def calculate_GRFFE_Tmunu_and_contractions(flux_dirn, mom_comp, gammaDD, betaU, alpha, ValenciavU, BU, sqrt4pi): GRHD.compute_sqrtgammaDET(gammaDD) GRHD.u4U_in_terms_of_ValenciavU__rescale_ValenciavU_by_applying_speed_limit( alpha, betaU, gammaDD, ValenciavU) GRFFE.compute_smallb4U_with_driftvU_for_FFE(gammaDD, betaU, alpha, GRHD.u4U_ito_ValenciavU, BU, sqrt4pi) GRFFE.compute_smallbsquared(gammaDD, betaU, alpha, GRFFE.smallb4_with_driftv_for_FFE_U) GRFFE.compute_TEM4UU(gammaDD, betaU, alpha, GRFFE.smallb4_with_driftv_for_FFE_U, GRFFE.smallbsquared, GRHD.u4U_ito_ValenciavU) GRFFE.compute_TEM4UD(gammaDD, betaU, alpha, GRFFE.TEM4UU) # Compute conservative variables in terms of primitive variables GRHD.compute_S_tildeD(alpha, GRHD.sqrtgammaDET, GRFFE.TEM4UD) global U, F # Flux F = alpha*sqrt{gamma}*T^i_j F = alpha * GRHD.sqrtgammaDET * GRFFE.TEM4UD[flux_dirn + 1][mom_comp + 1] # U = alpha*sqrt{gamma}*T^0_j = Stilde_j U = GRHD.S_tildeD[mom_comp]
def calculate_GRFFE_Tmunu_and_contractions(flux_dirn, mom_comp, gammaDD, betaU, alpha, ValenciavU, BU, sqrt4pi, phi_face, gammaUU): # GRHD.compute_sqrtgammaDET(gammaDD) sqrtgammaDET = sp.exp( sp.sympify(6) * phi_face) # phi_face is phi, e^(6*phi) = psi^6 = sqrtgamma GRHD.u4U_in_terms_of_ValenciavU__rescale_ValenciavU_by_applying_speed_limit( alpha, betaU, gammaDD, ValenciavU) GRFFE.compute_smallb4U(gammaDD, betaU, alpha, GRHD.u4U_ito_ValenciavU, BU, sqrt4pi) GRFFE.compute_smallbsquared(gammaDD, betaU, alpha, GRFFE.smallb4U) GRFFE.compute_TEM4UU(gammaDD, betaU, alpha, GRFFE.smallb4U, GRFFE.smallbsquared, GRHD.u4U_ito_ValenciavU, gammaUU) GRFFE.compute_TEM4UD(gammaDD, betaU, alpha, GRFFE.TEM4UU) # Compute conservative variables in terms of primitive variables GRHD.compute_S_tildeD(alpha, sqrtgammaDET, GRFFE.TEM4UD) global U, F # Flux F = alpha*sqrt{gamma}*T^i_j F = alpha * sqrtgammaDET * GRFFE.TEM4UD[flux_dirn + 1][mom_comp + 1] # alpha_sqrt_gamma*( b2*(u0_r*Ur[VX+offset])*U_LOWERr[UX] + 0.5*b2*kronecker_delta[flux_dirn][0] - smallbr[SMALLBX+offset]*smallb_lowerr[SMALLBX] ) # F = alpha*sqrtgammaDET*(GRFFE.smallbsquared*GRHD.u4U_ito_ValenciavU[0]* + sp.Rational(1,2)*GRFFE.smallbsquared*) # U = alpha*sqrt{gamma}*T^0_j = Stilde_j U = GRHD.S_tildeD[mom_comp]
def GiRaFFE_NRPy_P2C(gammaDD, betaU, alpha, ValenciavU, BU, sqrt4pi): # After recalculating the 3-velocity, we need to update the poynting flux: # We'll reset the Valencia velocity, since this will be part of a second call to outCfunction. # First compute stress-energy tensor T4UU and T4UD: GRHD.compute_sqrtgammaDET(gammaDD) GRHD.u4U_in_terms_of_ValenciavU__rescale_ValenciavU_by_applying_speed_limit( alpha, betaU, gammaDD, ValenciavU) GRFFE.compute_smallb4U_with_driftvU_for_FFE(gammaDD, betaU, alpha, GRHD.u4U_ito_ValenciavU, BU, sqrt4pi) GRFFE.compute_smallbsquared(gammaDD, betaU, alpha, GRFFE.smallb4_with_driftv_for_FFE_U) GRFFE.compute_TEM4UU(gammaDD, betaU, alpha, GRFFE.smallb4_with_driftv_for_FFE_U, GRFFE.smallbsquared, GRHD.u4U_ito_ValenciavU) GRFFE.compute_TEM4UD(gammaDD, betaU, alpha, GRFFE.TEM4UU) # Compute conservative variables in terms of primitive variables GRHD.compute_S_tildeD(alpha, GRHD.sqrtgammaDET, GRFFE.TEM4UD) global StildeD StildeD = GRHD.S_tildeD
