Predictor-corrector LU-SGS discontinuous Galerkin finite element method for conservation laws
type: Item
instance of: scholarly article
title: Predictor-corrector LU-SGS discontinuous Galerkin finite element method for conservation laws
zbMATH Open document ID: 1394.65102
DOI: 10.1155/2015/940257
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: Efficient implicit predictor-corrector LU-SGS discontinuous Galerkin (DG) approach for compressible Euler equations on unstructured grids is investigated by adding the error compensation of high-order term. The original LU-SGS and GMRES schemes for DG method are discussed. Van Albada limiter is employed to make the scheme monotone. The numerical experiments performed for the transonic inviscid flows around NACA0012 airfoil, RAE2822 airfoil, and ONERA M6 wing indicate that the present algorithm has the advantages of low storage requirements and high convergence acceleration. The computational efficiency is close to that of GMRES scheme, nearly 2.1 times greater than that of LU-SGS scheme on unstructured grids for 2D cases, and almost 5.5 times greater than that of RK4 on unstructured grids for 3D cases.
Mathematics Subject Classification ID: 65M60
zbMATH DE Number: 6927623
Wikidata QID: Q59120352
author: Xinrong Ma
author: Sanyang Liu
author: Gongnan Xie
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/940257
OpenAlex ID: W1555299298
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: A semi-implicit discontinuous Galerkin finite element method for the numerical solution of inviscid compressible flow
cites work: An efficient implicit discontinuous spectral Galerkin method
cites work: TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
cites work: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
cites work: The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
cites work: The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
cites work: Devising discontinuous Galerkin methods for nonlinear hyperbolic conservation laws
cites work: Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
cites work: A \(p\)-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids
cites work: Q4952252
cites work: \(p\)-multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
cites work: Discontinuous Galerkin solution of the Reynolds-averaged Navier-Stokes and \(k-\omega\) turbulence model equations
cites work: Locally divergence-free discontinuous Galerkin methods for MHD equations
cites work: ENO and WENO schemes with the exact conservation property for one-dimensional shallow water equations
cites work: Arbitrary high-order discontinuous Galerkin schemes for the magnetohydrodynamic equations
cites work: A discontinuous Galerkin method for the full two-fluid plasma model
cites work: The local discontinuous Galerkin method for three-dimensional shallow water flow
cites work: Implicit time integration schemes for the unsteady compressible Navier-Stokes equations: Laminar flow
cites work: A class of implicit upwind schemes for Euler simulations with unstructured meshes
cites work: Q4892010
cites work: A high-resolution procedure for Euler and Navier-Stokes computations on unstructured grids
cites work: Economical symmetrical quadrature rules for complete polynomials over a square domain
cites work: High degree efficient symmetrical Gaussian quadrature rules for the triangle
cites work: Q4255380
cites work: On the Choice of Wavespeeds for the HLLC Riemann Solver
cites work: Comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems
cites work: Approximate Riemann solvers, parameter vectors, and difference schemes
cites work: Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws.
cites work: A fast, matrix-free implicit method for compressible flows on unstructured grids
cites work: A reconstructed discontinuous Galerkin method based on a hierarchical WENO reconstruction for compressible flows on tetrahedral grids
description: scientific article; zbMATH DE number 6927623