Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part I. General formulation

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    A new space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics in time-dependent flow domains is presented. The discontinuous Galerkin discretization results in an efficient element-wise conservative upwind finite element method, which is particularly well suited for local mesh refinement. The upwind scheme uses a formulation of the HLLC flux applicable to moving meshes and several formulations for the stabilization operator to ensure monotone solutions around discontinuities are investigated. The non-linear equations of the space-time discretization are solved using a multigrid accelerated pseudo-time integration technique with an optimized Runge-Kutta method. The linear stability of the pseudo-time integration method is investigated for the linear advection equation. The numerical scheme is demonstrated with simulations of the flow field in a shock tube, a channel with a bump, and an oscillating NACA 0012 airfoil. These simulations show that the accuracy of the numerical discretization is $O(h^{5/2})$ in space for smooth subsonic flows, both on structured and locally refined meshes, and that the space-time adaptation can significantly improve the accuracy and efficiency of the numerical method.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente
    Number of pages42
    ISBN (Print)0169-2690
    Publication statusPublished - 2001

    Publication series

    PublisherDepartment of Applied Mathematics, University of Twente
    ISSN (Print)0169-2690


    • EWI-3419
    • MSC-76N15
    • MSC-65P25
    • multigrid technique
    • pseudo-time integration method
    • Arbitrary Lagrangian Eulerian (ALE)technique
    • Dynamic grid motion
    • Gas dynamics
    • Discontinuous Galerkin finite element method
    • Local mesh refinement
    • IR-65786
    • METIS-201429

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