Numerical Solution of the Polymer System by Front Tracking
作者： V. Haugse , K. H. Karlsen , K.-A. Lie , J. R. Natvig
关键词: Riemann hypothesis 、 Eigenvalues and eigenvectors 、 Discretization 、 Mathematical analysis 、 Piecewise 、 Hyperbolic systems 、 Front (oceanography) 、 Tracking (particle physics) 、 Constant (mathematics) 、 Mathematics 、 Calculus
摘要: The paper describes the application of front tracking to polymer system, an example a nonstrictly hyperbolic system. Front computes piecewise constant approximations based on approximate Riemann solutions and exact waves. It is well known that method may introduce blowup initial total variation for data along curve where two eigenvalues system are identical. demonstrated by numerical examples converges correct solution after finite time, this time decreases with discretization parameter.
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sci-hub.se 参考文章(26)
Knut‐Andreas Lie, Front tracking for one-dimensional quasilinear hyperbolic equations with variable coefficients Numerical Algorithms. ,vol. 24, pp. 275- 298 ,(2000) , 10.1023/A:1019157629824
Knut-Andreas Lie, A Dimensional Splitting Method for Quasilinear Hyperbolic Equations with Variable Coefficients Bit Numerical Mathematics. ,vol. 39, pp. 683- 700 ,(1999) , 10.1023/A:1022339223716
Runar Holdahl, Helge Holden, Knut-Andreas Lie, UNCONDITIONALLY STABLE SPLITTING METHODS FOR THE SHALLOW WATER EQUATIONS Bit Numerical Mathematics. ,vol. 39, pp. 451- 472 ,(1999) , 10.1023/A:1022366502335
Guang-Shan Jiang, Eitan Tadmor, Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws SIAM Journal on Scientific Computing. ,vol. 19, pp. 1892- 1917 ,(1998) , 10.1137/S106482759631041X
Eli L Isaacson, J.Blake Temple, Analysis of a singular hyperbolic system of conservation laws Journal of Differential Equations. ,vol. 65, pp. 250- 268 ,(1986) , 10.1016/0022-0396(86)90037-9
J.A. Sethian, A.J. Chorin, Paul Concus, Numerical Solution of the Buckley-Leverett Equations annual simulation symposium. ,(1983) , 10.2523/12254-MS
Nils Henrik Risebro, A front-tracking alternative to the random choice method Proceedings of the American Mathematical Society. ,vol. 117, pp. 1125- 1139 ,(1993) , 10.1090/S0002-9939-1993-1120511-X
Helge Holden, Knut-Andreas Lie, Nils Henrik Risebro, An Unconditionally Stable Method for the Euler Equations Journal of Computational Physics. ,vol. 150, pp. 76- 96 ,(1999) , 10.1006/JCPH.1998.6164
N.H Risebro, A Tveito, A front tracking method for conservation laws in one dimension Journal of Computational Physics. ,vol. 101, pp. 130- 139 ,(1992) , 10.1016/0021-9991(92)90047-3
Blake Temple, Global solution of the cauchy problem for a class of 2 × 2 nonstrictly hyperbolic conservation laws Advances in Applied Mathematics. ,vol. 3, pp. 335- 375 ,(1982) , 10.1016/S0196-8858(82)80010-9