A new convergent and universally bounded interpolation scheme for the treatment of advection: application to viscoelastic simulations

• Type: Article in International Conference Proceedings Book
• Date: 2002

Authors

M. A. Alves (Author) FEUP; P. J. Oliveira (Author) Other; F. T. Pinho (Author) FEUP

Conference proceedings National

Title: Erheo

Pages: 121-124

ERHEO2002

Scientific classification

FOS: Engineering and technology

Other information

Abstract (EN): Accurate predictions of viscoelastic flows require discretisation schemes for convection of at least second-order accuracy. In an important paper, Godunov [1] demonstrated that all monotone (bounded) linear schemes could be at most firstorder accurate. The only way to avoid this limitation is thus the development of nonlinear composite schemes, usually referred to as highresolution schemes (HRS). Several discretisation schemes were proposed in the last years based on either the total variation diminishing framework (TVD) [2], on the normalised variable formulation (NVF) [3], or others. The NVF approach has been extended to non-uniform grids yielding the normalised variable and space formulation (NVSF) [4], to be used here. Although HRS¿s have seen widespread usage in the last years, there are still some convergence difficulties with these methods [5]. This work aims at developing a new HRS with good accuracy and enhanced convergence properties. The new scheme, named Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection (CUBISTA), has similar accuracy to the well-known SMART scheme [6], both being thirdorder accurate on uniform meshes. The upper-convected Maxwell (UCM) model was selected to assess the performance of the CUBISTA scheme due to the hyperbolic nature and the known numerical difficulties of these stress equations. The benchmark flow of a UCM fluid in a 4:1 planar contraction is used to compare the performance of different highresolution schemes, and thus serving to illustrate the superiority of the CUBISTA scheme in terms of iterative convergence (robustness).

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 4