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ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications pp 67–80Cite as

RKDG with WENO Type Limiters

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Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 113))

Abstract

The discontinuous Galerkin (DG) method is a spatial discretization procedure for convection dominated equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters, which is termed as RKDG when TVD Runge-Kutta method is applied for time discretization. It has the advantage of flexibility in handling complicated geometry, h − p adaptivity, and efficiency of parallel implementation and has been used successfully in many applications. However, the limiters used to control spurious oscillations in the presence of strong shocks are less robust than the strategies of essentially non-oscillatory (ENO) and weighted ENO (WENO) finite volume and finite difference methods. In this chapter, we will describe the procedure of using WENO and Hermite WENO finite volume methodology as limiters for RKDG methods on unstructure meshes, with the goal of obtaining a robust and high order limiting procedure to simultaneously obtain uniform high order accuracy and sharp, non-oscillatory shock transition for RKDG methods.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, Jiangsu, China, 210093

    Jianxian Qiu

  2. College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China, 210016

    Jun Zhu

Authors
  1. Jianxian Qiu
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  2. Jun Zhu
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Editor information

Editors and Affiliations

  1. German Aerospace Center (DLR), Braunschweig, Germany

    Norbert Kroll

  2. Airbus Deutschland GmbH, Bremen, Germany

    Heribert Bieler

  3. von Karman Institute for Fluid Dynamics (VKI), Rhode-St-Genese, Belgium

    Herman Deconinck

  4. ONERA, Châtillon, France

    Vincent Couaillier

  5. NLR, Amsterdam, The Netherlands

    Harmen van der Ven

  6. EADS Deutschland, Manching, Germany

    Kaare Sørensen

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© 2010 Springer-Verlag Berlin Heidelberg

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Qiu, J., Zhu, J. (2010). RKDG with WENO Type Limiters. In: Kroll, N., Bieler, H., Deconinck, H., Couaillier, V., van der Ven, H., Sørensen, K. (eds) ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03707-8_6

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  • DOI: https://doi.org/10.1007/978-3-642-03707-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03706-1

  • Online ISBN: 978-3-642-03707-8

  • eBook Packages: EngineeringEngineering (R0)

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