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A High-OrderDiscontinuous GalerkinMethod for the Two-Dimensional Time-Domain Maxwell’s Equations on Curved Mesh 被引量:1
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作者 hongqiang lu Yida Xu +2 位作者 Yukun Gao Wanglong Qin Qiang Sun 《Advances in Applied Mathematics and Mechanics》 SCIE 2016年第1期104-116,共13页
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 unstru... 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 mesh.The element interfaces on solid boundary are treated in both curved way and straight way.Numerical 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 observed.Both 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 size.More importantly,this CFD-based high-order DG method for the Maxwell’s equations is very suitable for complex geometries. 展开更多
关键词 Maxwell’s equations discontinuous Galerkin method curved mesh radar crosssection.
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A Straightforward hp-Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods 被引量:1
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作者 hongqiang lu Qiang Sun 《Advances in Applied Mathematics and Mechanics》 SCIE 2014年第1期135-144,共10页
In this paper,high-order Discontinuous Galerkin(DG)method is used to solve the two-dimensional Euler equations.A shock-capturing method based on the artificial viscosity technique is employed to handle physical discon... In this paper,high-order Discontinuous Galerkin(DG)method is used to solve the two-dimensional Euler equations.A shock-capturing method based on the artificial viscosity technique is employed to handle physical discontinuities.Numerical tests show that the shocks can be captured within one element even on very coarse grids.The thickness of the shocks is dominated by the local mesh size and the local order of the basis functions.In order to obtain better shock resolution,a straightforward hp-adaptivity strategy is introduced,which is based on the high-order contribution calculated using hierarchical basis.Numerical results indicate that the hp-adaptivity method is easy to implement and better shock resolution can be obtained with smaller local mesh size and higher local order. 展开更多
关键词 HP-ADAPTIVITY shock capturing discontinuous Galerkin
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