High-order Runge–Kutta type large time-stepping schemes for the compressible Euler equations

Abstract

This paper establishes a class of up to fourth-order large time-stepping schemes for the compressible Euler equations under the stabilization technique framework. The proposed schemes do not destroy the accuracy of the underlying strong-stability-preserving Runge–Kutta (SSPRK) schemes, and their time step is at most $s$ times that of the forward Euler time step of the underlying $s$-stage, $p$th-order SSPRK schemes. Numerical experiments are presented to validate the effectiveness of the proposed schemes.