def GiRaFFE_NRPy_P2C(gammaDD,betaU,alpha, ValenciavU,BU, sqrt4pi): # After recalculating the 3-velocity, we need to update the poynting flux: # We'll reset the Valencia velocity, since this will be part of a second call to outCfunction. # First compute stress-energy tensor T4UU and T4UD: GRHD.compute_sqrtgammaDET(gammaDD) # GRHD.u4U_in_terms_of_ValenciavU__rescale_ValenciavU_by_applying_speed_limit(alpha, betaU, gammaDD, ValenciavU) R = sp.sympify(0) for i in range(3): for j in range(3): R += gammaDD[i][j] * ValenciavU[i] * ValenciavU[j] u4U_ito_ValenciavU = ixp.zerorank1(DIM=4) u4U_ito_ValenciavU[0] = 1 / (alpha * sp.sqrt(1 - R)) # u^i = u^0 ( alpha v^i_{(n)} - beta^i ), where v^i_{(n)} is the Valencia 3-velocity for i in range(3): u4U_ito_ValenciavU[i + 1] = u4U_ito_ValenciavU[0] * (alpha * ValenciavU[i] - betaU[i]) GRFFE.compute_smallb4U_with_driftvU_for_FFE(gammaDD, betaU, alpha, u4U_ito_ValenciavU, BU, sqrt4pi) GRFFE.compute_smallbsquared(gammaDD, betaU, alpha, GRFFE.smallb4_with_driftv_for_FFE_U) GRFFE.compute_TEM4UU(gammaDD, betaU, alpha, GRFFE.smallb4_with_driftv_for_FFE_U, GRFFE.smallbsquared, u4U_ito_ValenciavU) GRFFE.compute_TEM4UD(gammaDD, betaU, alpha, GRFFE.TEM4UU) # Compute conservative variables in terms of primitive variables GRHD.compute_S_tildeD(alpha, GRHD.sqrtgammaDET, GRFFE.TEM4UD) global StildeD StildeD = GRHD.S_tildeD
def generate_everything_for_UnitTesting(): # First define hydrodynamical quantities u4U = ixp.declarerank1("u4U", DIM=4) B_tildeU = ixp.declarerank1("B_tildeU", DIM=3) # Then ADM quantities gammaDD = ixp.declarerank2("gammaDD", "sym01", DIM=3) betaU = ixp.declarerank1("betaU", DIM=3) alpha = sp.symbols('alpha', real=True) # Then numerical constant sqrt4pi = sp.symbols('sqrt4pi', real=True) # First compute stress-energy tensor T4UU and T4UD: import GRHD.equations as GHeq GHeq.compute_sqrtgammaDET(gammaDD) compute_B_notildeU(GHeq.sqrtgammaDET, B_tildeU) compute_smallb4U(gammaDD, betaU, alpha, u4U, B_notildeU, sqrt4pi) compute_smallb4U_with_driftvU_for_FFE(gammaDD, betaU, alpha, u4U, B_notildeU, sqrt4pi) compute_smallbsquared(gammaDD, betaU, alpha, smallb4U) compute_TEM4UU(gammaDD, betaU, alpha, smallb4U, smallbsquared, u4U) compute_TEM4UD(gammaDD, betaU, alpha, TEM4UU) # Compute conservative variables in terms of primitive variables GHeq.compute_S_tildeD(alpha, GHeq.sqrtgammaDET, TEM4UD) global S_tildeD S_tildeD = GHeq.S_tildeD # Next compute fluxes of conservative variables GHeq.compute_S_tilde_fluxUD(alpha, GHeq.sqrtgammaDET, TEM4UD) global S_tilde_fluxUD S_tilde_fluxUD = GHeq.S_tilde_fluxUD # Then declare derivatives & compute g4DDdD gammaDD_dD = ixp.declarerank3("gammaDD_dD", "sym01", DIM=3) betaU_dD = ixp.declarerank2("betaU_dD", "nosym", DIM=3) alpha_dD = ixp.declarerank1("alpha_dD", DIM=3) GHeq.compute_g4DD_zerotimederiv_dD(gammaDD, betaU, alpha, gammaDD_dD, betaU_dD, alpha_dD) # Finally compute source terms on tau_tilde and S_tilde equations GHeq.compute_S_tilde_source_termD(alpha, GHeq.sqrtgammaDET, GHeq.g4DD_zerotimederiv_dD, TEM4UU) global S_tilde_source_termD S_tilde_source_termD = GHeq.S_tilde_source_termD
