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ESTIMATION OF GRID-INDEPENDENT SOLUTIONS ON NON-UNIFORM AND UNSTRUCTURED GRIDS USING GENERALIZED RICHARDSON EXTRAPOLATION

DOI: 10.1615/ICHMT.2015.IntSympAdvComputHeatTransf.1930
page 1811

Bantwal Rabi Baliga
Heat Transfer Laboratory, Department of Mechanical Engineering, McGill University, 817 Sherbrooke St. W., Montreal, QC H3A 2K6, Canada

Sinopsis

A procedure for estimating effectively grid-independent solutions on non-uniform and unstructured grids is proposed. The key features of the proposed procedure are based on the use of pattern-preserving (or proportional) refinement of the aforementioned grids and extensions of ideas first proposed by Richardson (1910, 1927). He referred to these ideas as a "deferred approach to the limit" and stated that this approach can be thought of as "returning to the manner in which they did things before the calculus was invented". A similar line of thinking is stated in the seminal work of Patankar (1980) on finite volume methods. Benchmarking of the proposed procedure was done by comparing the effectively grid-independent results to analytical solutions, some of which were constructed using a special technique described in works of Patankar (1980) and Roache (2002), who refers to it as the "method of manufactured solutions". The numerical solutions used in these demonstrations of the proposed extrapolation procedure were obtained using finite volume methods and control-volume finite element methods for predictions of heat transfer and fluid flow. Details of the proposed extrapolation procedure, the benchmarking exercises, the results, and related discussions will be presented.

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