# step 1: Take K old
K_1 = Expression("(x[0] > w && x[0] < 1- w && x[1] < 0.5 || x[1] >= 0.5 && x[1] < 0.7 )? 0.0:1.0", w=w)
# step 2: Send it to Stokes solver
U, P, K_Func = stokes_solver(w=w, mesh=mesh, Vspace=Vspace, Pspace=Pspace, Wspace=Wspace, K_array=K_1, n=n)
# step 3: calculate the WSS over it and its bdry
WSS = WSS(U=U, ShearStressSpace=ShearStressSpace)
WSS_bdry = WSS_bdry(K_Func=K_Func, DPspace=DPspace, WSS=WSS)
# Step 4: This is the diffucult step. we need to create an indicator function now
ind_f = ind_func_expr(WSS_bdry=WSS_bdry)
# works!! finally
# step 5: add together old and new K functions
# ind_f is a function in DG0 space and old K function is inPspace
# have to solve this first
K_new = K_update(ind_func=ind_f, K_Func=K_Func)
plot(K_new, interactive=True, title="K new ")
# doesnt look that great, lets try capping
# step 6: capping
K_capped = capping(K_new)
plot(K_capped, interactive=True, title="K capped")
# actually looks really good,
# step 7: run fluid trough it
U, P, K_Funcs = stokes_solver(w=w, mesh=mesh, Vspace=Vspace, Pspace=Pspace, Wspace=Wspace, K_array=K_capped, n=n)
def iterative(K_1): U, P, K_Func = stokes_solver(w=w, mesh=mesh, Vspace=Vspace, Pspace=Pspace, Wspace=Wspace, DG1=Pspace, K_array=K_1, n=n ) # Verification: # alternative 1: # construct an analytical solution # method of manufactored solutions # first come up with a random slution # plut into PDE # doesnt solve original homogeneous PDE exactly # residual is then considered the source term # alternative 2: # really fine mesh , solve a blind model on that mesh # this is reference(considered exact) solution # actual convergence test(after alt 1 or 2): # mesh refinement test refining the mesh see if rate of convergence goes to 2. # mesh.refine() OR refine(mesh) # give a mesh, creates new mesh that is finer. # for each mesh solve PDE # compute difference of u_e - u # in a norm # for each mesh # start with a very coarse one # after halfin 4 times,gives a really fine mesh and solving will get slow. # example: # for p2, half the mesh size # error reduction of factor 4 # do it at the beginning # Magne: # WSS skal naturlig veare i DG1. # og det fungerte aa bytte Pspace m DG1 wss = WSS(U=U, DG1= DG1) #Pspace) #,interesting_domain = interesting_domain_proj) bdry_ = bdry(K_Func = K_Func, DG1 = DG1) # Simon: # DG1 osgaa inneholder CG1 ind_f = ind_func(bdry=bdry_, WSS = project(wss, DG1), DG1 = DG0, interesting_domain = interesting_domain_proj) K_new = K_update(ind_func = ind_f, K_Func = K_Func) #wss_bdry = WSS_bdry(K_Func, DG0, WSS) plot(K_new, interactive = True, title = 'K new ') K_capped = capping(K_new) plot(K_capped, interactive = False, title = 'K capped') stokes_solver(w=w, mesh=mesh, Vspace=Vspace, Pspace=Pspace, Wspace=Wspace, K_array=K_capped, n=n ) return K_capped
# strict inequality or not for 0.7 gives different results, but they are infact made the same by capping
K_1 = Expression('(x[0] > w && x[0] < 1- w && x[1] < 0.5 || x[1] >= 0.5 && x[1] <= 0.7 )? 0.0:1.0', w=w)
#------test 1--------------------------------
ind_func = ind_func_expr(w=w, Pspace=Pspace) # interpolated to CG1
plot(ind_func, interactive = True, title = 'ind func created with an expre')
K_Func = interpolate(K_1, Pspace) # control
plot(K_Func, interactive = True, title = 'old K ') # old K
K_Func_new = K_update(ind_func, K_Func)
plot(K_Func_new, interactive = True, title = 'K updated') # updated K
capping(K_Func_new)
K_capped = capping(K_Func_new)
plot(K_capped, interactive = True, title = 'K capped')
# Test 1 contionued with more calculations
U, P, K_Func = stokes_solver(w=w, mesh=mesh, Vspace=Vspace, Pspace=Pspace, Wspace=Wspace, K_array=K_capped, n=n )
WSS = WSS(U=U, ShearStressSpace= ShearStressSpace)
WSS_bdry = WSS_bdry(K_Func=K_Func, DPspace=DPspace, WSS=WSS)
