# ------------------------ semi-Lagrangian Method --------------------------------
if scheme_option == 2:
print ""
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
#----------------------------------------------------------------------------------
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))
# Mini Element
elif polynomial_option == 2:
w_d = semiLagrangian.Mini2D(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))
# Quad Element
elif polynomial_option == 3: