Commun. Comput. Phys., 1 (2006), pp. 192-206.


Upwind and High-Resolution Methods for Compressible Flow:

Bram van Leer 1*

1 W. M. Keck Foundation Laboratory for Computational Fluid Dynamics, Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48108-2140, USA.

Received 2 August 2005; Accepted (in revised version) 21 October 2005
Communicated by Kun Xu

Abstract

In this paper I review three key topics in CFD that have kept researchers busy for half a century. First, the concept of upwind differencing, evident for 1-D linear advection. Second, its implementation for nonlinear systems in the form of high-resolution schemes, now regarded as classical. Third, its genuinely multidimensional implementation in the form of residual-distribution schemes, the most recent addition. This lecture focuses on historical developments; it is not intended as a technical review of methods, hence the lack of formulas and absence of figures.


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Key words: Upwind difference; high-resolution method; compressible flow; nonlinear conservation laws.


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Correspondence to: Bram van Leer , W. M. Keck Foundation Laboratory for Computational Fluid Dynamics, Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48108-2140, USA. Email: bram@umich.edu
† This article is based on a presentation made at the 16th AIAA Computational Fluid Dynamcis Conference, held in Orlando, FL, 23-26, June 2003; it first appeared as AIAA Paper 2003-3559.
 

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