A Cartesian Method with Second-Order Pressure Resolution for Incompressible Flows with Large Density Ratios

An Eulerian method to numerically solve incompressible bifluid problems with high density ratio is presented. This method can be considered as an improvement of the Ghost Fluid method, with the specificity of a sharp second-order numerical scheme for the spatial resolution of the discontinuous ellip...

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Autores principales:	Michel Bergmann, Lisl Weynans
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	incompressible Navier–Stokes equations projection method finite differences Cartesian grid immersed interfaces level-set Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85
Acceso en línea:	https://doaj.org/article/8f65e18989604e7dbb77d0d4efba2ceb
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id	oai:doaj.org-article:8f65e18989604e7dbb77d0d4efba2ceb
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spelling	oai:doaj.org-article:8f65e18989604e7dbb77d0d4efba2ceb2021-11-25T17:31:41ZA Cartesian Method with Second-Order Pressure Resolution for Incompressible Flows with Large Density Ratios10.3390/fluids61104022311-5521https://doaj.org/article/8f65e18989604e7dbb77d0d4efba2ceb2021-11-01T00:00:00Zhttps://www.mdpi.com/2311-5521/6/11/402https://doaj.org/toc/2311-5521An Eulerian method to numerically solve incompressible bifluid problems with high density ratio is presented. This method can be considered as an improvement of the Ghost Fluid method, with the specificity of a sharp second-order numerical scheme for the spatial resolution of the discontinuous elliptic problem for the pressure. The Navier–Stokes equations are integrated in time with a fractional step method based on the Chorin scheme and discretized in space on a Cartesian mesh. The bifluid interface is implicitly represented using a level-set function. The advantage of this method is its simplicity to implement in a standard monofluid Navier–Stokes solver while being more accurate and conservative than other simple classical bifluid methods. The numerical tests highlight the improvements obtained with this sharp method compared to the reference standard first-order methods.Michel BergmannLisl WeynansMDPI AGarticleincompressible Navier–Stokes equationsprojection methodfinite differencesCartesian gridimmersed interfaceslevel-setThermodynamicsQC310.15-319Descriptive and experimental mechanicsQC120-168.85ENFluids, Vol 6, Iss 402, p 402 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	incompressible Navier–Stokes equations projection method finite differences Cartesian grid immersed interfaces level-set Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85
spellingShingle	incompressible Navier–Stokes equations projection method finite differences Cartesian grid immersed interfaces level-set Thermodynamics QC310.15-319 Descriptive and experimental mechanics QC120-168.85 Michel Bergmann Lisl Weynans A Cartesian Method with Second-Order Pressure Resolution for Incompressible Flows with Large Density Ratios
description	An Eulerian method to numerically solve incompressible bifluid problems with high density ratio is presented. This method can be considered as an improvement of the Ghost Fluid method, with the specificity of a sharp second-order numerical scheme for the spatial resolution of the discontinuous elliptic problem for the pressure. The Navier–Stokes equations are integrated in time with a fractional step method based on the Chorin scheme and discretized in space on a Cartesian mesh. The bifluid interface is implicitly represented using a level-set function. The advantage of this method is its simplicity to implement in a standard monofluid Navier–Stokes solver while being more accurate and conservative than other simple classical bifluid methods. The numerical tests highlight the improvements obtained with this sharp method compared to the reference standard first-order methods.
format	article
author	Michel Bergmann Lisl Weynans
author_facet	Michel Bergmann Lisl Weynans
author_sort	Michel Bergmann
title	A Cartesian Method with Second-Order Pressure Resolution for Incompressible Flows with Large Density Ratios
title_short	A Cartesian Method with Second-Order Pressure Resolution for Incompressible Flows with Large Density Ratios
title_full	A Cartesian Method with Second-Order Pressure Resolution for Incompressible Flows with Large Density Ratios
title_fullStr	A Cartesian Method with Second-Order Pressure Resolution for Incompressible Flows with Large Density Ratios
title_full_unstemmed	A Cartesian Method with Second-Order Pressure Resolution for Incompressible Flows with Large Density Ratios
title_sort	cartesian method with second-order pressure resolution for incompressible flows with large density ratios
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/8f65e18989604e7dbb77d0d4efba2ceb
work_keys_str_mv	AT michelbergmann acartesianmethodwithsecondorderpressureresolutionforincompressibleflowswithlargedensityratios AT lislweynans acartesianmethodwithsecondorderpressureresolutionforincompressibleflowswithlargedensityratios AT michelbergmann cartesianmethodwithsecondorderpressureresolutionforincompressibleflowswithlargedensityratios AT lislweynans cartesianmethodwithsecondorderpressureresolutionforincompressibleflowswithlargedensityratios
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A Cartesian Method with Second-Order Pressure Resolution for Incompressible Flows with Large Density Ratios

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