Development of an efficient unstructured Finite Volume solver for anew conservation lawinfast structural dynamics

Abstract

In this paper, the Jameson-Schmidt-Turkel scheme (JST) is implemented to solve a new mixed methodology in fast transient dynamics [1, 2]. The use of this numerical technique leads to a significant cost reduction compared to standard Finite Volume methods, which require the use of linear reconstruction and slope limiters to guarantee second order accuracy. Crucially, the JST algorithm is specially designed to be used in conjunction with unstructured meshes and is particularly suited for problems with discontinuities, since the artificial dissipation term appearing in the scheme includes an implicit shock capturing term. All of the above ingredients enable the efficient simulation of realistic large scale problems within the context of fast structural dynamics. In this paper, the JST scheme has been combined with a two-stage Total Variation Diminishing (TVD) Runge-Kutta time integrator. The capabilities of the resulting numerical technique, including the preservation of angular momentum and the excellent behaviour in bending dominated scenarios, are demonstrated for a series of benchmark problems. The solutions will be compared with solutions obtained using other methodologies, such cell centred upwind Finite Volume, Two Step Taylor Galerkin or Stream Upwind Petrov Galerkin (SUPG) [4] [3] [6] [5].