A new Mean Preserving Moving Least Squares method for Arbitrary Order Finite Volume schemes

Luis Ramírez, Laura Edreira, Iván Couceiro, Pablo Ouro, Xesús Nogueira and Ignasi Colominas

Applied Mathematics and Computation, 2023, vol. 443, issue C

Abstract: In this paper we propose a new arbitrary-order Finite Volume method for the numerical solution of the Euler and Navier-Stokes equations on unstructured grids. Arbitrary order is achieved using a modified Moving Least Squares reconstruction, which preserves the mean values of the conservative variables. Hence, the proposed scheme changes the traditional error functional of the MLS reconstruction in order to compare the cell-averaged values. Several benchmark problems are used to assess the proposed scheme’s accuracy and performance, to show that arbitrary order of convergence can be achieved. Furthermore, the proposed method is applied to the numerical solution of the Navier-Stokes equations and its ability to simulate turbulent flows is verified.

Keywords: Finite Volume; Moving Least Squares; Mean Preserving; Very high-order methods; Compressible flows (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322008360

DOI: 10.1016/j.amc.2022.127768

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