A = np.copy(Mr)/dt
vorticityRHS = sps.lil_matrix.dot(A,w_d)
vorticityRHS = vorticityRHS + (1.0/Re)*vorticityNeumannVector
vorticityRHS = np.multiply(vorticityRHS,vorticityAux2BC)
vorticityRHS = vorticityRHS + vorticityDirichletVector
w = scipy.sparse.linalg.cg(vorticityLHS,vorticityRHS,w, maxiter=1.0e+05, tol=1.0e-05)
w = w[0].reshape((len(w[0]),1))
# Quad Element
elif polynomial_option == 3:
w_d = semiLagrangian.Quad2D(numNodes, neighborsElements, IEN, x, y, vxSL, vySL, dt, w)
A = np.copy(M)/dt
vorticityRHS = sps.lil_matrix.dot(A,w_d)
vorticityRHS = vorticityRHS + (1.0/Re)*vorticityNeumannVector
vorticityRHS = np.multiply(vorticityRHS,vorticityAux2BC)
vorticityRHS = vorticityRHS + vorticityDirichletVector
w = scipy.sparse.linalg.cg(vorticityLHS,vorticityRHS,w, maxiter=1.0e+05, tol=1.0e-05)
w = w[0].reshape((len(w[0]),1))
#----------------------------------------------------------------------------------
#---------- Step 4 - Solve the streamline equation --------------------------------
print ' -----------------------'
print ' SEMI-LAGRANGIAN METHOD:'
print ' -----------------------'
start_SL_time = time()
# Linear Element
if polynomial_option == 0 or polynomial_option == 1:
vx_d, vy_d = semiLagrangian.Linear2D(numNodes, neighborsElements, IEN, x, y, vxALE, vyALE, dt, vx, vy)
# Mini Element
elif polynomial_option == 2:
vx_d, vy_d, c_d = semiLagrangian.Mini2D(numNodes, neighborsElements, IEN, x, y, vxALE, vyALE, dt, vx, vy, c)
# Quad Element
elif polynomial_option == 3:
w_d, c_d = semiLagrangian.Quad2D(numNodes, neighborsElements, IEN, x, y, vxALE, vyALE, dt, w, c)
end_SL_time = time()
SL_time = end_SL_time - start_SL_time
print ' time duration: %.1f seconds' %SL_time
#----------------------------------------------------------------------------------
# ------------------------ SOLVE LINEAR EQUATIONS ----------------------------------
print ""
print ' ----------------------------'
print ' SOLVE THE LINEARS EQUATIONS:'
vorticityRHS = vorticityRHS + (1.0 / Re) * vorticityNeumannVector
vorticityRHS = np.multiply(vorticityRHS, vorticityAux2BC)
vorticityRHS = vorticityRHS + vorticityDirichletVector
w = scipy.sparse.linalg.cg(vorticityLHS,
vorticityRHS,
w,
maxiter=1.0e+05,
tol=1.0e-05)
w = w[0].reshape((len(w[0]), 1))
# Quad Element
elif polynomial_option == 3:
scheme_name = 'Semi Lagrangian Quad'
w_d = semiLagrangian.Quad2D(numNodes, neighborsElements, IEN, z, r,
vz, vr, dt, w)
A = np.copy(Mr) / dt
vorticityRHS = sps.lil_matrix.dot(A, w_d)
vorticityRHS = vorticityRHS + (1.0 / Re) * vorticityNeumannVector
vorticityRHS = np.multiply(vorticityRHS, vorticityAux2BC)
vorticityRHS = vorticityRHS + vorticityDirichletVector
w = scipy.sparse.linalg.cg(vorticityLHS,
vorticityRHS,
w,
maxiter=1.0e+05,
tol=1.0e-05)
w = w[0].reshape((len(w[0]), 1))
#----------------------------------------------------------------------------------