A Study on the accuracy of finite volume numerical models with non-rectangular mesh

Abstract

During numerical simulation of complex geometries and flow depth variations, non-rectangular computational cells are to be generated. However, application of this kind of mesh cause numerical errors. A 3-D model, which was verified and validated before, was used to illustrate the problem in a simple open channel flow. A zigzag computational mesh was used to study the effect of non-rectangular cells on the accuracy of the model. Results showed that water surface and velocity profiles oscillated around the correct answer. Investigating the reason for this oscillation showed that assuming constant velocity at non-rectangular computational cell surfaces, which is a usual practice in all numerical schemes, cause this error. Variation of velocity at mesh surfaces was then added to the computation model and as a result, the oscillations in velocity profiles and water surface were eliminated. Further analysis showed that this is a general problem in any finite volume model with non-rectangular mesh.