# return the K_func
# store it to xdmf file to open it paraview
# 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,
mesh = UnitSquareMesh(n,n)
Pspace = FunctionSpace(mesh, 'CG',1)
Vspace = VectorFunctionSpace(mesh, 'Lagrange', 2)
Pspace = FunctionSpace(mesh, 'Lagrange', 1)
Wspace = MixedFunctionSpace([Vspace, Pspace])
ShearStressSpace=FunctionSpace(mesh, 'DG', 1)
DPspace = FunctionSpace(mesh, 'DG', 0)
# 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