def generate_everything_for_UnitTesting(): # First define hydrodynamical quantities u4U = ixp.declarerank1("u4U", DIM=4) rho_b, P, epsilon = sp.symbols('rho_b P epsilon', real=True) B_tildeU = ixp.declarerank1("B_tildeU", DIM=3) # Then ADM quantities gammaDD = ixp.declarerank2("gammaDD", "sym01", DIM=3) KDD = ixp.declarerank2("KDD", "sym01", DIM=3) betaU = ixp.declarerank1("betaU", DIM=3) alpha = sp.symbols('alpha', real=True) # Then numerical constant sqrt4pi = sp.symbols('sqrt4pi', real=True) # First compute smallb4U & smallbsquared from BtildeU, which are needed # for GRMHD stress-energy tensor T4UU and T4UD: GRHD.compute_sqrtgammaDET(gammaDD) GRFFE.compute_B_notildeU(GRHD.sqrtgammaDET, B_tildeU) GRFFE.compute_smallb4U(gammaDD, betaU, alpha, u4U, GRFFE.B_notildeU, sqrt4pi) GRFFE.compute_smallbsquared(gammaDD, betaU, alpha, GRFFE.smallb4U) # Then compute the GRMHD stress-energy tensor: compute_GRMHD_T4UU(gammaDD, betaU, alpha, rho_b, P, epsilon, u4U, GRFFE.smallb4U, GRFFE.smallbsquared) compute_GRMHD_T4UD(gammaDD, betaU, alpha, GRHDT4UU, GRFFET4UU) # Compute conservative variables in terms of primitive variables global rho_star, tau_tilde, S_tildeD GRHD.compute_rho_star(alpha, GRHD.sqrtgammaDET, rho_b, u4U) GRHD.compute_tau_tilde(alpha, GRHD.sqrtgammaDET, T4UU, GRHD.rho_star) GRHD.compute_S_tildeD(alpha, GRHD.sqrtgammaDET, T4UD) rho_star = GRHD.rho_star tau_tilde = GRHD.tau_tilde S_tildeD = GRHD.S_tildeD # Then compute v^i from u^mu GRHD.compute_vU_from_u4U__no_speed_limit(u4U) # Next compute fluxes of conservative variables global rho_star_fluxU, tau_tilde_fluxU, S_tilde_fluxUD GRHD.compute_rho_star_fluxU(GRHD.vU, GRHD.rho_star) GRHD.compute_tau_tilde_fluxU(alpha, GRHD.sqrtgammaDET, GRHD.vU, T4UU, GRHD.rho_star) GRHD.compute_S_tilde_fluxUD(alpha, GRHD.sqrtgammaDET, T4UD) rho_star_fluxU = GRHD.rho_star_fluxU tau_tilde_fluxU = GRHD.tau_tilde_fluxU S_tilde_fluxUD = GRHD.S_tilde_fluxUD # Then declare derivatives & compute g4DD_zerotimederiv_dD gammaDD_dD = ixp.declarerank3("gammaDD_dD", "sym01", DIM=3) betaU_dD = ixp.declarerank2("betaU_dD", "nosym", DIM=3) alpha_dD = ixp.declarerank1("alpha_dD", DIM=3) GRHD.compute_g4DD_zerotimederiv_dD(gammaDD, betaU, alpha, gammaDD_dD, betaU_dD, alpha_dD) # Then compute source terms on tau_tilde and S_tilde equations global s_source_term, S_tilde_source_termD GRHD.compute_s_source_term(KDD, betaU, alpha, GRHD.sqrtgammaDET, alpha_dD, T4UU) GRHD.compute_S_tilde_source_termD(alpha, GRHD.sqrtgammaDET, GRHD.g4DD_zerotimederiv_dD, T4UU) s_source_term = GRHD.s_source_term S_tilde_source_termD = GRHD.S_tilde_source_termD