A multi-limiter method for simulating complex flows on large grids

Abstract

This paper presents a novel method for aiding the convergence of complex flows simulations on large grids. In this work, large grids are considered those that are of the order of 100 × 106 cells or more. These large grids, which, for example, model the flow around a powered airplane, are typically difficult to generate and modify. If a high-fidelity solution is needed, as in the case of predicting sonic boom, the amount of numerical dissipation must be minimized. This reduced dissipation, however, may result in solution divergence, triggered by improperly resolved large gradients due to grid deficiency. Using a highly dissipative limiter for the entire grid could avoid solution divergence, but the resulting solution may be less accurate. To avoid the loss of solution accuracy due to too much numerical dissipation, we present an approach in which the flow solver uses two limiters: a low-dissipation limiter for the vast majority of the computational domain, and a high-dissipation limiter for the regions where the grid is not adequate for capturing the flow variation and would otherwise lead to the divergence of the solution. The paper demonstrates that (1) the overall solution is not modified by the local use of the high-dissipation limiter, and (2) for a case in which the use of low-dissipation limiter (Venkatakrishnan) resulted in solution divergence, a converged solution is obtained by using the low-dissipation limiter on the vast majority of the grid and a high-dissipation limiter (van Albada) on the region where the mesh was problematic. The effect of a local high-dissipation limiter on the overall solution is explored on a double-wedge canonical airfoil. The multi-limiter approach is then used to predict the near field pressure of the X-59 airplane.