Multi-Rate Time Integration on Overset Meshes

TL;DR

This paper introduces multi-rate Adams-Bashforth integrators for overset mesh CFD simulations, enabling independent time stepping on different meshes to improve efficiency without sacrificing accuracy or stability.

Contribution

The work develops and demonstrates a class of multi-rate Adams-Bashforth schemes tailored for SBP-SAT discretized Navier-Stokes equations on overset meshes, improving computational efficiency and stability.

Findings

MRAB schemes offer significant stability improvements.

MRAB reduces computational cost in overset mesh simulations.

Effective in large-scale parallel implementations.

Abstract

Overset meshes are an effective tool for the computational fluid dynamic simulation of problems with complex geometries or multiscale spatio-temporal features. When the maximum allowable timestep on one or more meshes is significantly smaller than on the remaining meshes, standard explicit time integrators impose inefficiencies for time-accurate calculations by requiring that all meshes advance with the smallest timestep. With the targeted use of multi-rate time integrators, separate meshes can be time-marched at independent rates to avoid wasteful computation while maintaining accuracy and stability. This work applies time-explicit multi-rate integrators to the simulation of the compressible Navier-Stokes equations discretized on overset meshes using summation-by-parts (SBP) operators and simultaneous approximation term (SAT) boundary conditions. We introduce a class of multi-rate Adams-Bashforth (MRAB) schemes that offer significant stability improvements and computational efficiencies for SBP-SAT methods. We present numerical results that confirm the efficacy of MRAB integrators, outline a number of implementation challenges, and demonstrate a reduction in computational cost enabled by MRAB. We also investigate the use of our method in the setting of a large-scale distributed-memory parallel implementation where we discuss concerns involving load balancing and communication efficiency.