On the accuracy of finite-difference and finite-element methods for the simulation of some incompressible flows

摘要

Four different finite-difference (FD) approximations and a finite-element (FE) scheme are compared with regard to their accuracy. The relative accuracy of the different schemes is problem dependent and it is not possible to estimate, a priori the accuracy of a given scheme. In the case of finite-differences first, second, fourth and sixth order approximations are used. In the case of finite-elements a non-upwinding artificial viscosity is used. The different numerical schemes have been applied to the simulation of the flow in a lid-driven cavity and in a bifurcating channel. In the former case, the absolute accuracy of each scheme could be determined. The FD scheme with upwinding turned out to be more accurate only for low Reynolds numbers (Re), whereas the artificial viscosity used with the FE is relatively more accurate with increasing Re. In the case of the bifurcating channel the FD and the FE schemes use different types of boundary conditions. Nevertheless the agreement between the results is, graphically, very good.