Optimal Runge-Kutta smoothers for the \(p\)-multigrid discontinuous Galerkin solution of the 1D Euler equations

DOI10.1016/j.jcp.2010.04.030zbMath1220.65130OpenAlexW2002759527MaRDI QIDQ550853

Francesco Bassi, Antonio Ghidoni, Stefano Rebay

Publication date: 13 July 2011

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2010.04.030

zbMATH Keywords

algorithmnumerical examplesEuler equationsadvection equationexplicit Runge-Kutta\(p\)-multigriderror dampinghigh-order accurate discontinuous Galerkin

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Initial value problems for first-order hyperbolic systems (35L45)

Related Items

Conservation properties of iterative methods for implicit discretizations of conservation laws, An implicit matrix-free discontinuous Galerkin solver for viscous and turbulent aerodynamic simulations, Optimizing a multigrid Runge-Kutta smoother for variable-coefficient convection-diffusion equations, Steepest descent optimisation of Runge-Kutta coefficients for second order implicit finite volume CFD codes, Efficient solvers of discontinuous Galerkin discretization for the Cahn-Hilliard equations, \(hp\)-Multigrid as Smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. I: Multilevel analysis, Preconditioning for modal discontinuous Galerkin methods for unsteady 3D Navier-Stokes equations, \(p\)-multigrid high-order discontinuous Galerkin solution of compressible flows

Cites Work

• Unnamed Item
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• \(p\)-multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Implicit solution of the unsteady Euler equations for high-order accurate discontinuous Galerkin discretizations
• Discontinuous Galerkin solution of the Reynolds-averaged Navier-Stokes and \(k-\omega\) turbulence model equations
• \(h\)-multigrid for space-time discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
• High-order discontinuous Galerkin methods using an \(hp\)-multigrid approach
• A \(p\)-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• High‐order accuratep‐multigrid discontinuous Galerkin solution of the Euler equations
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Numerical Solution of the Euler Equations with a Multiorder Discontinuous Finite Element Method
• The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems
• An efficient implicit discontinuous spectral Galerkin method