A new mean preserving moving least squares method for arbitrary order finite volume schemes

Ramírez, Luis, Edreira, Laura, Couceiro, Iván, Ouro, Pablo ORCID: https://orcid.org/0000-0001-6411-8241, Nogueira, Xesús and Colominas, Ignasi 2022. A new mean preserving moving least squares method for arbitrary order finite volume schemes. Applied Mathematics and Computation 443 , 127768. 10.1016/j.amc.2022.127768

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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.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Engineering
Publisher:	Elsevier
ISSN:	0096-3003
Date of First Compliant Deposit:	18 January 2023
Date of Acceptance:	29 November 2022
Last Modified:	03 May 2023 08:44
URI:	https://orca.cardiff.ac.uk/id/eprint/155912

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