The implicit formulation of flux-vector-splitting scheme with application to transonic flows

This paper presents an efficient implicit solver for transonic shock-tube flow, generated for a needle-free epidermal delivery of powdered vaccines. This transient transonic flow exhibits complicated flow phenomena. We proposed a unique method of implicit formation on the basis of analysing a model equation, which can separately deal with convection, diffusion and source terms. By combining this idea with flux-vector-splitting, an implicit flux-vector-splitting solver of the Navier–Stokes equations, which can avoid approximate-factorization (AF) or block-bidiagonalization, is developed. Numerical experiments show that it has obvious superiority over the conventional flux-vector-splitting scheme in terms of convergence and computing cost, meanwhile maintaining a high accuracy and robustness.