Postlimiters and Simple Dirty-Cell Detection for Three-Dimensional Unstructured (Unlimited) Aerodynamic Simulations

Abstract

The postlimiter (simple a posteriori slope limiter) is an anti-slope-limiting mechanism to preserve nominal second order in space as much as possible. This technique has been demonstrated to increase resolutions of two-dimensional simulations up to four times in each dimension [Kitamura, K., and Hashimoto, A., “Simple a posteriori Slope Limiter (Post Limiter) for High Resolution and Efficient Flow Computations,” Journal of Computational Physics, Vol. 341, July 2017, pp. 313–340]. This paper extends the postlimiter to three dimensions with an emphasis on ”dirty” (meaning ill-shaped) cells, which arise in practical three-dimensional (3-D) unstructured grids over complex geometries. Gradient accuracy is known to significantly deteriorate on dirty cells, and a slope limiter needs to be applied. However, the original postlimiter does not recognize dirty cells and deactivates a slope limiter. To address this issue, a simple dirty-cell detection method is proposed and incorporated into the postlimiter. The 3-D version of postlimiter (referred to as “postlimiter 3”) is successfully incorporated into fast aerodynamic routine (FaSTAR), a 3-D unstructured grid flow solver is developed at the Japan Aerospace Exploration Agency. Postlimiter 3 can handle general 3-D unstructured grids. Numerical examples support its efficiency, accuracy, robustness, and applicability to a wide spectrum of aerodynamic problems of high engineering importance.