Mesh Adaptation for Computational Fluid Dynamics, Volume 2

3Multi-rate Time Advancing

We have seen that for steady problems, flows with singularities can be computed with second-order convergence by mesh adaptative strategies, that is, the best possible convergence when scheme’s truncation is of second order. We have pointed out that mesh-adaptative strategies combined with usual time advancing seem to have a convergence barrier limiting the convergence order to a number notably smaller than two. One way to recover the convergence order partly or totally is through multi-rate time stepping. This chapter focuses on showing this property and describing a particular multi-rate method applying easily to unstructured finite-volume approximation. We discuss the details of its implementation, in particular with massive parallelism. Two examples show that, even without mesh adaptation, the method increases efficiency.

3.1. Introduction

A frequent configuration in CFD calculations combines an explicit time-advancing scheme for accuracy and a computational grid with a very small portion of much smaller elements than in the remaining mesh.

A first example is the hybrid RANS/LES simulation of high Reynolds number flows around bluff bodies. In that case, very thin boundary layers must be addressed with extremely small cells. When applying explicit time advancing, the computation is penalized by the very small time-step to be applied (CFL number close to unity). But the boundary layer is not the only interesting region of the computational domain. ...