A strong conservative Riemann solver for the solution of the coupled Maxwell and Navier–Stokes equations

The coupled system of the Navier–Stokes and Maxwell equations are recast into a strong conservative form, which allows the fluid coupling to the Maxwell system to be written in terms of flux divergence rather than explicit source terms. This effectively removes source terms from the Navier–Stokes equations, although retaining an exact coupling to the electromagnetics. While this relieves the stiff source terms and potentially stabilizes the system, it introduces a much more complicated eigenstructure to the governing equations. The flux Jacobian and eigenvectors for this strong conservative system are presented in the current paper for the first time. An approximate Riemann solver based upon these eigenvectors is then introduced and tested. The solver is implemented in a preconditioned, dual-time implicit form. Validations for classic one- and two-dimensional problems are presented, and the performances of the new formulation and the traditional source-coupled formulation are compared.