Simple and robust contact-discontinuity capturing central algorithms for high speed compressible flows

Simple Central Algorithms for Capturing Contact-Discontinuity in Multi-Component Mixture Equations with Stiffened Gas Equation of State.

“…This work uses a new simple central scheme based on generalized Riemann invariants that can detect stable contact discontinuities with perfect gas EOS as described in [24,25]. Consider a general quasi-linear hyperbolic system as given by (13).…”

“…GRI has been discussed in [25] in detail, and the numerical diffusion coefficient α I using GRI is given by (23).…”

“…Numerical experimentation has revealed that this numerical diffusion evaluated by (24) or (25), although adequate to capture the contact discontinuities exactly, is not sufficient for the case of shocks located at the cell interface. So in order to generalize the diffusion for any case the Riemann Invariant based Contact-discontinuity Capturing Algorithm (RICCA) is designed with the following coefficient of numerical diffusion:…”

“…where δ is a small number and a I is the speed of sound evaluated with corresponding EOS formulation at the interface. Using (26) it can be seen that for the case of a steady contact discontinuity at the interface where sign(|∆p I |) = 0, the coefficient α I becomes identical to the expression in (25) resulting in an exact capture of the steady contact discontinuity. On the other hand, if a shock is located at the interface, in which case sign(|∆p I |) = 1, the expression for the coefficient in (26) becomes max(|V nL |, |V nR |) + a I , which is a Rusanov (LLF) type diffusion and should be adequate near the shocks.…”