A high-order residual-based viscosity finite element method for incompressible variable density flow

In this paper, we introduce a high-order accurate finite element method for incompressible variable density flow. The method uses high-order Taylor-Hood velocity-pressure elements in space and backward differentiation formula (BDF) time stepping in time. This way of discretization leads to two main...

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Bibliographic Details
Published in:Journal of computational physics Vol. 497; p. 112608
Main Authors: Lundgren, Lukas, Nazarov, Murtazo
Format: Journal Article
Language:English
Published: 15.01.2024
Subjects:
Artificial compressibility
Artificial viscosity
Beräkningsvetenskap med inriktning mot numerisk analys
Incompressible variable density flow
Preconditioning
Residual viscosity
Scientific Computing with specialization in Numerical Analysis
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:In this paper, we introduce a high-order accurate finite element method for incompressible variable density flow. The method uses high-order Taylor-Hood velocity-pressure elements in space and backward differentiation formula (BDF) time stepping in time. This way of discretization leads to two main issues: ( i ) a saddle point system that needs to be solved at each time step; a stability issue when the viscosity of the flow goes to zero or if the density profile has a discontinuity. We address the first issue by using Schur complement preconditioning and artificial compressibility approaches. We observed similar performance between these two approaches. To address the second issue, we introduce a modified artificial Guermond-Popov viscous flux where the viscosity coefficients are constructed using a newly developed residual-based shock-capturing method. Numerical validations confirm high-order accuracy for smooth problems and accurately resolved discontinuities for problems in 2D and 3D with varying density ratios.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2023.112608