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Nonlinear corrector for Reynolds‐averaged Navier‐Stokes equations
Author(s) -
Frazza Loïc,
Loseille Adrien,
Dervieux Alain,
Alauzet Frédéric
Publication year - 2019
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4764
Subject(s) - nonlinear system , residual , mathematics , reynolds number , computational fluid dynamics , navier–stokes equations , vertex (graph theory) , mesh generation , numerical analysis , predictor–corrector method , reynolds averaged navier–stokes equations , mathematical analysis , mathematical optimization , finite element method , algorithm , mechanics , physics , turbulence , graph , quantum mechanics , discrete mathematics , compressibility , thermodynamics
Summary The scope of this paper is to present a nonlinear error estimation and correction for Navier‐Stokes and Reynolds‐averaged Navier‐Stokes equations. This nonlinear corrector enables better solution or functional output predictions at fixed mesh complexity and can be considered in a mesh adaptation process. After solving the problem at hand, a corrected solution is obtained by solving again the problem with an added source term. This source term is deduced from the evaluation of the residual of the numerical solution interpolated on the h /2 mesh. To avoid the generation of the h /2 mesh (which is prohibitive for realistic applications), the residual at each vertex is computed by local refinement only in the neighborhood of the considered vertex. One of the main feature of this approach is that it automatically takes into account all the properties of the considered numerical method. The numerical examples point out that it successfully improves solution predictions and yields a sharp estimate of the numerical error. Moreover, we demonstrate the superiority of the nonlinear corrector with respect to linear corrector that can be found in the literature.