Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy
type: Item
instance of: scholarly article
title: Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy
zbMATH Open document ID: 0961.65078
author: Dinshaw S. Balsara
author: Chi-Wang Shu
published in: Journal of Computational Physics
publication date: 2001-05-16T00:00:00Z
review text: This paper concerns a finite difference scheme for numerical integration of the hyperbolic conservation law problems \[ U_t+\text{div } F(U)=0, \] where \(U\in {\mathbb R^m}\), \(F(U)\in {\mathbb R^d}\), and \(F\) represents the flux. The right-hand-side of this equation is transformed by introduction of the numerical flux on the space grid, and the problem is treated as a system of ordinary differential equations. To integrate this system numerically a special kind of explicite Runge-Kutta method is used. In order to insure the possibly high order of accuracy a special technique of interpolation with delimiters is used. This technique allows also to estimate (locally) the regularity of the solution and to preserve the monotonicity. The paper contains tables of coefficients of interpolation formulas. The results of numerical tests are presented.
reviewed by: Krzysztof Moszyński
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 1462879
zbMATH Keywords: hyperbolic conservation law
zbMATH Keywords: numerical examples
zbMATH Keywords: weighted essentially nonoscillatory schemes
zbMATH Keywords: monotonicity preservation
zbMATH Keywords: finite difference scheme
zbMATH Keywords: Runge-Kutta method
MaRDI profile type: Publication
full work available at URL: jcph.2000.6443
OpenAlex ID: W2048941652
cites work: A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations
cites work: An upwind differencing scheme for the equations of ideal magnetohydrodynamics
cites work: Comparison of Numerical Methods for the Calculation of Two-Dimensional Turbulence
cites work: Local adaptive mesh refinement for shock hydrodynamics
cites work: Finite-volume implementation of high-order essentially nonoscillatory schemes in two dimensions
cites work: Comparison of two formulations for high-order accurate essentially nonoscillatory schemes
cites work: Q3747653
cites work: The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
cites work: The piecewise parabolic method (PPM) for gas-dynamical simulations
cites work: A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
cites work: An analysis of numerical errors in large-eddy simulations of turbulence
cites work: The artificial compression method for computation of shocks and contact discontinuities. I. Single conservation laws
cites work: High resolution schemes for hyperbolic conservation laws
cites work: ENO schemes with subcell resolution
cites work: Uniformly high order accurate essentially non-oscillatory schemes. III
cites work: Efficient implementation of weighted ENO schemes
cites work: Weak solutions of nonlinear hyperbolic equations and their numerical computation
cites work: The nirvana scheme applied to one‐dimensional advection
cites work: Large-eddy simulations of shear flows
cites work: Weighted essentially non-oscillatory schemes
cites work: Inertial range structures in decaying compressible turbulent flows
cites work: A contribution to the great Riemann solver debate
cites work: A numerical study of the convergence properties of ENO schemes
cites work: Approximate Riemann solvers, parameter vectors, and difference schemes
cites work: Q3817996
cites work: Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics
cites work: Notes on the Eigensystem of Magnetohydrodynamics
cites work: Efficient implementation of essentially nonoscillatory shock-capturing schemes
cites work: Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
cites work: Numerical experiments on the accuracy of ENO and modified ENO schemes
cites work: High-order ENO schemes applied to two- and three-dimensional compressible flow
cites work: A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
cites work: On the Construction and Comparison of Difference Schemes
cites work: Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
cites work: High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
cites work: Numerical Viscosity and the Entropy Condition for Conservative Difference Schemes
cites work: Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
cites work: The numerical simulation of two-dimensional fluid flow with strong shocks
cites work: An artificial compression method for ENO schemes: The slope modification method
DOI: 10.1006/JCPH.2000.6443
description: scientific article; zbMATH DE number 1462879