 First-Order Methods for SystemsEleuterio F. Toro ()
Chapter Chapter 10 in Computational Algorithms for Shallow Water Equations, 2024, pp 189-223 from Springer Abstract: Abstract First-order monotone numerical methods for non-linear systems of hyperbolic conservation laws are studied. Some of these form the bases for constructing higher-order schemes in successive chapters. Algorithms for one-dimensional PDEs are first presented; these include the Godunov upwind scheme [1] in conjunction with the exact Riemann solver; the Random Choice Method (RCM) of Glimm [2]; Flux-Vector Splitting (FVS) methods; and centred schemes, such as the Lax–Friedrichs [3], Lax–Wendroff [3] and FORCE methods [4, 5]. There follows the finite volume framework for PDEs in multiple space dimensions on unstructured meshes, including definitions for semi-discrete and fully discrete schemes; the rotated Riemann problem from the rotational invariance of the two-dimensional shallow water equations; the intercell numerical flux and determination of edge lengths, normals and cell areas in two space dimensions, in order to completely specify the numerical methods. Some examples are shown, in order to illustrate the performance of selected schemes studied, as compared against exact solutions for a suite of carefully selected test problems. Date: 2024 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-61395-1_10 Ordering information: This item can be ordered from DOI: 10.1007/978-3-031-61395-1_10 Access Statistics for this chapter More chapters in Springer Books from Springer |
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