Abstract
In this paper, modified Rusanov's third order difference scheme for quasilinear hyperbolic system of partial differential equation in non-conservative form has been presented. The method is then applied to study the unsteady motion of converging cylindrical shock waves in radiation gas dynamics. It is concluded that a cylindrical shock wave in a radiating gas increases in strength as it is propagating towards the axis. It is also observed that the effect of radiation heat transfer is to decrease the growth rate of shock strength when it is propagating towards the axis. Further, it is concluded that the effect of radiation heat transfer is to delay the shock convergence with axis and thus increase the convergence time. In the process the detailed behaviour near the axis at the time of shock coalescence is studied. The effects of various controlling parameters on the numerical results are also studied.
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