Numerical Simulations Of Material Interfaces Using Conservative Front Tracking Method

In this thesis, the author uses the conservative front-tracking method developed by Mao De-kang in [Mao De-kang, Towards front-tracking based on conservation in two space dimensions II, tracking discontinuities in capturing fashion, J. Comput. Phys.,226(2007), pp.1550-1588] and [Mao De-kang, Towards front-tracking based on conservation in two space dimensions, SIAM J. Sci. Comput.,22(1), (2000), pp.113-152] to numerically simulate several two-dimensional material interface problems. The purposes of this work are 1) to verify the efficiency and effectiveness of the method for material interface simulations, and 2) to numerically study the problems to be simulated.Firstly, the author numerically simulates the two shock-bubble interaction ex-periments in [J. F. Haas and B. Sturtevant, Interaction of weak shock waves with cylindrical and spherical gas inhomo-geneities, J. Fluid Mech.,181,41-76 (1987)]. Our numerical results in the early time are qualitatively and quantitatively in good agreement with that of the experiments and numerical simulations done by other people. Moreover, our simulation also give clear pictures of the largely deformed interfaces in the late time of the experiments when the experiments and most nu-merical simulations failed to do so.Secondly, the author numerically simulates two single-mode Richtmyer-Meshkov instability experiments, Benjamin's air-SF6 experiment in [R. Benjamin, D. Besnard and J. Haas, Shock and reshock of an unstable interface, LANL Report, LA-UR 92-1185,(1993).] and Meshkov's air-He experiments in [E. E. Meshkov, Instability of a shock wave accelerated interface between two gases, NASA Tech. Trans. F-13, (1970), pp.074], and computed results are compared with that obtained in [Holmes, R. L., Grove, J. W. and Sharp, D. H. Numerical investigation of Richtmyer-Meshkov instability using front-tracking. J. Fluid Mech.,301,51-64(1995)]. Our numerical simulations confirm the improvements madeby Holmes et al on the agreement be-tween the experiments and numerical simulations.