Numerical Solution of the Time-Dependent Navier–Stokes Equation for Variable Density–Variable Viscosity. Part I
Abstract
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.
The theory including stability bounds and a second order splitting method is dealt with in Part II of the study.
Keywords:
Navier–Stokes equations, variable density, variable viscosity, operator splitting methods, regularization, phase-field model, finite elements, iterative methods, preconditioningHow to Cite
Share
License
Copyright (c) 2015 The Author(s). Published by Vilnius Gediminas Technical University.
This work is licensed under a Creative Commons Attribution 4.0 International License.
View article in other formats
Published
Issue
Section
Copyright
Copyright (c) 2015 The Author(s). Published by Vilnius Gediminas Technical University.
License
This work is licensed under a Creative Commons Attribution 4.0 International License.