A moving mesh method for one-dimensional hyperbolic conservation laws (Q2706469)

The authors describe an adaptive method for solving one-dimensional systems of conservation laws which is based on a high resolution Godunov-type method for the physical equations together with a moving mesh partial differential equation (PDE) for the motion of the spatial grid points. Technically, a semi-implicit ansatz is chosen that couples the moving mesh equation to an explicit scheme for the physical PDE -- namely the wave propagation method by \textit{R. J. LeVeque} [J. Comput. Phys. 131, No. 2, 327-353 (1997; Zbl 0872.76075)] implemented within CLAWPACK -- which results in a two-step predictor-corrector method. Numerical tests show that the developed method gives a more accurate resolution of discontinuities in comparison with computations on a fixed, uniform mesh while the computational work is at about the same level.