Abstract
A new staggered-grid, finite-volume method for the numerical simulation of isothermal viscoelastic liquids is presented. The main features of this method are the use of a primitive variable formulation, the location of the velocities, pressures and stresses on different staggered grids and the use of a third-order difference scheme for the discretization of the constitutive equations. The method is applied to a sudden-expansion, viscoelastic-flow problem for a range of Weissenberg numbers. For one case the mesh has been refined to demonstrate that the method is robust and viscoelastic effects are not filtered out as the mesh size decreases. All the computations have been performed on a PC equipped with a floating-point coprocessor. Although the method has been defined for, and applied to, two-dimensional problems, the technique is readily extendable to three dimensions without excessive cost.
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