The semi-Lagrangian advection scheme is implemented on a new quasi-uniform overset （Yin-Yang） grid on the sphere. The Yin-Yang grid is a newly developed grid system in spherical geometry with two perpendicularly-ori...The semi-Lagrangian advection scheme is implemented on a new quasi-uniform overset （Yin-Yang） grid on the sphere. The Yin-Yang grid is a newly developed grid system in spherical geometry with two perpendicularly-oriented latitude-longitude grid components （called Yin and Yang respectively） that overlapp each other, and this effectively avoids the coordinate singularity and the grid convergence near the poles. In this overset grid, the way of transferring data between the Yin and Yang components is the key to maintaining the accuracy and robustness in numerical solutions. A numerical interpolation for boundary data exchange, which maintains the accuracy of the original advection scheme and is computationally efficient, is given in this paper. A standard test of the solid-body advection proposed by Williamson is carried out on the Yin-Yang grid. Numerical results show that the quasi-uniform Yin-Yang grid can get around the problems near the poles, and the numerical accuracy in the original semi-Lagrangian scheme is effectively maintained in the Yin-Yang grid.展开更多
We give a brief discussion of some of the contributions of Peter Lax to Com- putational Fluid Dynamics. These include the Lax-Friedrichs and Lax-Wendroff numerical schemes. We also mention his collaboration in the 198...We give a brief discussion of some of the contributions of Peter Lax to Com- putational Fluid Dynamics. These include the Lax-Friedrichs and Lax-Wendroff numerical schemes. We also mention his collaboration in the 1983 HLL Riemann solver. We de- velop two-dimensional Lax-Friedrichs and Lax-Wendroff schemes for the Lagrangian form of the Euler equations on triangular grids. We apply a composite scheme that uses a Lax- Friedrichs time step as a dissipative filter after several Lax-Wendroff time steps. Numerical results for Noh＇s infinite strength shock problem, the Sedov blast wave problem, and the Saltzman piston problem are presented.展开更多
A 3D dynamic core of the non-hydrostatic model GRAPES（Global/Regional Assimilation and Prediction System） is developed on the Yin-Yang grid to address the polar problem and to enhance the computational efficiency. T...A 3D dynamic core of the non-hydrostatic model GRAPES（Global/Regional Assimilation and Prediction System） is developed on the Yin-Yang grid to address the polar problem and to enhance the computational efficiency. Three-dimensional Coriolis forcing is introduced to the new core, and full representation of the Coriolis forcing makes it straightforward to share code between the Yin and Yang subdomains. Similar to that in the original GRAPES model, a semi-implicit semi-Lagrangian scheme is adopted for temporal integration and advection with additional arrangement for cross-boundary transport. Under a non-centered second-order temporal and spatial discretization, the dry nonhydrostatic frame is summarized as the solution of an elliptical problem. The resulting Helmholtz equation is solved with the Generalized Conjugate Residual solver in cooperation with the classic Schwarz method. Even though the coefficients of the equation are quite different from those in the original model, the computational procedure of the new core is just the same. The bi-cubic Lagrangian interpolation serves to provide Dirichlet-type boundary conditions with data transfer between the subdomains. The dry core is evaluated with several benchmark test cases, and all the tests display reasonable numerical stability and computing performance. Persistency of the balanced flow and development of both the mountain-induced Rossby wave and Rossby–Haurwitz wave confirms the appropriate installation of the 3D Coriolis terms in the semi-implicit semi-Lagrangian dynamic core on the Yin-Yang grid.展开更多
The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view. In this paper, the typical spherical sym- metry properties of the numerical schemes are discus...The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view. In this paper, the typical spherical sym- metry properties of the numerical schemes are discussed, and an area weighted scheme is extended from a Lagrangian method to an arbitrary Lagrangian and Eulerian （ALE） method. Numerical results are presented to compare three discrete configurations, i.e., the control volume scheme, the area weighted scheme, and the plane scheme with the addition of a geometrical source. The fact that the singularity arises from the geometri- cal source term in the plane scheme is illustrated. A suggestion for choosing the discrete formulation is given when the strong shock wave problems are simulated.展开更多
An overset grid methodology is developed for the fully coupled analysis of fluid-structure interaction (FSI) problems. The overset grid approach alleviates some of the computational geometry difficulties traditionally...An overset grid methodology is developed for the fully coupled analysis of fluid-structure interaction (FSI) problems. The overset grid approach alleviates some of the computational geometry difficulties traditionally associated with Arbitrary-Lagrangian-Eulerian (ALE) based, moving mesh methods for FSI. Our partitioned solution algorithm uses separate solvers for the fluid (finite volume method) and the structure (finite element method), with mesh motion computed only on a subset of component grids of our overset grid assembly. Our results indicate a significant reduction in computational cost for the mesh motion, and element quality is improved. Numerical studies of the benchmark test demonstrate the benefits of our overset mesh method over traditional approaches.展开更多
基金This paper is sponsored by the National Natural Science Foundation of China （No. 40575050） the National Key Program for Developing Basic Reseach （＂973＂） （No. 2004CB418306）.
