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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 the compressible Euler and Navier-Stokes equations that is second-order accurate in time and space and guaranteed to be invariant domain preserving. This means the method maintains important physical invariantsand is guaranteed to be stable without the use of ad-hoc tuning parameters. We discuss the underlying algebraic discretization technique based on collocation and convex limiting, and briefly comment on a high-performance implementation. We conclude with a short overview of concrete applications to related hyperbolic equations such as the shallow water equations and the Euler-Poisson system.
Host: Eric Tovar