High-order upwind residual distribution schemes on isoparametric curved elements

Residual distribution schemes on curved geometries are discussed in the context of higher order spatial discretization for hyperbolic conservation laws. The discrete solution, defined by a Finite Element space based on triangular Lagrangian Pk elements, is globally continuous. A natural sub-triangul...

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Bibliographic Details
Published in:Journal of computational physics 2011-02, Vol.230 (4), p.890-906
Main Authors: Vymazal, Martin, Quintino, Tiago, Villedieu, Nadège, Deconinck, Herman
Format: Article
Language:English
Subjects:
Approximation
Boundaries
Computational techniques
Curved
Curvilinear geometry
Discretization
Exact sciences and technology
High-order
Mathematical analysis
Mathematical methods in physics
Multidimensional upwind
Physics
Residual distribution
Reuse
Transformations
Triangles
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Summary:Residual distribution schemes on curved geometries are discussed in the context of higher order spatial discretization for hyperbolic conservation laws. The discrete solution, defined by a Finite Element space based on triangular Lagrangian Pk elements, is globally continuous. A natural sub-triangulation of these elements allows to reuse the simple distribution schemes previously developed for linear P1 triangles. The paper introduces curved elements with piecewise quadratic and cubic approximation of the boundaries of the domain, using standard sub- or isoparametric transformation. Numerical results for the Euler equations confirm the predicted order of accuracy, showing the importance of a higher order approximation of the geometry.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2010.05.027