Geodesic
Comparison of gradient approximation methods in schemes designed for scale-resolving simulations
Matematičeskoe modelirovanie, Tome 31 (2019) no. 10, pp. 7-21

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Various methods for improved accuracy approximation of the gradients entering the diffusion fluxes are considered. Linear combinations of 2$^{\mathrm{nd}}$ order difference schemes for a non-uniform grid that transform into 4$^{\mathrm{th}}$ order schemes in the uniform case were investigated. We also considered 3$^{\mathrm{rd}}$ and 4$^{\mathrm{th}}$ order schemes for approximating gradients on a non-uniform grid in the normal and tangent directions to the cell face, respectively, based on Lagrange polynomials. The initial testing was carried out on one-dimensional functions: a smooth Gauss function and a piecewise linear function. Next, the schemes were applied in direct numerical simulation of the Taylor–Green vortex.
Keywords: approximation order
Mots-clés : diffusion fluxes, gradients. 
@article{MM_2019_31_10_a1,
     author = {S. Bakhne and S. M. Bosniakov and S. V. Mikhailov and A. I. Troshin},
     title = {Comparison of gradient approximation methods in schemes designed for scale-resolving simulations},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {7--21},
     publisher = {mathdoc},
     volume = {31},
     number = {10},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2019_31_10_a1/}
}
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S. Bakhne; S. M. Bosniakov; S. V. Mikhailov; A. I. Troshin. Comparison of gradient approximation methods in schemes designed for scale-resolving simulations. Matematičeskoe modelirovanie, Tome 31 (2019) no. 10, pp. 7-21. http://geodesic.mathdoc.fr/item/MM_2019_31_10_a1/