A moving mesh method for one-dimensional hyperbolic conservation laws
We develop an adaptive method for solving one-dimensional systems of hyperbolic conservation laws that employs a high resolution Godunov-type scheme for the physical equations, in conjunction with a moving mesh PDE governing the motion of the spatial grid points. Many other moving mesh methods devel...
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| Veröffentlicht in: | SIAM journal on scientific computing 2001, Vol.22 (5), p.1791-1813 |
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| container_title | SIAM journal on scientific computing |
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| creator | STOCKIE, John M MACKENZIE, John A RUSSELL, Robert D |
| description | We develop an adaptive method for solving one-dimensional systems of hyperbolic conservation laws that employs a high resolution Godunov-type scheme for the physical equations, in conjunction with a moving mesh PDE governing the motion of the spatial grid points. Many other moving mesh methods developed to solve hyperbolic problems use a fully implicit discretization for the coupled solution-mesh equations, and so suffer from a significant degree of numerical stiffness. We employ a semi-implicit approach that couples the moving mesh equation to an efficient, explicit solver for the physical PDE, with the resulting scheme behaving in practice as a two-step predictor-corrector method. In comparison with computations on a fixed, uniform mesh, our method exhibits more accurate resolution of discontinuities for a similar level of computational work. |
| doi_str_mv | 10.1137/s1064827599364428 |
| format | Article |
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| identifier | ISSN: 1064-8275 |
| ispartof | SIAM journal on scientific computing, 2001, Vol.22 (5), p.1791-1813 |
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| source | SIAM Journals Online |
| subjects | Accuracy Applied mathematics Compressible flows shock and detonation phenomena Conservation laws Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) Mathematical analysis Mathematics Methods Numerical analysis Numerical analysis. Scientific computation Partial differential equations Partial differential equations, initial value problems and time-dependant initial-boundary value problems Physics Propagation Sciences and techniques of general use Shock-wave interactions and shock effects |
| title | A moving mesh method for one-dimensional hyperbolic conservation laws |
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