A fractional step θ-method for viscoelastic fluid flow using a SUPG approximation

In this article a fractional step θ-method is described and studied for the approximation of time dependent viscoelastic fluid flow equations, using the Johnson-Segalman constitutive model. The θ-method implementation allows the velocity and pressure approximations to be decoupled from the stress, reducing the number of unknowns resolved at each step of the method. The constitutive equation is stabilized using a Streamline Upwinded Petrov-Galerkin (SUPG)-method. A priori error estimates are given for the approximation scheme. Numerical computations supporting the theoretical results and demonstrating the θ-method are also presented.

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