Enriched galerkin-characteristics finite element method for incompressible navier-stokes equations

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Output type: Journal article

UM6P affiliated Publication?: Yes


Publisher: Society for Industrial and Applied Mathematics

Publication year: 2021

Journal: SIAM Journal on Scientific Computing (1064-8275)

Volume number: 43

Issue number: 2

Start page: A1336

End page: A1361

ISSN: 1064-8275

eISSN: 1095-7197

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85105882908&doi=10.1137%2f20M1335923&partnerID=40&md5=0150476611614ac0ece7aa910c33e9bc

Languages: English (EN-GB)

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We propose a class of adaptive enriched Galerkin-characteristics finite element methods for efficient numerical solution of the incompressible Navier-Stokes equations in primitive variables. The proposed approach combines the modified method of characteristics to deal with convection terms, the finite element discretization to manage irregular geometries, a direct conjugate gradient algorithm to solve the Stokes problem, and an adaptive L2-projection using quadrature rules to improve the efficiency and accuracy of the method. In the present study, the gradient of the velocity field is used as an error indicator for adaptation of enrichments by increasing the number of quadrature points where it is needed without refining the mesh. Unlike other adaptive finite element methods for incompressible Navier-Stokes equations, linear systems in the proposed enriched Galerkin-characteristics finite element method preserve the same structure and size at each refinement in the adaptation procedure. We examine the performance of the proposed method for a coupled Burgers problem with known analytical solution and for the benchmark problem of flow past a circular cylinder. We also solve a transport problem in the Mediterranean Sea to demonstrate the ability of the method to resolve complex flow features in irregular geometries. Comparisons to the conventional Galerkin-characteristics finite element method are also carried out in the current work. The computed results support our expectations for an accurate and highly efficient enriched Galerkin-characteristics finite element method for incompressible Navier-Stokes equations. © 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.


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Last updated on 2021-20-09 at 23:22