The Finite Volume Method in Computational Fluid Dynamics by F. Moukalled L. Mangani & M. Darwish

Author:F. Moukalled, L. Mangani & M. Darwish
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

11.2.4 The Upwind Scheme

When examining the discretization procedure described above, it is noticed that the reason for obtaining these positive coefficients is because of the adopted linear symmetric profile. A linear symmetric profile gives equal weights to the two nodes sharing the face with no directional preference, which is appropriate for non-directional phenomena with an elliptic type term, such as the diffusion term. It is simply not adequate for the convection term [4].

A scheme that is more compatible with the advection process is the upwind scheme [4, 6] schematically displayed in Fig. 11.6. The upwind scheme basically mimics the basic physics of advection in that the cell face value is made dependent on the upwind nodal value, i.e., dependent on the flow direction. In this case the cell face values for the configuration displayed in Fig. 11.6 are given by

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