Numerical Analysis and Scientific Computing Seminar | Gennaro Coppola, Structure-preserving discretization of compressible-flow equations

In the context of numerical simulation of multiscale fluid dynamics problems, as in the case of Direct or Large Eddy Simulations of turbulent flows, an important topic is the design of robust and accurate numerical methods, that can efficiently handle high Reynolds number and/or under resolved simulations, for which nonlinear instabilities are a major issue. To this aim, modern numerical methods are usually required to satisfy some symmetries of the continuous governing equations, which typically amount to the discrete enforcement of the induced balance of suitably selected secondary quantities. The resulting discretizations have shown increased robustness and reliability, and are usually referred to as structure-preserving or physics-compatible methods.

In this talk, the design and applications of structure-preserving methods for compressible flow equations are reviewed from the founding ideas up to recent developments. Kinetic Energy Preserving (KEP) schemes, which are the most established and used among them, are firstly illustrated with reference to the spatial discretization.  More recent developments as Entropy Conservative (EC) and Pressure Equilibrium Preserving (PEP) formulations are also discussed. Finally, current research on the extension of such approaches to non-ideal gas models are illustrated.