On the selection of the stable explicit first order difference scheme13;

Deshpande, MD (1992) On the selection of the stable explicit first order difference scheme13;. Technical Report. National Aeronautical Laboratory, Bangalore, India.

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Abstract

Selection of a stable scheme for a given order of accuracy13; is not straightforward, specially if the problem is13; multidimensional and the order of accuracy of the difference scheme is high. This study is made to establish a13; systematic procedure for the same. von Neumann stability13; analysis is used to select the stablest explicit 3-point13; first order scheme for the one-dimensional convection- diffusion equation such that the allowable time13; increment t is the largest. By proper upwind biassing the13; stability limit on the diffusion number d can be increased13; to a maximum of 1/Rc where Rc is the cell Reynolds number. This is an improvement over the value. 1/C2+Rc) for the first upwind scheme. When Rc -+00 this optimum scheme tends to the first upwind scheme. For small values of R. viz. R lt;2 downwind biassing improves the stability. A comparison is made between the steady and unsteady approaches keeping stability in mind.13;

Item Type: Monograph (Technical Report)
Uncontrolled Keywords: Stability analysis;Difference scheme;Upwind-bias
Subjects: ENGINEERING > Fluid Mechanics and Thermodynamics
Depositing User: Smt Bhagya Rekha KA
Date Deposited: 09 Aug 2006
Last Modified: 24 May 2010 04:18
URI: http://nal-ir.nal.res.in/id/eprint/2409

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