A stable second‐order mass‐weighted upwind scheme for unstructured meshes

In this paper, an original second‐order upwind scheme for convection terms is described and implemented in the context of a Control‐Volume Finite‐Element Method (CVFEM). The proposed scheme is a second‐order extension of the first‐order MAss‐Weighted upwind (MAW) scheme proposed by Saabas and Baliga (Numer. Heat Transfer 1994; 26B :381–407). The proposed second‐order scheme inherits the well‐known stability characteristics of the MAW scheme, but exhibits less artificial viscosity and ensures much higher accuracy. Consequently, and in contrast with nearly all second‐order upwind schemes available in the literature, the proposed second‐order MAW scheme does not need limiters. Some test cases including two pure convection problems, the driven cavity and steady and unsteady flows over a circular cylinder, have been undertaken successfully to validate the new scheme. The verification tests show that the proposed scheme exhibits a low level of artificial viscosity in the pure convection problems; exhibits second‐order accuracy for the driven cavity; gives accurate reattachment lengths for low‐Reynolds steady flow over a circular cylinder; and gives constant‐amplitude vortex shedding for the case of high‐Reynolds unsteady flow over a circular cylinder. Copyright © 2005 John Wiley & Sons, Ltd.