cs, k2, im, jm)
norm, ninf = f_norm.compute_norml2inf(res ,im, jm, gh)
if it == 1:
for i in range(5):
norm[i] = max(norm[i],1.e-15)
ninf[i] = max(ninf[i],1.e-15)
norm0m1 = 1./norm
ninf0m1 = 1./ninf
# Iterative Linear Algebra Loop to solve Newton: Solve resd = -res ==> J w_sol = - res
lasolver = 'direct'
if lasolver == 'gmres':
nl2res = 1.
print(" GMRES Not Yet implemented ")
sys.exit(2)
else:
# construct Jacobian
wd = _np.zeros((im+2*gh, jm+2*gh,5), order='F')
resd = _np.zeros((im+2*gh, jm+2*gh,5), order='F')
nbentry = im*jm * (2*gh+1)*(2*gh+1) * 5*5
Jac = _np.zeros((nbentry), order='F')
IA = _np.zeros((nbentry), dtype=_np.int32, order='F')
JA = _np.zeros((nbentry), dtype=_np.int32, order='F')
timeinjac = timeit.time.time()
## relaxed on diag:
r = _np.max([norm[:3]*norm0m1[:3], ninf[:3]*ninf0m1[:3]])
cflm1 = r*dtm1
print('iter = ', it)
print("1/cfl = ", cflm1)
print(norm)
coefdiag = cflm1 * vol[gh:-gh,gh:-gh]
for m in range(5):
for l in range(1 + 2*gh):
for k in range(1 + 2*gh):
wd *= 0.
f_misc.testvector(wd,m,l,k,gh,im,jm)
# w[:gh,:,:] = 0.
# w[:,:gh,:] = 0.
# w[-gh:,:,:] = 0.
# w[:,-gh:,:] = 0.
flininflow(w,wd,'Ilo',interf1,field,nx,ny,gam,im,jm)
# finflow(w,'Ilo', interf1, field,im,jm)
flinnoref(w,wd,wbd,'Jhi',interf4,nx,ny,gam,gh,im,jm)
# flinoutflow(w,wd,'Ihi', interf2, im, jm, gh)
flinoutflow(w,wd,'Ihi', interf2, pinf,True,gam,nx,ny,im, jm, gh)
# foutflow(w,'Ihi', interf2, im, jm, gh)
flinwall(w,wd,'Jlo', gam, interf3, gh, im, jm)
if 'dnc' in sch:
flinsch(res, resd, w, wd, x0, y0, nx, ny, xc, yc, vol, volf, gh, cp, cv, prandtl, gam, rgaz, cs, muref, tref, cs, k2, k4, im, jm)
# flinsch(res, resd, w, wd, x0, y0, nx, ny, xc, yc, vol, volf, gh, cp, cv, prandtl, gam, rgaz, cs, muref, tref, cs, k2, k4, im, jm, eps2ar, eps4ar, divu2ar, vort2ar)
else:
flinsch(res, resd, w, wd, x0, y0, nx, ny, xc, yc, vol, volf, gh, cp, cv, prandtl, gam, rgaz, cs, muref, tref, cs, k2, im, jm)
## Finite Difference method (FD)
# epsilon = 1.e-6 #1.e-8 at order 1 #1.e-6 at order 2
# res1 = _np.zeros((im + 2*gh , jm + 2*gh , 5), order='F')
# w2 = w + epsilon*wd
# w2[:gh,:,:] = 0.
# w2[:,:gh,:] = 0.
# w2[-gh:,:,:] = 0.
# w2[:,-gh:,:] = 0.
# # finflow(w2,'Ilo', interf1, field,im,jm)
# finflow(w2,'Ilo',interf1,field,nx,ny,gam,im,jm)
# fnoref(w2,wbd,'Jhi',interf4,nx,ny,gam,gh,im,jm)
# foutflow(w2,'Ihi', interf2, im, jm, gh)
# fwall(w2,'Jlo', gam, interf3, gh, im, jm)
# if 'dnc' in sch:
# fsch(res1, w2, x0, y0, nx, ny, xc, yc, vol, volf, gh, cp, cv, prandtl, gam, rgaz, cs, muref, tref, cs, k2, k4, im, jm)
# else:
# fsch(res1, w2, x0, y0, nx, ny, xc, yc, vol, volf, gh, cp, cv, prandtl, gam, rgaz, cs, muref, tref, cs, k2, im, jm)
# resd = (res1 - res) / epsilon
## OR Finite Difference at order 2
# resm1 = _np.zeros((im + 2*gh , jm + 2*gh , 5), order='F')
# wm = w - epsilon*wd
# wm[:gh,:,:] = 0.
# wm[:,:gh,:] = 0.
# wm[-gh:,:,:] = 0.
# wm[:,-gh:,:] = 0.
# # finflow(wm,'Ilo', interf1, field,im,jm)
# finflow(wm,'Ilo',interf1,field,nx,ny,gam,im,jm)
# fnoref(wm,wbd,'Jhi',interf4,nx,ny,gam,gh,im,jm)
# foutflow(wm,'Ihi', interf2, im, jm, gh)
# fwall(wm,'Jlo', gam, interf3, gh, im, jm)
# if 'dnc' in sch:
# fsch(resm1, wm, x0, y0, nx, ny, xc, yc, vol, volf, gh, cp, cv, prandtl, gam, rgaz, cs, muref, tref, cs, k2, k4, im, jm)
# else:
# fsch(resm1, wm, x0, y0, nx, ny, xc, yc, vol, volf, gh, cp, cv, prandtl, gam, rgaz, cs, muref, tref, cs, k2, im, jm)
# resd = (res1 - resm1) / (2*epsilon)
f_misc.computejacobianfromjv_relaxed(Jac,IA,JA,resd,m,l,k,gh,coefdiag)
# if it == ite:
# f_misc.computejacobianfromjv(Jac,IA,JA,resd,m,l,k,gh,im,jm)
# else:
# f_misc.computejacobianfromjv_relaxed(Jac,IA,JA,resd,m,l,k,gh,coefdiag)
## Remove the zero stored
timeinremove = timeit.time.time()
timeconstructjac += (timeinremove - timeinjac)/ite
mini = 2.e-16
IA, JA, Jac = remove_zero_jac(IA, JA, Jac, mini)
nbentry = _np.shape(Jac)[0]
print(nbentry)