An Eulerian Interface-Sharpening Algorithm for Compressible Gas Dynamics

We describe a novel Eulerian interface-sharpening approach for the efficient numerical resolution of interfaces arising from inviscid compressible flow in more than one space dimension. The algorithm uses the single-phase compressible Euler equations as the model system, and introduces auxiliary differential terms to the model so as to neutralize numerical diffusion that is inevitable when the original Euler system is solved by a diffused interface method. A standard fractional-step method is employed to solve the proposed model equations in two steps, yielding an easy implementation of the algorithm. Preliminary results obtained using an anti-diffusion based model system are shown to demonstrate the feasibility of the algorithm for sharpening compressible interfaces numerically.