Spectral collocation domain decomposition method for viscoelastic flow simulations in model porous geometries

A domain decomposition spectral collocation (DDSC) method is developed for the solution of steady-state, non-linear viscoelastic flow problems. It is applied in simulations of viscoelastic flows through model porous media, represented by arrays of cylinders. The technique uses a splitting of the computational domain in sub-elements, in a fashion similar to finite elements. At each element, the solution is represented by using high-order, orthogonal polynomials. Static condensation is used for the solution of the linearized system of equations, resulting from the application of Newton's method. This approach is suggested by the limited connectivity between neighboring elements. Mesh converged solutions have been obtained for the flow of an Oldroyd-B fluid through a square array of cylinders, up to We = 5.0 and for the flow past a single row of cylinders, up to to We = 4.0.