Computations of nonlinear wave interaction in shock-wave focusing process using finite volume TVD schemes

Abstract

An upwind and a symmetric finite difference TVD scheme have been extended to cell-centered finite volume methods. These newly extended schemes have been used to analyze a shock-wave focusing phenomenon that is dominated by complex nonlinear interaction of shock waves. Numerical solutions obtained from these two schemes successfully resolved all the waves evolving through the focusing process with reasonable accuracy and resolution. The phenomenon near the focal region was found to be strongly affected by the gas dynamic nonlinearities of shock waves. The computed solutions showed good agreement with experimental data and, thus, demonstrated the accuracy and reliability of the present numerical schemes as applied to the analysis of complex unsteady shock-shock interaction problems. The present numerical simulation has clearly revealed the mechanism of shock-shock/expansion wave interaction in a shock-wave focusing process, which determines the wave-front geometries at and beyond the focus and confines the pressure amplification at the focal region, In addition, some comparisons have been made for the performance of both schemes considering the effect of the limiter functions and those results are proposed. Copyright (C) 1996 Elsevier Science Ltd