APPLICATION OF SPECTRAL ELEMENTS TO VISCOELASTIC CREEPING FLOWS

The spectral element method is analyzed for the simulation of viscoela stic fluid flows in plane and cylindrical geometries. The implementati on of the method and choices of functional spaces is discussed in deta il. The method is then applied to the case of the Maxwell-B fluid and compared with the so-called 4 x 4 SUPG finite element method on the pe rturbed channel flow problem. Analysis of the rate of convergence of t he method is provided as well as thorough discussion on the decomposit ion of the geometry in spectral elements: the choice is between the h- vs. p-refinement. A comparison with other numerical (e.g. pseudo-spec tral) methods is performed for the flow of the Maxwell-B fluid in a wa vy tube. In each test case, very good agreement is found.