Boris Diskin, National Institute of Aerospace


Computational analysis tools for large-scale computational fluid dynamics codes


Abstract: There is a pressing need to develop practical methods for verification and validation of large-scale computational fluid dynamics (CFD) codes used in industry and research communities. The codes may involve many complications including unstructured grid formulations, various interacting physical models, multiscale interactions, etc. Classical numerical analysis methods have severe limitations in assessing accuracy and efficiency of practical CFD codes. In this talk, a new computational approach to analyzing practical solvers is introduced and illustrated with many examples. Specifically, a general, efficient, accurate, and practical computational tool, downscaling (DS) test, is introduced and applied for studying accuracy of finite-volume discretization (FVD) schemes on general unstructured grids. The DS test plays a critical role in correcting a misconception that the discretization accuracy of FVD schemes on irregular grids is directly linked to convergence of truncation errors. DS test allows separate analysis of the interior, boundaries, and singularities that could be useful even in structured-grid settings. There are many new findings arising from the use of the DS test analysis. DS test proved also to be useful for analyzing convergence rates of common iterative solvers, such as defect-correction iterations. Another group of computational analysis methods, idealized relaxation (IR) and idealized coarse-grid (ICG) iterations, have been developed for quantitative analysis of efficiency of multigrid solutions. The analysis is applied to available, imperfect multigrid solvers that deal with practical CFD problems. The tests are focused on the main parts of a multigrid cycle, relaxation and coarse-grid correction. In these idealized iterations, one part of the cycle (relaxation for IR iterations and coarse-grid correction for ICG iterations) is replaced with an idealized imitation known to be efficient; its complementary part is the actual part of a two-grid cycle. The analysis compares performances of the actual cycle and idealized iterations. The IR and ICG iterations are very general and can be directly applied in the most complicated simulations including complex geometries, and unstructured mixed-element grids. The results of this analysis are not single-number estimates; they are rather convergence patterns of the iterations that may either confirm or refute expectations indicating what part of the actual solver is inefficient in carrying out the assigned task. The generality of the analysis makes it a valuable tool for analyzing complicated large-scale computational problems, where no other analysis methods are currently available. The analysis proved sensitive to very delicate details of the actual multigrid cycle, pointing clearly to the inefficient part of the tested algorithm.

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