Communications on Applied Mathematics and Computation >

2024 , Vol. 6 >Issue 3: 1575 - 1599

DOI: https://doi.org/10.1007/s42967-023-00272-y

ORIGINAL PAPERS

RKDG Methods with Multi-resolution WENO Limiters for Solving Steady-State Problems on Triangular Meshes

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  • 1 State Key Laboratory of Mechanics and Control of Mechanical Structures and Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, Jiangsu, China;
    2 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA;
    3 School of Mathematical Sciences and Fujian Provincial, Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen 361005, Fujian, China

Received date: 2022-11-08

  Revised date: 2023-03-10

  Accepted date: 2023-03-15

  Online published: 2024-12-20

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Abstract

In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constIn this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L2 projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steadystate simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.

Key words： RKDG method; Steady-state problem; Multi-resolution WENO limiter; Triangular mesh; Machine zero

Cite this article

Jun Zhu, Chi-Wang Shu, Jianxian Qiu . RKDG Methods with Multi-resolution WENO Limiters for Solving Steady-State Problems on Triangular Meshes[J]. Communications on Applied Mathematics and Computation, 2024 , 6(3) : 1575 -1599 . DOI: 10.1007/s42967-023-00272-y

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