A class of multidomain hybrid methods of direct discontinuous Galerkin(DDG)methods and central difference(CD)schemes for the viscous terms is pro-posed in this paper.Both conservative and nonconservative coupling mode...A class of multidomain hybrid methods of direct discontinuous Galerkin(DDG)methods and central difference(CD)schemes for the viscous terms is pro-posed in this paper.Both conservative and nonconservative coupling modes are dis-cussed.To treat the shock wave,the nonconservative coupling mode automatically switch to conservative coupling mode to preserve the conservative property when discontinuities pass through the artificial interface.To maintain the accuracy of the hybrid methods,the Lagrange interpolation polynomials and their derivatives are reconstructed to handle the coupling cells in the DDG subdomain,while the values of ghost points for the CD subdomain are calculated by the approximate polynomials from the DDG methods.The linear stabilities of these methods are demonstrated in detail through von-Neumann analysis.The multidomain hybrid DDG and CD meth-ods are then extended to one-and two-dimensional hyperbolic-parabolic equations.Numerical results validate that the multidomain hybrid methods are high-order ac-curate in the smooth regions,robust for viscous shock simulations and capable to save computational cost.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12001031).
文摘A class of multidomain hybrid methods of direct discontinuous Galerkin(DDG)methods and central difference(CD)schemes for the viscous terms is pro-posed in this paper.Both conservative and nonconservative coupling modes are dis-cussed.To treat the shock wave,the nonconservative coupling mode automatically switch to conservative coupling mode to preserve the conservative property when discontinuities pass through the artificial interface.To maintain the accuracy of the hybrid methods,the Lagrange interpolation polynomials and their derivatives are reconstructed to handle the coupling cells in the DDG subdomain,while the values of ghost points for the CD subdomain are calculated by the approximate polynomials from the DDG methods.The linear stabilities of these methods are demonstrated in detail through von-Neumann analysis.The multidomain hybrid DDG and CD meth-ods are then extended to one-and two-dimensional hyperbolic-parabolic equations.Numerical results validate that the multidomain hybrid methods are high-order ac-curate in the smooth regions,robust for viscous shock simulations and capable to save computational cost.
