| Citation: | GONG Xiaoquan, WU Xiaojun, TANG Jing, et al. Application of r-grid adaptive for shock capturing in discontinuous Galerkin finite element method[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(10): 1889-1898. doi: 10.13700/j.bh.1001-5965.2021.0046(in Chinese)
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The discontinuous Galerkin (DG) method has been widely studied and applied because of its high-order accuracy and applicability to the unstructured grid. However, it still has problems such as poor convergence and limited robustness in numerical simulation flowfield with strong discontinuity. This problem is exacerbated by the uniformly distributed grid, which results in poor shock resolution. In order to solve the problem, an r-grid adaptive method was developed to aggregation and refinement grids in process of DG numerical simulation. The normalized pressure of grid points was taken as an important weight to calculate the driving force of grid points. At the same time, the ratio of the displacement variation of grid points to the initial distance between grid points was taken as another important weight. A Venkatakrishnan limiter suitable for DG was developed. Numerical results of interaction between two parallel NACA0012 airfoils and interaction between two parallel cylinders showed that the DG method based on r-grid adaptation can capture shock clearly and sharply, improve simulation accuracy, and has good convergence and robustness.
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