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
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
基金National Natural Science Foundation of China:No.11272152 and Aeronautical Science Foundation of China:No.20101552018.
文摘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.
基金the foundation of the National Natural Science Foundation of China(11272152)the Aeronautical Science Foundation of China(20101552018)。
文摘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.
