On the Accuracy of Finite Element and Finite Difference Predictions of Non-Newtonian Slot Pressures for a Maxwell Fluid.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Plane slow flow of a Maxwell fluid over a transverse slot is considered. Results are computed by a finite difference method FDM using the differential form of the constitutive equation, and by a finite element method FEM using the integral form. Even on fine grids, the two methods produce different results, particularly at low D sub e. However, extrapolation of the results to zero mesh spacing shows excellent agreement between the two methods. Hence both methods are convergent with mesh refinement, but high accuracy would require extremely fine meshes. An explanation is provided for why it is unreasonable to expert either method accurately to obtain the singular limit of P sub eN sub 1 as D sub e approaches limit of 0. Also an explanation for the errors at very low D sub e is offered. If we presume the second-order fluid SOE result holds for very low D sub e i. e. P sub e N sub 14, both the FEM and FDM predict only minor deviation from this value for the Maxwell fluid, in the range or sub e or .
- Fluid Mechanics