Particle and Flames in Radiative and Magnetic Flows

October 11-15, 2010
Lyon, France

Contribution of Keh-Ming Shyue


Front tracking methods for compressible multiphase flow


"Explosive fate of stars"


Front tracking, Godunov method, compressible multiphase flow, Rayleigh-Taylor problem, Richtmyer-Meshkov problem


In this talk, I will review two basic (i.e., the surface- and volume-based) approaches to front tracking in conjunction with high resolution shock capturing methods for nonlinear systems of conservation laws with source terms in more than one space dimension. In the algorithm, an underlying uniform grid is used with additional grid interfaces (points in 1D, curves in 2D, and surfaces in 3D) introduced at appropriate locations for tracked discontinuities. Conservative high resolution methods based on the large time step wave propagation approach are used on the resulting nonuniform grid. This method is stable even if some of the small cells created by the tracked interfaces are orders of magnitude smaller than the regular cells used to determine the time step. A fractional step or a quasi-steady approach is used to handle source terms. Several calculations are presented for problems involving shocks and interfaces (contact discontinuities and slip lines) arising in compressible multiphase flow. This includes some examples of the Rayleigh-Taylor and Richtmyer-Meshkov unstable interface problems.