Dispersion-relation-preserving finite difference schemes for computational acoustics
01 Aug 1993-Journal of Computational Physics (Academic Press Professional, Inc.)-Vol. 107, Iss: 2, pp 262-281
TL;DR: In this article, a set of radiation and outflow boundary conditions compatible with the DRP schemes is constructed, and a sequence of numerical simulations is conducted to test the effectiveness of the time-marching dispersion-relation-preserving (DRP) schemes.
About: This article is published in Journal of Computational Physics.The article was published on 1993-08-01. It has received 2202 citations till now. The article focuses on the topics: Finite difference & Finite difference method.
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TL;DR: This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and code parallelization.
Abstract: Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques
This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization
An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques
Will provide you with the knowledge required to develop and understand modern flow simulation codes
Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics
Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques
1,228 citations
Cites methods from "Dispersion-relation-preserving fini..."
...In this case, the function @ ( T ) corresponds to the limiter of Hemker and Koren [93]....
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...The variety reaches from the wave model of Roe [87], [88] over the algebraic scheme of Sidilkover [89] to the most advanced characteristic decomposition method [go]-[93]....
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TL;DR: A simple technique is adopted which ensures metric cancellation and thus ensures freestream preservation even on highly distorted curvilinear meshes, and metric cancellation is guaranteed regardless of the manner in which grid speeds are defined.
950 citations
TL;DR: Explicit numerical methods for spatial derivation, filtering, and time integration are proposed in this article with the aim of computing flow and noise with high accuracy and fidelity, and they are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to kΔx = π/2 corresponding to four points per wavelength.
883 citations
Cites background or methods from "Dispersion-relation-preserving fini..."
...In this work, following Tam and Webb [2], schemes are constructed from their dispersion properties....
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...[2,27] who provided both centered and backward DRP schemes with 7-point stencils....
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...However, instead of demanding an accuracy limit for about seven points per wavelength such as the DRP scheme [2], the spatial-discretization methods must calculate the waves up to four points per wavelength with the aim of dynamic LES subgrid models....
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...The first ones were relative to the spatial derivation with finite-difference schemes showing dispersive properties optimized in the wavenumber space: among them, the explicit Dispersion-Relation-Preserving (DRP) [2], implicit compact [3–7], and ENO schemes [8]....
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...This approach was particularly followed by Tam et al. [2,27] who provided both centered and backward DRP schemes with 7-point stencils....
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Iowa State University1, University of Michigan2, French Institute for Research in Computer Science and Automation3, University of Bergamo4, CD-adapco5, Von Karman Institute for Fluid Dynamics6, German Aerospace Center7, Glenn Research Center8, RWTH Aachen University9, University of California, Berkeley10, Air Force Research Laboratory11
TL;DR: The 1st International Workshop on High-Order CFD Methods was successfully held in Nashville, Tennessee, on January 7-8, 2012, just before the 50th Aerospace Sciences Meeting as mentioned in this paper.
Abstract: After several years of planning, the 1st International Workshop on High-Order CFD Methods was successfully held in Nashville, Tennessee, on January 7-8, 2012, just before the 50th Aerospace Sciences Meeting. The American Institute of Aeronautics and Astronautics, the Air Force Office of Scientific Research, and the German Aerospace Center provided much needed support, financial and moral. Over 70 participants from all over the world across the research spectrum of academia, government labs, and private industry attended the workshop. Many exciting results were presented. In this review article, the main motivation and major findings from the workshop are described. Pacing items requiring further effort are presented. © 2013 John Wiley & Sons, Ltd.
838 citations
TL;DR: The history and basic formulation of WENO schemes are reviewed, the main ideas in using WenO schemes to solve various hyperbolic PDEs and other convection dominated problems are outlined, and a collection of applications in areas including computational fluid dynamics, computational astronomy and astrophysics, semiconductor device simulation, traffic flow models, computational biology, and some non-PDE applications are presented.
Abstract: High order accurate weighted essentially nonoscillatory (WENO) schemes are relatively new but have gained rapid popularity in numerical solutions of hyperbolic partial differential equations (PDEs) and other convection dominated problems. The main advantage of such schemes is their capability to achieve arbitrarily high order formal accuracy in smooth regions while maintaining stable, nonoscillatory, and sharp discontinuity transitions. The schemes are thus especially suitable for problems containing both strong discontinuities and complex smooth solution features. WENO schemes are robust and do not require the user to tune parameters. At the heart of the WENO schemes is actually an approximation procedure not directly related to PDEs, hence the WENO procedure can also be used in many non-PDE applications. In this paper we review the history and basic formulation of WENO schemes, outline the main ideas in using WENO schemes to solve various hyperbolic PDEs and other convection dominated problems, and present a collection of applications in areas including computational fluid dynamics, computational astronomy and astrophysics, semiconductor device simulation, traffic flow models, computational biology, and some non-PDE applications. Finally, we mention a few topics concerning WENO schemes that are currently under investigation.
831 citations
Cites methods from "Dispersion-relation-preserving fini..."
...If one must use explicit finite difference schemes, then there is a systematic approach [162] to modify the coefficients of the finite difference approximation, with the objective of increasing the phase resolution (dispersion relation) at the price of lowering the order of accuracy for the same stencil....
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