Entropy Conserving and Kinetic Energy Preserving Numerical Methods for the Euler Equations Using Summation-by-Parts Operators

摘要

Considering the solution of hyperbolic conservation laws, high order methods can be very efficient, providing accurate numerical solutions with relatively low computational effort . In order to make use of this accuracy, stability has to be established. Mimicking estimates obtained on the continuous level via integration-by-parts, summation-by-parts (SBP) operators can be used. In short, SBP operators are discrete derivative operators equipped with a compatible quadrature providing a discrete analogue of the L~2 norm. The compatibility of discrete integration and differentiation mimics integration-by-parts on a discrete level. Combined with the weak enforcement of boundary conditions via simultaneous approximation terms (SATs) , highly efficient and stable semidiscretisations can be obtained at least for linear problems, see e.g. and references cited therein.