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math.NA2022
Diagonally implicit Runge-Kutta schemes: Discrete energy-balance laws and compactness properties
Abner J. Salgado, Ignacio Tomas
We study diagonally implicit Runge-Kutta (DIRK) schemes when applied to abstract evolution problems that fit into the Gelfand-triple framework. We introduce novel stability notions…
math.NA2022★ 24 cited
A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations
Yimin Lin, Jesse Chan, Ignacio Tomas
High-order entropy-stable discontinuous Galerkin methods for the compressible Euler and Navier-Stokes equations require the positivity of thermodynamic quantities in order to guara…