Revisiting the Least-Squares Procedure for Gradient Reconstruction on Unstructured Meshes

Jun 30, 2013

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Motivation. Originated from study of matrix dissipation versus upwind schemes for unstructured mesh RANS solverLeast Squares Gradient now standard technique for higher order accuracy with upwind schemesUnexpected behavior observed (with entropy fix). 1 week project ? 3 month investigation. Summary

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Revisiting the Least-Squares Procedure for Gradient Reconstruction on Unstructured Meshes

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Least Squares example

Least Squares example. There are 3 mountains u,y,z that from one site have been measured as 2474 ft., 3882 ft., and 4834 ft.. But from u, y looks 1422 ft. taller and the z looks 2354 ft. taller , and from y, z looks 950 ft. taller. Set up the overdetermined system. 2474 3882 4834 1422

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Regression tries to produce a “best fit equation” --- but what is “best” ? Criterion: minimize the sum of squared deviations of data points from the regression line. The Least Squares Principle. Least Squares. (Sum of squares about mean of Y) (Sum of squares about regression line).

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