Stockie, J.M. and MacKenzie, J.A. and Russell, R.D. (2001) A moving mesh method for onedimensional hyperbolic conservation laws. SIAM Journal on Scientific Computing, 22 (5). pp. 17911813. ISSN 10648275

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Abstract
We develop an adaptive method for solving onedimensional systems of hyperbolic conservation laws that employs a high resolution Godunovtype 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 solutionmesh equations, and so suffer from a significant degree of numerical stiffness. We employ a semiimplicit 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 twostep predictorcorrector 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.
Item type:  Article 

ID code:  4705 
Keywords:  moving mesh, adaptivity, equidistribution, shock capturing, hyperbolic conservation laws, finite volume methods, numerical mathematics, Mathematics, Physics, Computational Mathematics, Applied Mathematics 
Subjects:  Science > Mathematics Science > Physics 
Department:  Faculty of Science > Mathematics and Statistics 
Depositing user:  Strathprints Administrator 
Date Deposited:  12 Nov 2007 
Last modified:  20 Oct 2015 20:45 
URI:  http://strathprints.strath.ac.uk/id/eprint/4705 
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