Titlebook: Computational Algorithms for Shallow Water Equations; Eleuterio F. Toro Textbook 2024Latest edition The Editor(s) (if applicable) and The

Palpitation

,Elementary Waves in Shallow Water,he split two-dimensional shallow water equations. The dam-break problem is introduced as a physical, motivating example of a special case of a Riemann problem. Four possible wave patters in the solution of the Riemann problem are identified, each comprising rarefactions, shocks and contact discontin

性冷淡

Exact Riemann Solver: Wet Bed,ter equations for the case of a wet bed, that is for . (no vacuum). The computing algorithm is based on a detailed study of elementary waves in the Riemann problem performed in Chap. .. There are two steps in computing the complete solution. First, the water depth . and velocity . are found in the S

Ingredient

Exact Riemann Solver: Dry Bed,, or ., that is when .. The boundary separating regions of water and no water, called the wet/dry front, emerges from the exact solution of the Riemann problem as the edge (tail) of a strong rarefaction wave, which is the only wave present in the solution structure. This wet/dry front is a very fast

起波澜

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粗野

First-Order Methods for Systems,ng higher-order schemes in successive chapters. Algorithms for one-dimensional PDEs are first presented; these include the Godunov upwind scheme [.] in conjunction with the exact Riemann solver; the Random Choice Method (RCM) of Glimm [.]; Flux-Vector Splitting (FVS) methods; and centred schemes, su

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一大块

Second-Order Non-linear Methods,linear, in order to circumvent Godunov’s theorem, which is concerned with the phenomenon of spurious oscillations in the vicinity of large spatial gradients, shocks in particular. For the class of flux limiter methods considered, the non-linear character of the schemes results from enforcing total v

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ADER High-Order Methods,ogy is an unlimited-order, non-linear fully discrete one-step extension of Godunov’s method that operates in the finite volume and discontinuous Galerkin finite element frameworks. The approach is applicable to multidimensional systems in conservative and non-conservative forms, on structured and un