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A High-OrderDiscontinuous GalerkinMethod for the Two-Dimensional Time-Domain Maxwell’s Equations on curved mesh

Advances in Applied Mathematics and Mechanics 2016年第1期8卷 104-116页

作者： Hongqiang Lu Yida Xu Yukun Gao Wanglong Qin Qiang Sun College of Aerospace Engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016China

In this paper,a DG(Discontinuous Galerkin)method which has been widely employed in CFD(Computational Fluid Dynamics)is used to solve the twodimensional time-domain Maxwell’s equations for complex geometries on unstructured *** element interfaces on solid boundary are treated in both curved way and straight *** tests are performed for both benchmark problems and complex cases with varying orders on a series of grids,where the high-order convergence in accuracy can be *** the curved and the straight solid boundary implementation can give accurate RCS(Radar Cross-Section)results with sufficiently small mesh size,but the curved solid boundary implementation can significantly improve the accuracy when using relatively large mesh *** importantly,this CFD-based high-order DG method for the Maxwell’s equations is very suitable for complex geometries.

关键词： Maxwell’s equations discontinuous Galerkin method curved mesh radar crosssection.

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An h-Adaptivity DG Method on Locally curved Tetrahedral mesh for Solving Compressible Flows

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Transactions of Nanjing University of Aeronautics and Astronautics 2020年第5期37卷 702-712页

作者： AN Wei HUANG Zenghui LYU Hongqiang College of Aerospace Engineering Nanjing University of Aeronautics and AstronauticsNanjing 210016P.R.China Key Laboratory of Aerodynamic Noise Control China Aerodynamics Research and Development CenterMianyang 621000P.R.China State Key Laboratory of Aerodynamics China Aerodynamics Research and Development CenterMianyang 621000P.R.China

For the numerical simulation of compressible flows,normally different mesh sizes are expected in different *** example,smaller mesh sizes are required to improve the local numerical resolution in the regions where the physical variables vary violently(for example,near the shock waves or in the boundary layers)and larger elements are expected for the regions where the solution is smooth.h-adaptive mesh has been widely used for complex ***,there are two difficulties when employing h-adaptivity for high-order discontinuous Galerkin(DG)***,locally curved elements are required to precisely match the solid boundary,which significantly increases the difficulty to conduct the"refining"and"coarsening"operations since the curved information has to be ***,h-adaptivity could break the partition balancing,which would significantly affect the efficiency of parallel *** this paper,a robust and automatic h-adaptive method is developed for high-order DG methods on locally curved tetrahedral mesh,for which the curved geometries are maintained during the ***,the reallocating and rebalancing of the computational loads on parallel clusters are conducted to maintain the parallel *** results indicate that the introduced h-adaptive method is able to generate more reasonable mesh according to the structure of flow-fields.

关键词： h-adaptivity discontinuous Galerkin(DG)method curved mesh tetrahedral mesh compressible flows

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