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An Efficient Nonlinear Multigrid Solver for the Simulation of Rarefied Gas Cavity Flow
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作者 Zhicheng Hu guanghan li 《Communications in Computational Physics》 SCIE 2023年第7期357-391,共35页
We study efficient simulation of steady state for multi-dimensional rarefied gas flow,which is modeled by the Boltzmann equation with BGK-type collision term.A nonlinear multigrid solver is proposed to resolve the eff... We study efficient simulation of steady state for multi-dimensional rarefied gas flow,which is modeled by the Boltzmann equation with BGK-type collision term.A nonlinear multigrid solver is proposed to resolve the efficiency issue by the following approaches.The unified framework of numerical regularized moment method is first adopted to derive the high-quality discretization of the underlying problem.A fast sweeping iteration is introduced to solve the derived discrete problem more efficiently than the usual time-integration scheme on a single level grid.Taking it as the smoother,the nonlinear multigrid solver is then established to significantly improve the convergence rate.The OpenMP-based parallelization is applied in the implementation to further accelerate the computation.Numerical experiments for two lid-driven cavity flows and a bottom-heated cavity flow are carried out to investigate the performance of the resulting nonlinear multigrid solver.All results show the wonderful efficiency and robustness of the solver for both first-and second-order spatial discretization. 展开更多
关键词 Boltzmann equation moment method MULTIGRID rarefied gas flow steady state
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Closed Geodesics and Volume Growth of Open Manifolds with Sectional Curvature Bounded from Below 被引量:1
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作者 Yi SHI guanghan li Chuanxi WU 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2014年第1期93-100,共8页
In this paper, the relationship between the existence of closed geodesics and the volume growth of complete noncompact Riemannian manifolds is studied. First the authors prove a diffeomorphic result of such an n-m2nif... In this paper, the relationship between the existence of closed geodesics and the volume growth of complete noncompact Riemannian manifolds is studied. First the authors prove a diffeomorphic result of such an n-m2nifold with nonnegative sectional curvature, which improves Marenich-Toponogov's theorem. As an application, a rigidity theorem is obtained for nonnegatively curved open manifold which contains a clesed geodesic. Next the authors prove a theorem about the nonexistence of closed geodesics for Riemannian manifolds with sectional curvature bounded from below by a negative constant. 展开更多
关键词 Closed geodesic Sectional curvature Volume growth
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