A characteristics strategy for solving advection equations in 2D steady flows containing recirculating areas

摘要

Numerical modelling of non-Newtonian flows usually involves the coupling between equations of motion characterized by an elliptic character, and the fluid constitutive equation, which defines an advection problem linked to the fluid history. There are different numerical techniques to treat the hyperbolic character of advection equations. In non-recirculating flows, Eulerian discretisations can give an accurate mesh size dependent solution within a short computing time. However, the existence of steady recirculating flow areas induces additional difficulties. Actually, in these flows neither boundary conditions nor initial conditions are known. In a former paper we have proved that in such flows Eulerian techniques lead to solutions with significant deviations from the exact one. These deviations obviously decrease as the mesh density increases. In other paper, the authors have proved that some linear advection equations modelling non-Newtonian fluid behaviors have only one solution in steady recirculating flows. This solution is found imposing the solution periodicity along the closed streamlines, where the equation is integrated by the method of characteristics. In this paper we propose a characteristics algorithm for solving advection equations in general steady flows, which may contain recirculating areas.