The simple finite volume Lax-Wendroff weighted essentially nonoscillatory schemes for shallow water equations with bottom topography
type: Item
instance of: scholarly article
title: The simple finite volume Lax-Wendroff weighted essentially nonoscillatory schemes for shallow water equations with bottom topography
zbMATH Open document ID: 1426.76399
DOI: 10.1155/2018/2652367
author: Changna Lu
author: Luoyan Xie
author: Hong-Wei Yang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: A Lax-Wendroff-type procedure with the high order finite volume simple weighted essentially nonoscillatory (SWENO) scheme is proposed to simulate the one-dimensional (1D) and two-dimensional (2D) shallow water equations with topography influence in source terms. The system of shallow water equations is discretized using the simple WENO scheme in space and Lax-Wendroff scheme in time. The idea of Lax-Wendroff time discretization can avoid part of characteristic decomposition and calculation of nonlinear weights. The type of simple WENO was first developed by \textit{J. Zhu} and \textit{J. Qiu} [J. Comput. Phys. 318, 110--121 (2016; Zbl 1349.65365)], which is more simple than classical WENO fashion. In order to maintain good, high resolution and nonoscillation for both continuous and discontinuous flow and suit problems with discontinuous bottom topography, we use the same idea of SWENO reconstruction for flux to treat the source term in prebalanced shallow water equations. A range of numerical examples are performed; as a result, comparing with classical WENO reconstruction and Runge-Kutta time discretization, the simple Lax-Wendroff WENO schemes can obtain the same accuracy order and escape nonphysical oscillation adjacent strong shock, while bringing less absolute truncation error and costing less CPU time for most problems. These conclusions agree with that of finite difference Lax-Wendroff WENO scheme for shallow water equations, while finite volume method has more flexible mesh structure compared to finite difference method.
Mathematics Subject Classification ID: 76M12
Mathematics Subject Classification ID: 65M08
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 7018681
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/2652367
OpenAlex ID: W2790688579
cites work: An integrable coupling hierarchy of the MKdV\_integrable systems, its Hamiltonian structure and corresponding nonisospectral integrable hierarchy
cites work: Rational solutions and lump solutions to the generalized \((3+1)\)-dimensional shallow water-like equation
cites work: Binary Bargmann symmetry constraint associated with 3×3 discrete matrix spectral problem
cites work: Trigonal curves and algebro-geometric solutions to soliton hierarchies I
cites work: ZK-Burgers equation for three-dimensional Rossby solitary waves and its solutions as well as chirp effect
cites work: Dissipative nonlinear Schrödinger equation for envelope solitary Rossby waves with dissipation effect in stratified fluids and its solution
cites work: A new integro-differential equation for Rossby solitary waves with topography effect in deep rotational fluids
cites work: Forced ILW-Burgers equation as a model for Rossby solitary waves generated by topography in finite depth fluids
cites work: A new integrable symplectic map and the Lie point symmetry associated with nonlinear lattice equations
cites work: Mixed lump-kink solutions to the KP equation
cites work: A deformed reduced semi-discrete Kaup-Newell equation, the related integrable family and Darboux transformation
cites work: Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions
cites work: Two integrable lattice hierarchies and their respective Darboux transformations
cites work: Frobenius integrable decompositions of nonlinear evolution equations with modified term
cites work: A decomposition method for large-scale box constrained optimization
cites work: Positive and negative integrable hierarchies, associated conservation laws and Darboux transformation
cites work: Some modifications of Newton's method with higher-order convergence for solving nonlinear equations
cites work: Algebro-geometric solutions for a discrete integrable equation
cites work: Wavelet-based adaptation methodology combined with finite difference WENO to solve ideal magnetohydrodynamics
cites work: Q1686455
cites work: A maximum-principle-satisfying finite volume compact-WENO scheme for traffic flow model on networks
cites work: Simulations of shallow water equations by finite difference WENO schemes with multilevel time discretization
cites work: Weighted essential non-oscillatory schemes for tidal bore on unstructured meshes
cites work: On the eigenvalues of the ADER-WENO Galerkin predictor
cites work: Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method, III: Unstructured meshes
cites work: Weighted essentially non-oscillatory schemes
cites work: Efficient implementation of essentially nonoscillatory shock-capturing schemes
cites work: Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
cites work: Hybrid well-balanced WENO schemes with different indicators for shallow water equations
cites work: A new fifth order finite difference WENO scheme for solving hyperbolic conservation laws
cites work: Uniformly high order accurate essentially non-oscillatory schemes. III
cites work: Finite Difference WENO Schemes with Lax--Wendroff-Type Time Discretizations
cites work: Stochastic linear quadratic optimal control with constraint for discrete-time systems
cites work: Simulations of shallow water equations with finite difference Lax-Wendroff weighted essentially non-oscillatory schemes
cites work: A new type of finite volume WENO schemes for hyperbolic conservation laws
cites work: Mathematical balancing of flux gradient and source terms prior to using Roe's approximate Riemann solver.
cites work: Q4247279
cites work: Application of conservative residual distribution schemes to the solution of the shallow water equations on unstructured meshes
cites work: Efficient implementation of weighted ENO schemes
Wikidata QID: Q130203294
description: scientific article; zbMATH DE number 7018681