Momentum‐based approximation of incompressible multiphase fluid flows

• Published in: International journal for numerical methods in fluids 2018-03, Vol.86 (8), p.541-563
• Main Authors: Cappanera, Loïc, Guermond, Jean‐Luc, Herreman, Wietze, Nore, Caroline
• Format: Article
• Language: English
• Subjects: 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
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4467

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.