On the Accuracy of Finite Element and Finite Difference Predictions of Non-Newtonian Slot Pressures for a Maxwell Fluid
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 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 expect either method accurately to obtain the singular limit of P e /N 1 as D e → 0. Also an explanation for the errors at very low D e is offered. If we presume the the second-order fluid (SOE) result holds for very low D e (i. e. P e = N 1/4), both the FEM and FDM predict only minor deviation from this value for the Maxwell fluid, in the range 0 ≤ D e ≤ 1.
KeywordsError Model Mesh Refinement Finite Difference Method Discretization Error Error Indicator
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