Moving Meshes and Higher Order Finite Volume Reconstructions

International audienceIn this paper, we present and evaluate a moving mesh finite volume method for hyperbolic conservation laws. The method consists of two parts; a mesh moving scheme based on the algorithm of Tang and Tang, and a third order accurate bi-hyperbolic reconstruction which is an extension of Marquina's PHM. The resulting algorithm calculates the solution of the conservation laws directly in physical space, without any transformation of the computational grid or the hyperbolic equations. Numerical experiments in one and two space dimensions indicate high numerical accuracy of the method