On the Design of Algebraic Fractional Step Methods for Viscoelastic Incompressible Flows
Classical fractional step methods for viscous incompressible flows aim to uncouple the calculation of the velocity and the pressure. In the case of viscoelastic flows, a new variable appears, namely, a stress, which has an elastic and a viscous contribution. The purpose of this article is to present two families of fractional step methods for the time integration of this type of flows whose objective is to permit the uncoupled calculation of velocities, stresses and pressure, both families designed at the algebraic level. This means that the splitting of the equations is introduced once the spatial and the temporal discretizations have been performed. The first family is based on the extrapolation of the pressure and the stress in order to predict a velocity, then the calculation of a new stress, the pressure and then a correction to render the scheme stable. The second family has a discrete pressure Poisson equation as starting point; in this equation, velocities and stresses are extrapolated to compute a pressure, and from this pressure stresses and velocities can then be computed. This work presents an overview of methods previously proposed in our group, as well as some new schemes in the case of the second family.
KeywordsFractional step schemes Viscoelastic flows Pressure extrapolation Velocity extrapolation Inexact factorization
The author wishes to acknowledge the financial support received from project Elastic-Flow, ref. DPI2015-67857-R, from the Retos Investigación program of the Spanish Ministerio de Economía y Competitividad.
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