A method to trace sharp interface of two fluids in calculations involving shocks

A numerical method that can treat a contact discontinuity as a sharp discontinuity is proposed by introducing a density function. The surface of the density function representing the discontinuity can be described with alomost one grid on an Eulerian formulation throughout the calculation even if the surface distortion is large. The algorithm is based on the CIP (cubic-interpolated propagation) method combined with variable transformation. Smearings of the discontinuity are overcome without using any special treatment to the surface. Dependent variables on both sides of the surface are computed in a normal procedure. The present scheme is applied both to a compressible flow and quasi-incompressible flow accompanying shock discontinuities. The result exhibits advantages of this method in robustness and efficiency.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.