A nodal discontinuous Galerkin formulation based on Lagrange polynomials basis is used to simulate the acoustic wave propagation. Its dispersion and dissipation properties for the advection equation are investigated b...A nodal discontinuous Galerkin formulation based on Lagrange polynomials basis is used to simulate the acoustic wave propagation. Its dispersion and dissipation properties for the advection equation are investigated by utilizing an eigenvalue analysis. Two test problems of wave propagation with initial disturbance consisting of a Gaussian profile or rectangular pulse are performed. And the performance of the schemes in short,intermediate,and long waves is evaluated. Moreover,numerical results between the nodal discontinuous Galerkin method and finite difference type schemes are compared,which indicate that the numerical solution obtained using nodal discontinuous Galerkin method with a pure central flux has obviously high frequency oscillations for initial disturbance consisting of a rectangular pulse,which is the same as those obtained using finite difference type schemes without artificial selective damping. When an upwind flux is adopted,spurious waves are eliminated effectively except for the location of discontinuities. When a limiter is used,the spurious short waves are almost completely removed. Therefore,the quality of the computed solution has improved.展开更多
In this paper,Nodal discontinuous Galerkin method is presented to approxi-mate Time-domain Lorentz model equations in meta-materials.The upwind flux is cho-sen in spatial discrete scheme.Low-storage five-stage fourth-...In this paper,Nodal discontinuous Galerkin method is presented to approxi-mate Time-domain Lorentz model equations in meta-materials.The upwind flux is cho-sen in spatial discrete scheme.Low-storage five-stage fourth-order explicit Runge-Kutta method is employed in time discrete scheme.An error estimate of accuracy O(τ^(4)+h^(n))is proved under the L^(2)-norm,specially O(τ^(4)+h^(n+1))can be obtained.Numerical exper-iments for transverse electric(TE)case and transverse magnetic(TM)case are demon-strated to verify the stability and the efficiency of the method in low and higher wave frequency.展开更多
基金Supported by the National Natural Science Foundation of China(51106099,50976072)the Leading Academic Discipline Project of Shanghai Municipal Education Commission(J50501)
文摘A nodal discontinuous Galerkin formulation based on Lagrange polynomials basis is used to simulate the acoustic wave propagation. Its dispersion and dissipation properties for the advection equation are investigated by utilizing an eigenvalue analysis. Two test problems of wave propagation with initial disturbance consisting of a Gaussian profile or rectangular pulse are performed. And the performance of the schemes in short,intermediate,and long waves is evaluated. Moreover,numerical results between the nodal discontinuous Galerkin method and finite difference type schemes are compared,which indicate that the numerical solution obtained using nodal discontinuous Galerkin method with a pure central flux has obviously high frequency oscillations for initial disturbance consisting of a rectangular pulse,which is the same as those obtained using finite difference type schemes without artificial selective damping. When an upwind flux is adopted,spurious waves are eliminated effectively except for the location of discontinuities. When a limiter is used,the spurious short waves are almost completely removed. Therefore,the quality of the computed solution has improved.
基金supported by NSFC.China(NOs.11201501,11571389)the Program for Innovation Research in Central University of Finance and Economics+1 种基金The second author is Supported by NSFC.China(Grant Nos.11471296,11101384)the third author is supported in part by Defense Industrial Technology Development Program(B1520133015).
文摘In this paper,Nodal discontinuous Galerkin method is presented to approxi-mate Time-domain Lorentz model equations in meta-materials.The upwind flux is cho-sen in spatial discrete scheme.Low-storage five-stage fourth-order explicit Runge-Kutta method is employed in time discrete scheme.An error estimate of accuracy O(τ^(4)+h^(n))is proved under the L^(2)-norm,specially O(τ^(4)+h^(n+1))can be obtained.Numerical exper-iments for transverse electric(TE)case and transverse magnetic(TM)case are demon-strated to verify the stability and the efficiency of the method in low and higher wave frequency.
