Application of a New Hybrid Explicit-Implicit Flow Solver to 1D Unsteady Flows with Shock Waves

Introduction

Explicit numerical schemes are widely used to simulate essentially unsteady flows with shock waves (e.g., see [1, 2] and numerous references there) because the use of large time steps with implicit schemes is often not possible and necessary due to time accuracy requirements. However, for some flows the time step of explicit time marching becomes severely limited by particular conditions within a relatively small flow area, as compared to the rest of the computational domain where the stability condition admits much higher time steps. The situation can be termed as “temporally-stiff”.Out of many examples, we mention the simulations of blast wave propagation when a high pressure/ temperature balloon is used as a blast wave source. When the blast wave propagates away from its origin, a high-temperature (and hence, high speed of sound) spot remains at the explosion center, considerably reducing the allowable time step for the whole simulation. The same effect can be caused by high flow velocities existing just downstream of a sharp corner when a shock wave diffracts over it, or by small computational cells near some small-scale geometrical feature of the problem under study.