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Arbitrary Lagrangian-Eulerian discontinuous Galerkin method for 1D Euler equations. (English) Zbl 1405.65115
Klingenberg, Christian (ed.) et al., Theory, numerics and applications of hyperbolic problems I, Aachen, Germany, August 2016. Cham: Springer (ISBN 978-3-319-91544-9/hbk; 978-3-319-91545-6/ebook). Springer Proceedings in Mathematics & Statistics 236, 323-334 (2018).
Summary: We propose an explicit in time- discontinuous Galerkin scheme on moving grids using the arbitrary Lagrangian-Eulerian approach for one-dimensional Euler equations. The grid is moved with a velocity that is close to the local fluid velocity, which considerably reduces the numerical dissipation in the Riemann solvers. Local grid refinement and coarsening are performed to maintain the mesh quality and avoid very small or large cells. Second-, third-, and fourth-order methods are developed and several test cases are provided to demonstrate the accuracy of the proposed scheme.
For the entire collection see [Zbl 1398.65011].
MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q31 Euler equations
76M10 Finite element methods applied to problems in fluid mechanics
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