AUSM(ALE): A geometrically conservative arbitrary Lagrangian-Eulerian fluxsplitting scheme

A geometrically conservative one-dimensional (1D) arbitrary Lagrangian-Eule rian (ALE) version of the advective upstream splitting method (AUSM) shock capturing scheme is presented, The spatial discretization is based on a mod ified form of AUSM which splits the flux vector according to the eigenvalue s of the compressible Euler system in ALE form and recovers the original fl ux vector splitting in the absence of grid movement, The generalized form o f AUSM is given the name AUSM(ALE), Extension to second-order accuracy is a chieved by a piecewise linear reconstruction of the dependent variables wit h total variation diminishing limiting of slopes, The ALE formulation is co mpleted by incorporating an implicit time-averaged normals form of the geom etric conservation law for cylindrically and spherically symmetric time-dep endent finite volumes which is valid for any two-level time-integration met hod, The effectiveness of the method for both fixed and moving grids is dem onstrated via several 1D test problems including a standard shock tube prob lem and an infinite strength reflected shock problem, The method is then ap plied to a benchmark spherically symmetric underwater explosion problem to demonstrate the efficacy of the numerical procedure for problems of this ty pe. In the two-phase detonation problem the spherical surface separating th e expanding detonation-products gas bubble and the surrounding water is exp licitly tracked as a Lagrangian surface using AUSM(ALE) in conjunction with appropriate equations of state describing the detonation-products gas and water phases, The basic features of the spherically symmetric detonation pr oblem are discussed such as shock/free-surface interaction and late rime hy drodynamics.