Momentum‐based approximation of incompressible multiphase fluid flows

Summary We introduce a time stepping technique using the momentum as dependent variable to solve incompressible multiphase problems. The main advantage of this approach is that the mass matrix is time‐independent making this technique suitable for spectral methods. A level set method is applied to r...

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Bibliographic Details
Published in:International journal for numerical methods in fluids Vol. 86; no. 8; pp. 541 - 563
Main Authors: Cappanera, Loïc, Guermond, Jean‐Luc, Herreman, Wietze, Nore, Caroline
Format: Journal Article
Language:English
Published: Bognor Regis Wiley Subscription Services, Inc 20.03.2018
Wiley
Subjects:
Algorithms
Aluminium
Aluminum
Approximation
Compression
Computational fluid dynamics
Computer simulation
Conducting fluids
Dependent variables
Entropy
finite elements
Fluid flow
Fluid mechanics
Fluids
Incompressible flow
incompressible flows
Industrial production
level set method
magnetohydrodynamics
Mass matrix
Mathematical models
Maxwell's equations
Mechanics
Momentum
Multiphase
multiphase flows
Navier-Stokes equations
Physics
pseudo‐spectral methods
Solutions
Spectral methods
Surface tension
Viscosity
pseudo-spectral methods
multiphase flow
level set method
incompressible flows
finite elements
magnetohydrodynamics
ISSN:0271-2091, 1097-0363
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Summary:Summary We introduce a time stepping technique using the momentum as dependent variable to solve incompressible multiphase problems. The main advantage of this approach is that the mass matrix is time‐independent making this technique suitable for spectral methods. A level set method is applied to reconstruct the fluid properties such as density. We also introduce a stabilization method using an entropy‐viscosity technique and a compression technique to limit the flattening of the level set function. We extend our algorithm to immiscible conducting fluids by coupling the incompressible Navier‐Stokes and the Maxwell equations. We validate the proposed algorithm against analytical and manufactured solutions. Results on test cases such as Newton's bucket problem and a variation thereof are provided. Surface tension effects are tested on benchmark problems involving bubbles. A numerical simulation of a phenomenon related to the industrial production of aluminium is presented at the end of the paper. We introduce a time stepping technique using the momentum as dependent variable to solve incompressible multiphase problems. The mass matrix is time‐independent making this technique suitable for spectral methods. A level set method is applied to reconstruct the fluid properties such as density. The algorithm is validated over various tests cases, and a numerical simulation of a phenomenon related to the industrial production of aluminium is presented at the end of the paper.
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ISSN:0271-2091
1097-0363
DOI:10.1002/fld.4467