Numerically simulating the missing physical dissipations in a conservative front-tracking method

The Euler equations for inviscid and compressible flows are used for modeling interfacial instabilities, and in doing so all the physical dissipations are ignored under the consideration that they are extremely weak. However, numerical simulations of interfacial instabilities with numerical dissipations or with little dissipations suffer from nonphysical artifacts on the interfaces in late times of the interfacial developments. In this paper we introduce numerical dissipations for our previously developed conservative front-tracking method that simulate tangentially the missing physical dissipations in the Euler equations on the interfaces. Numerical examples show that they suppress numerical artifacts on the tracked interfaces and help to accomplish the simulations of interfacial instabilities on fine grids.