def Curl(u0, uh, c):
#c[2] = chebDerivative_3D(u0[1], c[2])
SFTc.Mult_DPhidT_3D(N[0], uh[1], uh[2], F_tmp[1], F_tmp[2])
c[2] = ifct(F_tmp[1], c[2])
Uc[:] = ifst(1j * K[1, :Nu] * uh[0, :Nu], Uc, ST)
c[2] -= Uc
#F_tmp[0] = -Cm.matvec(uh[2])
#F_tmp[0, u_slice] = SFTc.TDMA_3D(a0, b0, bc, c0, F_tmp[0, u_slice])
#c[1] = ifst(F_tmp[0], c[1], ST)
c[1] = ifct(F_tmp[2], c[1])
Uc[:] = ifst(1j * K[2] * uh[0, :Nu], Uc, ST)
c[1] += Uc
c[0] = ifst(1j * (K[1] * uh[2] - K[2] * uh[1]), c[0], ST)
return c
def solvePressure(P_hat, U_hat):
global F_tmp, F_tmp2
U_tmp4[:] = 0
U_tmp3[:] = 0
F_tmp2[:] = 0
Ni = F_tmp2
# dudx = 0 from continuity equation. Use Shen Dirichlet basis
# Use regular Chebyshev basis for dvdx and dwdx
F_tmp[0] = Cm.matvec(U_hat[0])
F_tmp[0, u_slice] = SFTc.TDMA_3D(a0, b0, bc, c0, F_tmp[0, u_slice])
dudx = U_tmp4[0] = ifst(F_tmp[0], U_tmp4[0], ST)
SFTc.Mult_DPhidT_3D(N[0], U_hat[1], U_hat[2], F_tmp[1], F_tmp[2])
dvdx = U_tmp4[1] = ifct(F_tmp[1], U_tmp4[1])
dwdx = U_tmp4[2] = ifct(F_tmp[2], U_tmp4[2])
dudy_h = 1j * K[1] * U_hat[0]
dudy = U_tmp3[0] = ifst(dudy_h, U_tmp3[0], ST)
dudz_h = 1j * K[2] * U_hat[0]
dudz = U_tmp3[1] = ifst(dudz_h, U_tmp3[1], ST)
Ni[0] = fst(U0[0] * dudx + U0[1] * dudy + U0[2] * dudz, Ni[0], ST)
U_tmp3[:] = 0
dvdy_h = 1j * K[1] * U_hat[1]
dvdy = U_tmp3[0] = ifst(dvdy_h, U_tmp3[0], ST)
dvdz_h = 1j * K[2] * U_hat[1]
dvdz = U_tmp3[1] = ifst(dvdz_h, U_tmp3[1], ST)
Ni[1] = fst(U0[0] * dvdx + U0[1] * dvdy + U0[2] * dvdz, Ni[1], ST)
U_tmp3[:] = 0
dwdy_h = 1j * K[1] * U_hat[2]
dwdy = U_tmp3[0] = ifst(dwdy_h, U_tmp3[0], ST)
dwdz_h = 1j * K[2] * U_hat[2]
dwdz = U_tmp3[1] = ifst(dwdz_h, U_tmp3[1], ST)
Ni[2] = fst(U0[0] * dwdx + U0[1] * dwdy + U0[2] * dwdz, Ni[2], ST)
F_tmp[0] = 0
SFTc.Mult_Div_3D(N[0], K[1, 0], K[2, 0], Ni[0, u_slice], Ni[1, u_slice],
Ni[2, u_slice], F_tmp[0, p_slice])
SFTc.Solve_Helmholtz_3D_complex(N[0], 1, F_tmp[0, p_slice], P_hat[p_slice],
u0N, u1N, u2N, LN)
return P_hat
def standardConvection(c):
c[:] = 0
U_tmp4[:] = 0
U_tmp3[:] = 0
# dudx = 0 from continuity equation. Use Shen Dirichlet basis
# Use regular Chebyshev basis for dvdx and dwdx
F_tmp[0] = Cm.matvec(U_hat0[0])
F_tmp[0, u_slice] = SFTc.TDMA_3D(a0, b0, bc, c0, F_tmp[0, u_slice])
dudx = U_tmp4[0] = ifst(F_tmp[0], U_tmp4[0], ST)
SFTc.Mult_DPhidT_3D(N[0], U_hat0[1], U_hat0[2], F_tmp[1], F_tmp[2])
dvdx = U_tmp4[1] = ifct(F_tmp[1], U_tmp4[1])
dwdx = U_tmp4[2] = ifct(F_tmp[2], U_tmp4[2])
#dudx = U_tmp4[0] = chebDerivative_3D(U0[0], U_tmp4[0])
#dvdx = U_tmp4[1] = chebDerivative_3D0(U0[1], U_tmp4[1])
#dwdx = U_tmp4[2] = chebDerivative_3D0(U0[2], U_tmp4[2])
dudy_h = 1j * K[1] * U_hat0[0]
dudy = U_tmp3[0] = ifst(dudy_h, U_tmp3[0], ST)
dudz_h = 1j * K[2] * U_hat0[0]
dudz = U_tmp3[1] = ifst(dudz_h, U_tmp3[1], ST)
c[0] = fss(U0[0] * dudx + U0[1] * dudy + U0[2] * dudz, c[0], ST)
U_tmp3[:] = 0
dvdy_h = 1j * K[1] * U_hat0[1]
dvdy = U_tmp3[0] = ifst(dvdy_h, U_tmp3[0], ST)
dvdz_h = 1j * K[2] * U_hat0[1]
dvdz = U_tmp3[1] = ifst(dvdz_h, U_tmp3[1], ST)
c[1] = fss(U0[0] * dvdx + U0[1] * dvdy + U0[2] * dvdz, c[1], ST)
U_tmp3[:] = 0
dwdy_h = 1j * K[1] * U_hat0[2]
dwdy = U_tmp3[0] = ifst(dwdy_h, U_tmp3[0], ST)
dwdz_h = 1j * K[2] * U_hat0[2]
dwdz = U_tmp3[1] = ifst(dwdz_h, U_tmp3[1], ST)
c[2] = fss(U0[0] * dwdx + U0[1] * dwdy + U0[2] * dwdz, c[2], ST)
c *= -1
return c
