A Numerical Method for an Incompressible Fluid with Computational Cells of High Aspect Ratio

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<p>A numerical simulation of incompressible fluid dynamics is developed for computational cells having an aspect ratio larger than 10. In most cases, stability and precision of the existing numerical methods strongly depend on the distortion of cells, although cells with high aspect ratio are required in many situations of water systems such as rivers, lakes and oceans. The proposed method is based on the projection method with Helmholtz–Hodge decomposition of three dimensional Navier–Stokes equations, and is composed of two Poisson’s equations for long and short components of cell size, respectively. To demonstrate the ability of the method, three examples are calculated: (1) flow in a rectangular channel, (2) free surface motion in a shallow channel, and (3) flow in a shallow bay. As a result, it was observed that the proposed method can be easily applied to the prediction of three-dimensional flows using highly distorted computational cells.</p>

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