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| 基于p4est的自适应间断伽辽金方法研究 |
| Discontinuous Galerkin method on adaptive Cartesian grid based on p4set |
| 投稿时间：2024-06-27 修订日期：2024-08-15 |
| DOI： |
| 中文关键词: DG 自适应笛卡尔网格 新型混合限制器 激波捕捉 |
| 英文关键词:DG adaptive Cartesian grid new hybrid limiter shock capturing |
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| 中文摘要: |
| 间断伽辽金(DG)方法因其高精度、易并行等优良特性而得到了广泛的应用，网格自适应(AMR)技术已被广泛采用，与同等级全局细化相比，AMR可以大大降低计算量，提高计算效率。本文结合DG和AMR的优点，基于p4est开源库将一种新型混合限制器应用到自适应笛卡尔网格上的DG方法中，该限制器具有高精度、紧凑性和鲁棒性且其构造非常简单，并通过激波探测器来捕捉激波，本文比较了新型混合限制器和总变分有界(TVB)限制器的性能，结果表明前者的性能明显优于后者，通过一系列Euler方程和Navier-Stokes方程数值算例验证了本文方法的可行性和高效性，结果表明新型混合限制器在AMRDG方法中表现出良好的性能，具有较小的耗散和很好的激波捕捉能力，在保证高精度的前提下大大提高了计算效率。 |
| 英文摘要: |
| The discontinuous Galerkin (DG) method has been widely adopted due to its excellent properties such as high accuracy and ease of parallelization, the adaptive mesh refinement (AMR) technique has been widely adopted to improve computational efficiency with much less computational cost compared with uniform global refinement to the same level with AMR. This paper combines the advantages of DG and AMR, a new hybrid limiter is applied to the DG method on adaptive Cartesian grid based on p4est, an opensource library. The limiter exhibits advantages of high precision, compactness, robustness, and ease of implementation. The shock wave capturing with shock indictor and the performance of the new hybrid limiter is compared with that of the total variational bounded (TVB) limiter in this paper, the result shows that the performance of the former is significantly better than that of the latter. A series of numerical examples for Euler equations and Navier-Stokes equations are used to verify the feasibility and efficiency of the proposed method, the results show that the new hybrid limiter performs very well in the AMRDG method, it has lower dissipation and great shock capture ability, and the computational efficiency is greatly improved while the accuracy is guaranteed. |
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