A Runge-Kutta–based WENO reconstruction on moving mesh for compressible fluids

In this paper, we construct a high-order moving mesh method based on total variation diminishing Runge-Kutta and weighted essential nonoscillatory reconstruction for compressible fluid system. Beginning with the integral form of fluid system, we get the semidiscrete system with an arbitrary mesh velocity. We use weighted essential nonoscillatory reconstruction to get the space accuracy on moving meshes, and the time accuracy is obtained by modified Runge-Kutta method; the mesh velocity is determined by moving mesh method. One- and two-dimensional numerical examples are presented to demonstrate the efficient and accurate performance of the scheme.