]*>","")" /> 解Hamilton-Jacobi方程的无振荡局部加密方法

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解Hamilton-Jacobi方程的无振荡局部加密方法

李祥贵,陈光南,江松   

  1. 石油大学应用数学系;应用物理与计算数学研究所;应用物理与计算数学研究所 山东 257062 ;北京 100088 ;北京 100088
  • 出版日期:2001-03-20 发布日期:2001-03-20

李祥贵,陈光南,江松. 解Hamilton-Jacobi方程的无振荡局部加密方法[J]. 数值计算与计算机应用, 2001, 22(3): 217-224.

NON-OSCILLATORY ADAPTIVE LOCAL REFINEMENT METHODS FOR SOLVING HAMILTON-JACOBI EQUATIONS

  1. Li Xianggui (Department of Applied Mathematics, University of Petroleum, Shandong 257062) Chen Guangnan Jiang Song (Institute of Applied Physics and Computational Mathematics, Beijing 100088)
  • Online:2001-03-20 Published:2001-03-20
In this paper, non-oscillatory numerical schemes with high order of accuracy are presented for solving Hamilton-Jacobi equations on structured meshes; An adaptive local refinement method is developed for local regions where solutions of Hamilton-Jacobi equations varies sharply. Numerical results illustrate that the non-oscillatory schemes are stable and the adaptive local refinement method im- proves the accuracy of numerical solutions and the resolution for discontinuity.
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[1] Berger M, Colella P, Local adaptive mesh refinement for shock hydrodynamics, J.Comput.Phys., 82 (1989), 62-84.
[2] Berger M, Leveque J L, Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems, SIAM J. Numer. Anal., 35 (1998), 2298-2316.
[3] Ewing R E, Lasarov R D, Vassilerski P 5, Local refinement techniques for elliptic problems on cell-centered grids. Math. of Computation, 56 (1991), 437-461.
[4] Harten A, Chatravarthy S R, Multi-dimensional ENO schemes for general geometries, ICASE Report No.71-76, (1991).
[5] Hock P, Rascle M, Hamilton-Jacobi equation on a manifold and applications to mesh generation or refinement. To appear
[6] un 5, Xin Z, relaxation schemes for curvature-dependent front propagation, Comm. Pure Appl. Math., 52 (1999), 1587-1615.
[7] Lafon F, Osher 5, High order two dimensional nonoscillatory methods for solving Hamilton-Jacobi scalar equations, J. Comput. Phys., 123 (1996), 235-253.
[8] Lions P L , Generalized Solutions of Hamilton-Jacobi Equations, Pitman, London, 1982.
[9] Osher 5, Fedkiw R P, Level Set Method, UCLA , preprint 00-08,USA.
[10] Osher 5, Shu C W, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations, SIAM J.Numer.Anal., 28 (1991), 907-922.
[11] Pedrosa O, Use of Hybrid Grid in Reservoir Simulation, Ph.D.thesis, Stanford University, 1984.
[12] Peng D, Merriman B, Osher 5, Zhao H, Kang M, A PDE based fast local level set method, J.Comput.Phys., 155 (1999), 410-438.
[13] Sethian J A, Level Set Methods and Fast Marching Methods, Cambridge Univ. Perss, 1999.
[14] Shu C W, Osher 5, Efficient implementation of essentially nonoscillatory shock-capturing schemes, J.Comput.Phys., 77 (1988), 439-471.
[15] Sussman M, Fatemi E, An efficient interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow, SIAM J. Sci. Comput., 20 (1999), 1165-1191.
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