Harten, Ami; Hyman, James M. Self-adjusting grid methods for one-dimensional hyperbolic conservation laws. (English) Zbl 0565.65049 J. Comput. Phys. 50, 235-269 (1983). It is shown how to automatically adjust the grid to follow the dynamics of the numerical solution of hyperbolic conservation laws. The grid motion is determind by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals. The resulting algorithm is a simple extension of many currently popular Godunov-type methods. Computer codes using one of these methods can be easily modified to add the moving mesh as an option. Numerical examples are given that illustrate the improved accuracy of Godunov’s and Roe’s methods on a self-adjusting mesh. Cited in 2 ReviewsCited in 169 Documents MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs 35L65 Hyperbolic conservation laws Keywords:self-adjusting grid methods; Godunov-type methods; Numerical examples Software:HLLE PDF BibTeX XML Cite \textit{A. Harten} and \textit{J. M. Hyman}, J. Comput. Phys. 50, 235--269 (1983; Zbl 0565.65049) Full Text: DOI References: [1] Burstein, S.Z., J. comput. phys., 1, 198, (1966) [2] Chorin, A.J., J. comput. phys., 22, 517, (1976) [3] Godunov, S.K., Mat. sb., 47, 271, (1959) [4] Harten, A., On the symmetric form of systems of conservation laws with entropy, Institute for computer applications in science and engineering report no. 81-34, (1981) [5] Harten, A., Math. comput., 32, 363, (1978) [6] Harten, A.; Hyman, J.M., Second-order self-adaptive grid methods for one-dimensional hyperbolic conservation laws, (1982), Los Alamos National Laboratory Los Alamos, N. Mex, in preparation [7] Harten, A.; Lax, P.D., SIAM J. numer. anal., 18, 2, 289, (1981) [8] Harten, A.; Lax, P.D.; Van Leer, B., On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, ICASE report, (1982), SIAM Rev., to appear. [9] Hyman, J.M., Adaptive mesh strategies for the numerical solution of differential equations, Los alamos national laboratory preprint LA-UR-81-2594, los alamos, N. mex., (1981) [10] Lax, P.D., Hyperbolic systems of conservation laws and the mathematical theory of shock waves, (1972), SIAM Philadelphia, Pa [11] Richtmyer, R.D.; Morton, K.W., Difference methods for initial-value problems, (1967), Interscience New York · Zbl 0155.47502 [12] Roe, P.L., (), 354-359 [13] Roe, P.L., J. comput. phys., 43, 357, (1982), to appear [14] Sod, G.A., J. comput. phys., 27, 1, 1, (1978) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.