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Multi-dimensional limiting process for finite volume methods on unstructured grids

机译：非结构网格上有限体积方法的多维限制过程

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摘要

This paper deals with a robust, accurate and efficient multi-dimensional limiting strategy on three-dimensional unstructured grids within the framework of finite volume method. The present limiting strategy is on the line of continuous efforts to extend the multi-dimensional limiting process (MLP) onto three-dimensional tetrahedral grids, which was originally proposed on structured and triangular grids. In previous works, it was observed that the MLP limiting shows several superior characteristics, such as efficient control of multi-dimensional oscillations and accurate capture of both discontinuous and continuous multi-dimensional flow features, on triangular as well as structured grids. The design principle of the MLP limiters is based on the multi-dimensional limiting condition and the maximum principle, which can ensure multi-dimensional monotonicity through the global/local l_∞ stability. Consequently, it can be shown that the MLP limiting does satisfy the local extremum diminishing (LED) condition in a truly multi-dimensional way. The present MLP slope limiters are formulated into the setting of the three-dimensional Euler system, and are refined to improve convergence characteristics for steady state problems without compromising the accuracy of computed results. Through various numerical analyses and computations, it is demonstrated that the proposed MLP limiters provide the same level of successful performances previously observed on triangular and structured grids.
机译：本文在有限体积方法的框架内，针对三维非结构化网格提出了一种鲁棒，准确，高效的多维限制策略。当前的限制策略是在不断努力的基础上，将多维限制过程（MLP）扩展到三维四面体网格上，该网格最初是在结构化网格和三角形网格上提出的。在以前的工作中，已经观察到MLP限制显示了几个优越的特性，例如有效控制多维振荡以及在三角形以及结构化网格上准确捕获不连续和连续的多维流特征。 MLP限制器的设计原理基于多维限制条件和最大原理，可以通过全局/局部l_∞稳定性来确保多维单调性。因此，可以证明，MLP限制确实以真正的多维方式满足了局部极值减小（LED）条件。当前的MLP斜率限制器被公式化为三维Euler系统的设置，并经过改进以改善稳态问题的收敛特性而不会影响计算结果的准确性。通过各种数值分析和计算，证明了所提出的MLP限制器可提供先前在三角形和结构化网格上观察到的相同水平的成功性能。

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