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

In the process of numerical simulation of complex geometries and ow depth variations, non-rectangular computational cells are generated. However, the application of this type of mesh causes numerical errors. A 3D model, which was verified and validated before, was used to shed light on the problem in a simple, open channel ow. 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 proles oscillated around the correct answer. Investigating the reason for this oscillation showed that assuming constant velocity on non-rectangular computational cell surfaces, which is a usual practice in all numerical schemes, cause this error. Variation of velocity on mesh surfaces was then added to the computation model and as a result, the oscillations in velocity proles and water surface were eliminated. Further analysis showed that this is a general problem in any finite volume method with a non-rectangular mesh.