https://hal.inria.fr/hal-01589344v3Duvigneau, RégisRégisDuvigneauACUMES - Analysis and Control of Unsteady Models for Engineering Sciences - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en AutomatiqueCOMUE UCA - COMUE Université Côte d'Azur (2015-2019)Isogeometric analysis for compressible flows using a Discontinuous Galerkin methodHAL CCSD2018isogeometric analysiscompressible flowsDiscontinuous Galerkinhigh-order scheme[INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA][MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP][MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC][SPI.MECA.MEFL] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]Duvigneau, Régis2018-02-01 16:22:312023-03-15 08:58:092018-02-01 17:07:01enJournal articleshttps://hal.inria.fr/hal-01589344v3/document10.1016/j.cma.2018.01.039https://hal.inria.fr/hal-01589344v2application/pdf3The 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.