Accession Number : ADA180768
Title : On the Accuracy of Finite Element and Finite Difference Predictions of Non-Newtonian Slot Pressures for a Maxwell Fluid.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : Malkus,David S. ; Webster,Michael F.
Report Date : DEC 1986
Pagination or Media Count : 35
Abstract : 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 e/N 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 1/4), both the FEM and FDM predict only minor deviation from this value for the Maxwell fluid, in the range < or = sub e < or =.
Descriptors : *VISCOUS FLOW, *SLOTS, FINITE DIFFERENCE THEORY, FINITE ELEMENT ANALYSIS, SHEAR PROPERTIES, REYNOLDS NUMBER, SHEAR STRESSES
Subject Categories : Fluid Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE