A MOOD-MUSCL hybrid formulation for the non-conservative shallow-water system
type: Item
instance of: scholarly article
title: A MOOD-MUSCL hybrid formulation for the non-conservative shallow-water system
zbMATH Open document ID: 1467.65100
author: Yanyan Li
published in: Journal of Scientific Computing
publication date: 2021-06-15T00:00:00Z
review text: The stability of the high-order finite volume method for hyperbolic systems is based on the use of non-linear procedures that prevent the presence of the so-called non-physical oscillations. Standard techniques use the a priori approach where the procedure is carried out with the current time step solution. The a posteriori approach lies on an advanced in time candidate solution and a posterior evaluation of its stability. The authors first present a comparison between these two approaches applied to non-conservative shallow-water equations together in the framework of second-order linear reconstruction. Such comparison led the author to propose a new hybrid version combining the most positive aspects of both methods.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65N08
Mathematics Subject Classification ID: 76M12
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 7359307
zbMATH Keywords: shallow-water
zbMATH Keywords: finite volume
zbMATH Keywords: high-order
zbMATH Keywords: non-conservative problem
zbMATH Keywords: MOOD
zbMATH Keywords: MUSCL
describes a project that uses: MOOD
describes a project that uses: SWASHES
MaRDI profile type: Publication
full work available at URL: s10915-021-01513-z
OpenAlex ID: W3164820588
cites work: On essentially non-oscillatory schemes on unstructured meshes: Analysis and implementation
cites work: A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
cites work: Q5863827
cites work: An admissibility and asymptotic preserving scheme for systems of conservation laws with source term on 2D unstructured meshes with high-order MOOD reconstruction
cites work: Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes
cites work: A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics
cites work: Direct arbitrary-Lagrangian-Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws
cites work: A posteriori limiting for 2D Lagrange plus remap schemes solving the hydrodynamics system of equations
cites work: Tsunami run-up and draw-down on a plane beach
cites work: A high-order finite volume method for systems of conservation laws-multi-dimensional optimal order detection (MOOD)
cites work: The MOOD method for the non-conservative shallow-water system
cites work: \textit{A posteriori} stabilized sixth-order finite volume scheme for one-dimensional steady-state hyperbolic equations
cites work: SWASHES: a compilation of shallow water analytic solutions for hydraulic and environmental studies
cites work: Limiter-free discontinuity-capturing scheme for compressible gas dynamics with reactive fronts
cites work: Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very high-order polynomials
cites work: The Multidimensional Optimal Order Detection method in the three‐dimensional case: very high‐order finite volume method for hyperbolic systems
cites work: A simple robust and accurate \textit{a posteriori} sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes
cites work: \textit{A posteriori} subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
cites work: WENO schemes on unstructured meshes using a relaxed \textit{a posteriori} MOOD limiting approach
cites work: An \textit{a posteriori}, efficient, high-spectral resolution hybrid finite-difference method for compressible flows
cites work: High order direct arbitrary-Lagrangian-Eulerian schemes on moving Voronoi meshes with topology changes
cites work: Q5558541
cites work: Uniformly high order accurate essentially non-oscillatory schemes. III
cites work: Efficient methods with higher order interpolation and MOOD strategy for compressible turbulence simulations
cites work: Simple a posteriori slope limiter (post limiter) for high resolution and efficient flow computations
cites work: Weighted essentially non-oscillatory schemes
cites work: A New Family of High Order Unstructured MOOD and ADER Finite Volume Schemes for Multidimensional Systems of Hyperbolic Conservation Laws
cites work: A pressure-based semi-implicit space-time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier-Stokes equations at all Mach numbers
cites work: A well-balanced scheme for the shallow-water equations with topography
cites work: A well-balanced scheme for the shallow-water equations with topography or Manning friction
cites work: Augmented versions of the HLL and HLLC Riemann solvers including source terms in one and two dimensions for shallow flow applications
cites work: High-accurate SPH method with multidimensional optimal order detection limiting
cites work: Restoration of the contact surface in the HLL-Riemann solver
cites work: Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
cites work: A Method for the Numerical Calculation of Hydrodynamic Shocks
cites work: \textit{A posteriori} correction of high-order discontinuous Galerkin scheme through subcell finite volume formulation and flux reconstruction
cites work: Space-time adaptive ADER discontinuous Galerkin finite element schemes with \textit{a posteriori} sub-cell finite volume limiting
DOI: 10.1007/S10915-021-01513-Z
description: scientific article; zbMATH DE number 7359307