flux_rs${XYZ}$_vf(j, k, l, [contxe + dir_idx(1), contxe + dir_idx(2), contxe + dir_idx(3)]) = F_hlld([2, 3, 4])
! Magnetic field
if (n == 0) then
    flux_rs${XYZ}$_vf(j, k, l, [B_idx%beg, B_idx%beg + 1]) = F_hlld([5, 6])
else
    flux_rs${XYZ}$_vf(j, k, l, [B_idx%beg + dir_idx(2) - 1, B_idx%beg + dir_idx(3) - 1]) = F_hlld([5, 6])

        B%L = [Bx0, qL_prim_rs${XYZ}$_vf(j, k, l, B_idx%beg), qL_prim_rs${XYZ}$_vf(j, k, l, B_idx%beg + 1)]
        B%R = [Bx0, qR_prim_rs${XYZ}$_vf(j + 1, k, l, B_idx%beg), qR_prim_rs${XYZ}$_vf(j + 1, k, l, B_idx%beg + 1)]
    else ! 2D/3D: Bx, By, Bz as variables
        B%L = [qL_prim_rs${XYZ}$_vf(j, k, l, B_idx%beg + dir_idx(1) - 1), &
               qL_prim_rs${XYZ}$_vf(j, k, l, B_idx%beg + dir_idx(2) - 1), &
               qL_prim_rs${XYZ}$_vf(j, k, l, B_idx%beg + dir_idx(3) - 1)]
        B%R = [qR_prim_rs${XYZ}$_vf(j + 1, k, l, B_idx%beg + dir_idx(1) - 1), &
               qR_prim_rs${XYZ}$_vf(j + 1, k, l, B_idx%beg + dir_idx(2) - 1), &
               qR_prim_rs${XYZ}$_vf(j + 1, k, l, B_idx%beg + dir_idx(3) - 1)]
    end if
end if

! Sum properties of all fluid components
rho%L = 0._wp; gamma%L = 0._wp; pi_inf%L = 0._wp; qv%L = 0._wp
rho%R = 0._wp; gamma%R = 0._wp; pi_inf%R = 0._wp; qv%R = 0._wp
!$acc loop seq
do i = 1, num_fluids
    rho%L = rho%L + alpha_rho_L(i)
    gamma%L = gamma%L + alpha_L(i)*gammas(i)
    pi_inf%L = pi_inf%L + alpha_L(i)*pi_infs(i)
    qv%L = qv%L + alpha_rho_L(i)*qvs(i)

    rho%R = rho%R + alpha_rho_R(i)
    gamma%R = gamma%R + alpha_R(i)*gammas(i)
    pi_inf%R = pi_inf%R + alpha_R(i)*pi_infs(i)
    qv%R = qv%R + alpha_rho_R(i)*qvs(i)
end do

pres_mag%L = 0.5_wp*sum(B%L**2._wp)
pres_mag%R = 0.5_wp*sum(B%R**2._wp)
E%L = gamma%L*pres%L + pi_inf%L + 0.5_wp*rho%L*vel_rms%L + qv%L + pres_mag%L
E%R = gamma%R*pres%R + pi_inf%R + 0.5_wp*rho%R*vel_rms%R + qv%R + pres_mag%R ! includes magnetic energy
H_no_mag%L = (E%L + pres%L - pres_mag%L)/rho%L
H_no_mag%R = (E%R + pres%R - pres_mag%R)/rho%R ! stagnation enthalpy here excludes magnetic energy (only used to find speed of sound)

! (2) Compute fast wave speeds
call s_compute_speed_of_sound(pres%L, rho%L, gamma%L, pi_inf%L, H_no_mag%L, alpha_L, vel_rms%L, 0._wp, c%L)
call s_compute_speed_of_sound(pres%R, rho%R, gamma%R, pi_inf%R, H_no_mag%R, alpha_R, vel_rms%R, 0._wp, c%R)
call s_compute_fast_magnetosonic_speed(rho%L, c%L, B%L, norm_dir, c_fast%L, H_no_mag%L)
call s_compute_fast_magnetosonic_speed(rho%R, c%R, B%R, norm_dir, c_fast%R, H_no_mag%R)

! (3) Compute contact speed s_M [Miyoshi Equ. (38)]
s_L = min(vel%L(1) - c_fast%L, vel%R(1) - c_fast%R)
s_R = max(vel%R(1) + c_fast%R, vel%L(1) + c_fast%L)

pTot_L = pres%L + pres_mag%L
pTot_R = pres%R + pres_mag%R

s_M = (((s_R - vel%R(1))*rho%R*vel%R(1) - &
        (s_L - vel%L(1))*rho%L*vel%L(1) - pTot_R + pTot_L)/ &
       ((s_R - vel%R(1))*rho%R - (s_L - vel%L(1))*rho%L))

! (4) Compute star state variables
rhoL_star = rho%L*(s_L - vel%L(1))/(s_L - s_M)
rhoR_star = rho%R*(s_R - vel%R(1))/(s_R - s_M)
p_star = pTot_L + rho%L*(s_L - vel%L(1))*(s_M - vel%L(1))/(s_L - s_M)
E_starL = ((s_L - vel%L(1))*E%L - pTot_L*vel%L(1) + p_star*s_M)/(s_L - s_M)
E_starR = ((s_R - vel%R(1))*E%R - pTot_R*vel%R(1) + p_star*s_M)/(s_R - s_M)

