R-parameter: A local truncation error based adaptive framework for finite volume compressible flow solvers

Ganesh, N and Shende, Nikhil V and Balakrishnan, N (2009) R-parameter: A local truncation error based adaptive framework for finite volume compressible flow solvers. In: Computers & Fluids, 38 (9). pp. 1799-1822.

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Abstract

A residual-based strategy to estimate the local truncation error in a finite volume framework for steady compressible flows is proposed. This estimator, referred to as the -parameter, is derived from the imbalance arising from the use of an exact operator on the numerical solution for conservation laws. The behaviour of the residual estimator for linear and non-linear hyperbolic problems is systematically analysed. The relationship of the residual to the global error is also studied. The -parameter is used to derive a target length scale and consequently devise a suitable criterion for refinement/derefinement. This strategy, devoid of any user-defined parameters, is validated using two standard test cases involving smooth flows. A hybrid adaptive strategy based on both the error indicators and the -parameter, for flows involving shocks is also developed. Numerical studies on several compressible flow cases show that the adaptive algorithm performs excellently well in both two and three dimensions.

Item Type:	Journal Article
Additional Information:	copyright of this article belongs to Elsevier Science.
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering (Formerly, Aeronautical Engineering)
Date Deposited:	21 Dec 2009 09:25
Last Modified:	19 Sep 2010 05:43
URI:	http://eprints.iisc.ernet.in/id/eprint/22746

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