A Large Time Step Wave-Adding Simple Scheme for Unsteady Compressible Flows

Abstract

In this paper, we construct a large time step wave-adding scheme (LTS-WA) for unsteady Euler equations in compressible flows with a much simpler strategy in the wave-adding procedure, named LTS-WAS. The new method does not need to calculate coefficients of contribution and also add the waves according to their types and families, which makes the scheme easy for coding and optimisation. The new scheme has a high speedup ratio, and its formulation is the same in scalar and system cases. The scheme is extended to 3D compressible flows using the dimension split method. Numerical experiments show that the new scheme maintains the advantages of the original LTS-WA scheme at large CFL numbers, and has a higher efficiency.

KEYWORDS:

• Large time step
• wave adding simple method
• compressible flow
• Euler equation
• computational fluid dynamics

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.