A Study on Numerical Schemes for More Accurate and Efficient Computations of Free-Surface Flows by Finite Difference Method〔含討論〕

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Some new numerical approaches are studied in the numerical simulation of free-surface flow around a submerged NACA 0012 hydrofoil based on the solving of full 2-D laminar incompressible Navier-Stokes equations. First, a new finite difference scheme for the calculation of the free-surface elevation is studied where the third derivative term of the wave elevation is additionally introduced in the Eulerian expression of the free-surface boundary condition. Some investigations concerning the new formulation for both the free-surface and downstream boundary conditions are done. The paper presents a comparative analysis with simulations performed by using the classical MAC method, emphasizing an acceleration of the wave elevation. More schematic computations, studies on the grid size, a finite difference scheme for the free-surface computations and some special treatments of the open boundaries are carried out. It is pointed out that according to the proposed formulation, the new numerical method becomes more efficient, primarily due to the fact that the elevation is much accelerated and because the increasing of the grid size does not affect the accuracy of the final results. The total CPU time can also be decreased while the flow characteristics are preserved.
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