Discretization Techniques of Height Function Method for Greater Increased Accuracy of Mass Conservation

Boonchai LERTNUWAT

Abstract


A height function method has been used to solve the shape of free surfaces in incompressible viscous flows for hydrodynamics. Three proposed discretization techniques for the height function method are developed with particular attention to the law of mass conservation. The concept of the proposed techniques is to place a control volume on the most appropriate location in any staggered grid system. First, the proposed techniques and the conventional technique are verified with a simple problem whose exact solution is known. Then, all numerical techniques are examined with a more complicated problem to investigate their accuracy. The simulated results of the proposed techniques are compared to those of conventional technique. Finally, it is concluded that (1) the proposed techniques will give better results than the conventional technique if the grid resolution is sufficiently fine, (2) the first proposed technique gives poorer results than the other proposed techniques, and (3) the second proposed technique gives better results than the third proposed technique, but the third proposed technique is easier to apply due to its explicit form of the equation.

doi:10.14456/WJST.2015.14

Keywords


Finite volume method, free surface, height function method, hydrodynamic, two-phase flow

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References


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