The optimal nearly-analytic discrete(ONAD) method is a new numerical method developed in recent years for solving the wave equation.Compared with other methods,such as popularly-used finite-difference methods,the ONAD...The optimal nearly-analytic discrete(ONAD) method is a new numerical method developed in recent years for solving the wave equation.Compared with other methods,such as popularly-used finite-difference methods,the ONAD method can effectively suppress the numerical dispersion when coarse grids are used.In this paper,the ONAD method is extended to solve the 2-dimensional SH-wave equation in the spherical coordinates.To investigate the accuracy and the efficiency of the ONAD method,we compare the numerical results calculated by the ONAD method and other methods for both the homogeneous model and the inhomogeneous IASP91 model.The comparisons indicate that the ONAD method for solving the SH-wave equation in the spherical coordinates has the advantages of less numerical dispersion,small memory requirement for computer codes,and fast calculation.As an application,we use the ONAD method to simulate the SH-wave propagating between the Earth's surface and the core-mantle boundary(CMB).Meanwhile,we investigate the SH-wave propagating in the mantle through analyzing the wave-field snapshots in different times and synthetic seismograms.展开更多
A discontinuous Galerkin method based on an artificial viscosity model is investigated in the context of the simulation of compressible turbulence. The effects of artificial viscosity on shock capturing ability, broad...A discontinuous Galerkin method based on an artificial viscosity model is investigated in the context of the simulation of compressible turbulence. The effects of artificial viscosity on shock capturing ability, broadband accuracy and under-resolved instability are examined combined with various orders and mesh resolutions. For shock-dominated flows, the superior accuracy of high order methods in terms of discontinuity resolution are well retained compared with lower ones. For under-resolved simulations, the artificial viscosity model is able to enhance stability of the eighth order discontinuous Galerkin method despite of detrimental influence for accuracy. For multi-scale flows, the artificial viscosity model demonstrates biased numerical dissipation towards higher wavenumbers. Capability in terms of boundary layer flows and hybrid meshes is also demonstrated.It is concluded that the fourth order artificial viscosity discontinuous Galerkin method is comparable to typical high order finite difference methods in the literature in terms of accuracy for identical number of degrees of freedom, while the eighth order is significantly better unless the under-resolved instability issue is raised. Furthermore, the artificial viscosity discontinuous Galerkin method is shown to provide appropriate numerical dissipation as compensation for turbulent kinetic energy decaying on moderately coarse meshes, indicating good potentiality for implicit large eddy simulation.展开更多
基金supported by National Science Fund of Distinguished Young Scholars of China(Grant No. 40725012)40821002)National Natural Science Foundation of China (Grant No. 41074073)
文摘The optimal nearly-analytic discrete(ONAD) method is a new numerical method developed in recent years for solving the wave equation.Compared with other methods,such as popularly-used finite-difference methods,the ONAD method can effectively suppress the numerical dispersion when coarse grids are used.In this paper,the ONAD method is extended to solve the 2-dimensional SH-wave equation in the spherical coordinates.To investigate the accuracy and the efficiency of the ONAD method,we compare the numerical results calculated by the ONAD method and other methods for both the homogeneous model and the inhomogeneous IASP91 model.The comparisons indicate that the ONAD method for solving the SH-wave equation in the spherical coordinates has the advantages of less numerical dispersion,small memory requirement for computer codes,and fast calculation.As an application,we use the ONAD method to simulate the SH-wave propagating between the Earth's surface and the core-mantle boundary(CMB).Meanwhile,we investigate the SH-wave propagating in the mantle through analyzing the wave-field snapshots in different times and synthetic seismograms.
基金supported by the National Natural Science Foundation of China(Grant No.11402016)the Fundamental Research Funds for the Central Universities(Grant Nos.50100002014105020&50100002015105033)
文摘A discontinuous Galerkin method based on an artificial viscosity model is investigated in the context of the simulation of compressible turbulence. The effects of artificial viscosity on shock capturing ability, broadband accuracy and under-resolved instability are examined combined with various orders and mesh resolutions. For shock-dominated flows, the superior accuracy of high order methods in terms of discontinuity resolution are well retained compared with lower ones. For under-resolved simulations, the artificial viscosity model is able to enhance stability of the eighth order discontinuous Galerkin method despite of detrimental influence for accuracy. For multi-scale flows, the artificial viscosity model demonstrates biased numerical dissipation towards higher wavenumbers. Capability in terms of boundary layer flows and hybrid meshes is also demonstrated.It is concluded that the fourth order artificial viscosity discontinuous Galerkin method is comparable to typical high order finite difference methods in the literature in terms of accuracy for identical number of degrees of freedom, while the eighth order is significantly better unless the under-resolved instability issue is raised. Furthermore, the artificial viscosity discontinuous Galerkin method is shown to provide appropriate numerical dissipation as compensation for turbulent kinetic energy decaying on moderately coarse meshes, indicating good potentiality for implicit large eddy simulation.
