John Chrispell, Clemson University


A Fractional Step $\theta$-Method for Time Dependent Viscoelastic Fluid Flow

Abstract:  The accurate numerical approximation of viscoelastic fluid flow poses two difficulties: the large number of unknowns in the approximating algebraic system (corresponding to velocity, pressure, and stress), and the different mathematical types of the modeling equations. An appealing approximation approach is to use an operator splitting method which decouples the conservation of momentum equation from the constitutive equation. This split reduces the size of the linear systems that need to be solved and separates the parabolic and hyperbolic equations into different substeps. In this presentation, we describe the approximation scheme for the viscoelastic modeling equations, present numerical simulations, and give a-priori error estimates.

Advisor: Vince Ervin (Clemson)