 |
Center for Nonlinear Studies |
Structure preserving numerical methods provide theoretical guarantees of reliability for situations where ad-hoc stabilization techniques can fail. In this talk we present fully discrete approximation techniques for hyperbolic conservation equations which are at the core of various multi-physics models relevant to LANL applications. The technique,based on either continuous or discontinuous finite elements,is shown to be high-order accurate in time and space and guaranteed to be invariant domain preserving.
We discuss the underlying algebraic discretization technique based on collocation and convex limiting, and how the scheme is implemented in the open-source hydrodynamic solver framework ryujin. We comment in particular on how the implementation exploits parallelism on instruction set level(SIMD vectorization), multithreading and process-level OpenMPI parallelization, and performance optimization of the compute kernels. We conclude with a short overview of concrete applications related to hyperbolic equations such as the shallow water equations, the compressible Euler equations and Navier-Stokes equations, as well as the Euler-Poisson system.
We gratefully acknowledge the support of the U.S. Department of Energy through the LANL/LDRD Program and the Information Science and Technology Institute (ISTI) for this work.
Host: Eric Tovar (T-5/CNLS)