Isogeometric analysis for compressible flows using a Discontinuous Galerkin method

Abstract : The objective of this work is to investigate a Discontinuous Galerkin (DG) method for compressible Euler equations, based on an isogeometric formulation: the partial differential equations governing the flow are solved on rational parametric elements, that preserve exactly the geometry of boundaries defined by Non-Uniform Rational B-Splines (NURBS), while the same rational approximation space is adopted for the solution. We propose a new approach to construct a DG-compliant computational domain based on NURBS boundaries and examine the resulting modifications that occur in the DG method. Some two-dimensional test- cases with analytical solutions are considered to assess the accuracy and illustrate the capabilities of the proposed approach. The critical role of boundary curvature is especially investigated. Finally, a shock capturing strategy based on artificial viscosity and local refinement is adapted to this isogeometric context and is demonstrated for a transonic flow.
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Submitted on : Thursday, February 1, 2018 - 4:22:31 PM
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Régis Duvigneau. Isogeometric analysis for compressible flows using a Discontinuous Galerkin method. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2018, 333, ⟨10.1016/j.cma.2018.01.039⟩. ⟨hal-01589344v3⟩

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