Efficient High-Order Discretizations for Computational Fluid Dynamics

1. Front Matter

   Pages i-vii

   PDF

2. The Discontinuous Galerkin Method: Derivation and Properties

   • Martin Kronbichler

   Pages 1-55

3. High-Performance Implementation of Discontinuous Galerkin Methods with Application in Fluid Flow

   • Martin Kronbichler

   Pages 57-115

4. Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier–Stokes Equations

   • Andrew R. Winters, David A. Kopriva, Gregor J. Gassner, Florian Hindenlang

   Pages 117-196

5. \(\mathbf {p}\)-Multigrid High-Order Discontinuous Galerkin Solution of Compressible Flows

   • A. Colombo, A. Ghidoni, G. Noventa, S. Rebay

   Pages 197-238

6. High-Order Accurate Time Integration and Efficient Implicit Solvers

   • Per-Olof Persson

   Pages 239-259

7. An Introduction to the Hybridizable Discontinuous Galerkin Method

   • Sonia Fernández-Méndez

   Pages 261-275

8. High-Order Methods for Simulations in Engineering

   • Rainald Löhner

   Pages 277-307

9. Back Matter

   Pages 309-311

   PDF

The book introduces modern high-order methods for computational fluid dynamics. As compared to low order finite volumes predominant in today's production codes, higher order discretizations significantly reduce dispersion errors, the main source of error in long-time simulations of flow at higher Reynolds numbers. A major goal of this book is to teach the basics of the discontinuous Galerkin (DG) method in terms of its finite volume and finite element ingredients. It also discusses the computational efficiency of high-order methods versus state-of-the-art low order methods in the finite difference context, given that accuracy requirements in engineering are often not overly strict.

The book mainly addresses researchers and doctoral students in engineering, applied mathematics, physics and high-performance computing with a strong interest in the interdisciplinary aspects of computational fluid dynamics. It is also well-suited for practicing computational engineers who would like to gain an overview of discontinuous Galerkin methods, modern algorithmic realizations, and high-performance implementations.

• hybridizable discontinuous Galerkin methods
• discontinuous Galerkin methods
• high-order discontinuous Galerkin methods
• computational fluid dynamics
• higher Reynolds numbers

• Institute for Computational Mechanics, Technical University Munich, Garching bei München, Germany

  Martin Kronbichler

• Department of Mathematics, University of California, Berkeley, Berkeley, USA

  Per-Olof Persson

Martin Kronbichler is a researcher at the Institute for Computational Mechanics, Technical University of Munich, Germany. His current research focus is on efficient high-order discontinuous Galerkin schemes and fast iterative solvers for flow problems as a PI in the exascale project ExaDG within the German exascale priority program SPPEXA.

Per-Olof Persson is an assistant professor in mathematics at the University of California in Berkeley, USA. He is the author of more than 100 scientific papers on various aspects of high-order methods, in particular on implicit solvers and mesh generation. His work has been central for the advancement of discontinuous Galerkin methods in computational fluid dynamics, including fluid-structure interaction.