文摘The semi-Lagrangian advection scheme is implemented on a new quasi-uniform overset （Yin-Yang） grid on the sphere. The Yin-Yang grid is a newly developed grid system in spherical geometry with two perpendicularly-oriented latitude-longitude grid components （called Yin and Yang respectively） that overlapp each other, and this effectively avoids the coordinate singularity and the grid convergence near the poles. In this overset grid, the way of transferring data between the Yin and Yang components is the key to maintaining the accuracy and robustness in numerical solutions. A numerical interpolation for boundary data exchange, which maintains the accuracy of the original advection scheme and is computationally efficient, is given in this paper. A standard test of the solid-body advection proposed by Williamson is carried out on the Yin-Yang grid. Numerical results show that the quasi-uniform Yin-Yang grid can get around the problems near the poles, and the numerical accuracy in the original semi-Lagrangian scheme is effectively maintained in the Yin-Yang grid.
基金performed under the auspices of the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No.DE-AC52-06NA25396supported in part by the Czech Science Foundation GrantP205/10/0814the Czech Ministry of Education grants MSM 6840770022 and LC528
文摘We give a brief discussion of some of the contributions of Peter Lax to Com- putational Fluid Dynamics. These include the Lax-Friedrichs and Lax-Wendroff numerical schemes. We also mention his collaboration in the 1983 HLL Riemann solver. We de- velop two-dimensional Lax-Friedrichs and Lax-Wendroff schemes for the Lagrangian form of the Euler equations on triangular grids. We apply a composite scheme that uses a Lax- Friedrichs time step as a dissipative filter after several Lax-Wendroff time steps. Numerical results for Noh＇s infinite strength shock problem, the Sedov blast wave problem, and the Saltzman piston problem are presented.
基金supported by the National Natural Science Foundation of China (Grant No. 41175095)the National Key Technology R&D Program(Grant No. 2012BAC22B01)a research project of the Chinese Academy of Meteorological Sciences (Grant No. 2014Z001)
文摘A 3D dynamic core of the non-hydrostatic model GRAPES（Global/Regional Assimilation and Prediction System） is developed on the Yin-Yang grid to address the polar problem and to enhance the computational efficiency. Three-dimensional Coriolis forcing is introduced to the new core, and full representation of the Coriolis forcing makes it straightforward to share code between the Yin and Yang subdomains. Similar to that in the original GRAPES model, a semi-implicit semi-Lagrangian scheme is adopted for temporal integration and advection with additional arrangement for cross-boundary transport. Under a non-centered second-order temporal and spatial discretization, the dry nonhydrostatic frame is summarized as the solution of an elliptical problem. The resulting Helmholtz equation is solved with the Generalized Conjugate Residual solver in cooperation with the classic Schwarz method. Even though the coefficients of the equation are quite different from those in the original model, the computational procedure of the new core is just the same. The bi-cubic Lagrangian interpolation serves to provide Dirichlet-type boundary conditions with data transfer between the subdomains. The dry core is evaluated with several benchmark test cases, and all the tests display reasonable numerical stability and computing performance. Persistency of the balanced flow and development of both the mountain-induced Rossby wave and Rossby–Haurwitz wave confirms the appropriate installation of the 3D Coriolis terms in the semi-implicit semi-Lagrangian dynamic core on the Yin-Yang grid.
基金Project supported by the National Natural Science Foundation of China(Nos.11471048 and U1630249)the Foundation of Chinese Academy of Engineering Physics(No.2014A0202010)the Foundation of Laboratory of Computational Physics(No.9140C690202140C69293)
文摘The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view. In this paper, the typical spherical sym- metry properties of the numerical schemes are discussed, and an area weighted scheme is extended from a Lagrangian method to an arbitrary Lagrangian and Eulerian （ALE） method. Numerical results are presented to compare three discrete configurations, i.e., the control volume scheme, the area weighted scheme, and the plane scheme with the addition of a geometrical source. The fact that the singularity arises from the geometri- cal source term in the plane scheme is illustrated. A suggestion for choosing the discrete formulation is given when the strong shock wave problems are simulated.
文摘An overset grid methodology is developed for the fully coupled analysis of fluid-structure interaction (FSI) problems. The overset grid approach alleviates some of the computational geometry difficulties traditionally associated with Arbitrary-Lagrangian-Eulerian (ALE) based, moving mesh methods for FSI. Our partitioned solution algorithm uses separate solvers for the fluid (finite volume method) and the structure (finite element method), with mesh motion computed only on a subset of component grids of our overset grid assembly. Our results indicate a significant reduction in computational cost for the mesh motion, and element quality is improved. Numerical studies of the benchmark test demonstrate the benefits of our overset mesh method over traditional approaches.
基金Supported by Doctoral Fund of Henan Polytechnic University(Grant No.60707/011)National Natural Science Foundation of China(Grant No.11402266)the Fund of the State Key Laboratory of Disaster Prevention&Mitigation of Explosion & Impact(PLA University of Science and Technology,Grant No.DPMEIKF201401)
