Module flux_compute 

CPU-side parallel flux and advection compute kernels.

Provides scalar and vector flux computation on structured 3-D Cartesian grids: upwind advection, central-difference divergence, Lax-Friedrichs flux splitting, Godunov interface reconstruction, limiter functions (minmod, superbee, van Leer), and a simple finite-volume time-stepping helper. All kernels use Rayon for data-parallel execution.

Structs

EulerState

Conservative variable vector for the Euler equations: [rho, rhou, rhov, rho*w, E].

FluxGrid3D

A 3-D scalar field stored in row-major order on a uniform Cartesian grid.

VectorFluxGrid3D

Three-component 3-D velocity / flux field.

Functions

advect_upwind_3d

Apply first-order upwind advection to a FluxGrid3D for one time step.

cfl_dt

Compute the CFL-limited maximum stable time step.

characteristic_decompose_2wave

Project a vector of conservative variables onto the characteristic variables for a simple 2-component advection system.

characteristic_limited_reconstruct

Apply a characteristic-based limiter to 1-D reconstruction.

characteristic_recompose_2wave

Reconstruct conservative variables from characteristic variables.

divergence_3d

Compute the divergence of a vector field at every interior cell.

euler_step_advect

Advance phi by one Euler time step using explicit upwind advection.

godunov_flux_advection

Godunov flux for a scalar advection equation u_t + a * u_x = 0.

godunov_flux_burgers

Godunov-type flux for Burgers’ equation u_t + (u²/2)_x = 0.

gradient_3d

Compute the gradient of a scalar field at every cell.

hll_flux

HLL (Harten-Lax-van Leer) numerical flux for a scalar conservation law.

hll_flux_euler_1d

HLL flux for 1-D Euler equations.

hll_wave_speeds

Estimate HLL wave speeds for the 1-D Euler equations.

hllc_flux_euler_1d

HLLC (Harten-Lax-van Leer-Contact) flux for 1-D Euler equations.

lax_friedrichs_advect_1d

Lax-Friedrichs advection update for a 1-D scalar array.

lax_friedrichs_flux

Lax-Friedrichs numerical flux at the interface between cells i and i+1.

mc_limiter

MC (Monotonised Central) limiter.

minmod

Minmod slope limiter: smallest slope among a and b with same sign.

minmod_ratio

Compute the minmod limiter in ratio form: phi(r) = max(0, min(1, r)).

muscl_reconstruct

Reconstruct left and right interface values from cell-centred values using the MUSCL scheme with a given limiter.

muscl_reconstruct_all

Apply MUSCL reconstruction across all interfaces in a 1-D array.

roe_flux_euler_1d

Roe flux for 1-D Euler equations (x-direction).

roe_flux_scalar

Roe-averaged scalar flux for a 1-D scalar conservation law.

superbee

Superbee limiter: most compressive TVD limiter.

superbee_ratio

Superbee limiter in ratio form: phi(r) = max(0, max(min(2r,1), min(r,2))).

tvd_rk2_advect

Advance phi using the TVD Runge-Kutta 2 (Heun) scheme.

upwind_flux_1d

First-order upwind advection flux for a scalar phi transported by uniform velocity vel in one dimension.

van_albada

Van Albada slope limiter: smooth TVD limiter with quadratic shape.

van_leer

Van Leer limiter: smooth TVD limiter.

van_leer_ratio

Van Leer limiter in ratio form: phi(r) = (r + |r|) / (1 + |r|).