Numerical Solution of the Time-Dependent Navier–Stokes Equation for Variable Density–Variable Viscosity. Part I

0455980 - ÚGN 2016 RIV LT eng J - Journal Article
Axelsson, Owe - Xin, H. - Neytcheva, M.
Numerical Solution of the Time-Dependent Navier–Stokes Equation for Variable Density–Variable Viscosity. Part I.
Mathematical Modeling and Analysis. Roč. 20, č. 2 (2015), s. 232-260. ISSN 1392-6292. E-ISSN 1648-3510
Institutional support: RVO:68145535
Keywords : variable density * phase-field model * Navier-Stokes equations * preconditioning * variable viscosity
Subject RIV: BA - General Mathematics
Impact factor: 0.468, year: 2015
http://www.tandfonline.com/doi/abs/10.3846/13926292.2015.1021395

We consider methods for the numerical simulations of variable density incompressible fluids, modelled by the Navier-Stokes equations. Variable density problems arise, for instance, in interfaces between fluids of different densities in multiphase flows such as appearing in porous media problems. We show that by solving the Navier-Stokes equation for the momentum variable instead of the velocity the corresponding saddle point problem, arising at each time step, no special treatment of the pressure variable is required and leads to an efficient preconditioning of the arising block matrix. This study consists of two parts, of which this paper constitutes Part I. Here we present the algorithm, compare it with a broadly used projectiontype method and illustrate some advantages and disadvantages of both techniques via analysis and numerical experiments. In addition we also include test results for a method, based on coupling of the Navier-Stokes equations with a phase-field model, where the variable density function is handled in a different way.
Permanent Link: http://hdl.handle.net/11104/0256609