! (5) Compute left/right state vectors and fluxes
U_L = [rho%L, rho%L*vel%L(1:3), B%L(2:3), E%L]
U_starL = [rhoL_star, rhoL_star*s_M, rhoL_star*vel%L(2:3), B%L(2:3), E_starL]
U_R = [rho%R, rho%R*vel%R(1:3), B%R(2:3), E%R]
U_starR = [rhoR_star, rhoR_star*s_M, rhoR_star*vel%R(2:3), B%R(2:3), E_starR]

! Compute the left/right fluxes
F_L(1) = U_L(2)
F_L(2) = U_L(2)*vel%L(1) - B%L(1)*B%L(1) + pTot_L
F_L(3:4) = U_L(2)*vel%L(2:3) - B%L(1)*B%L(2:3)
F_L(5:6) = vel%L(1)*B%L(2:3) - vel%L(2:3)*B%L(1)
F_L(7) = (E%L + pTot_L)*vel%L(1) - B%L(1)*(vel%L(1)*B%L(1) + vel%L(2)*B%L(2) + vel%L(3)*B%L(3))

F_R(1) = U_R(2)
F_R(2) = U_R(2)*vel%R(1) - B%R(1)*B%R(1) + pTot_R
F_R(3:4) = U_R(2)*vel%R(2:3) - B%R(1)*B%R(2:3)
F_R(5:6) = vel%R(1)*B%R(2:3) - vel%R(2:3)*B%R(1)
F_R(7) = (E%R + pTot_R)*vel%R(1) - B%R(1)*(vel%R(1)*B%R(1) + vel%R(2)*B%R(2) + vel%R(3)*B%R(3))
! Compute the star flux using HLL relation
F_starL = F_L + s_L*(U_starL - U_L)
F_starR = F_R + s_R*(U_starR - U_R)
! Compute the rotational (Alfvén) speeds
s_starL = s_M - abs(B%L(1))/sqrt(rhoL_star)
s_starR = s_M + abs(B%L(1))/sqrt(rhoR_star)
! Compute the double–star states [Miyoshi Eqns. (59)-(62)]
sqrt_rhoL_star = sqrt(rhoL_star); sqrt_rhoR_star = sqrt(rhoR_star)
vL_star = vel%L(2); wL_star = vel%L(3)
vR_star = vel%R(2); wR_star = vel%R(3)

! (6) Compute the double–star states [Miyoshi Eqns. (59)-(62)]
denom_ds = sqrt_rhoL_star + sqrt_rhoR_star
sign_Bx = sign(1._wp, B%L(1))
v_double = (sqrt_rhoL_star*vL_star + sqrt_rhoR_star*vR_star + (B%R(2) - B%L(2))*sign_Bx)/denom_ds
w_double = (sqrt_rhoL_star*wL_star + sqrt_rhoR_star*wR_star + (B%R(3) - B%L(3))*sign_Bx)/denom_ds
By_double = (sqrt_rhoL_star*B%R(2) + sqrt_rhoR_star*B%L(2) + sqrt_rhoL_star*sqrt_rhoR_star*(vR_star - vL_star)*sign_Bx)/denom_ds
Bz_double = (sqrt_rhoL_star*B%R(3) + sqrt_rhoR_star*B%L(3) + sqrt_rhoL_star*sqrt_rhoR_star*(wR_star - wL_star)*sign_Bx)/denom_ds

E_doubleL = E_starL - sqrt_rhoL_star*((vL_star*B%L(2) + wL_star*B%L(3)) - (v_double*By_double + w_double*Bz_double))*sign_Bx
E_doubleR = E_starR + sqrt_rhoR_star*((vR_star*B%R(2) + wR_star*B%R(3)) - (v_double*By_double + w_double*Bz_double))*sign_Bx
E_double = 0.5_wp*(E_doubleL + E_doubleR)

U_doubleL = [rhoL_star, rhoL_star*s_M, rhoL_star*v_double, rhoL_star*w_double, By_double, Bz_double, E_double]
U_doubleR = [rhoR_star, rhoR_star*s_M, rhoR_star*v_double, rhoR_star*w_double, By_double, Bz_double, E_double]

! (11) Choose HLLD flux based on wave-speed regions
if (0.0_wp <= s_L) then
    F_hlld = F_L
else if (0.0_wp <= s_starL) then
    F_hlld = F_L + s_L*(U_starL - U_L)
else if (0.0_wp <= s_M) then
    F_hlld = F_starL + s_starL*(U_doubleL - U_starL)
else if (0.0_wp <= s_starR) then
    F_hlld = F_starR + s_starR*(U_doubleR - U_starR)
else if (0.0_wp <= s_R) then
    F_hlld = F_R + s_R*(U_starR - U_R)
else
    F_hlld = F_R
end if

! (12) Reorder and write temporary variables to the flux array
! Mass
flux_rs${XYZ}$_vf(j, k, l, 1) = F_hlld(1) ! TODO multi-component
! Momentum
flux_rs${XYZ}$_vf(j, k, l, [contxe + dir_idx(1), contxe + dir_idx(2), contxe + dir_idx(3)]) = F_hlld([2, 3, 4])
! Magnetic field
if (n == 0) then
    flux_rs${XYZ}$_vf(j, k, l, [B_idx%beg, B_idx%beg + 1]) = F_hlld([5, 6])
else
    flux_rs${XYZ}$_vf(j, k, l, [B_idx%beg + dir_idx(2) - 1, B_idx%beg + dir_idx(3) - 1]) = F_hlld([5, 6])
end if
! Energy
flux_rs${XYZ}$_vf(j, k, l, E_idx) = F_hlld(7)