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Cavitating/non-cavitating flows simulation by third-order finite volume scheme and power-law preconditioning method

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Abstract

Equations of steady inviscid and laminar flows are solved by means of a third-order finite volume (FV) scheme. For this purpose, a cell-centered discretization technique is employed. In this technique, the flow parameters at the cell faces are computed using a third-order weighted averages procedure. A fourth-order artificial dissipation is used for stability of the solution. In order to achieve the steady-state situation, four-step Runge-Kutta explicit time integration method is applied. An advanced progressive preconditioning method, named the power-law preconditioning method, is used for faster convergence. In this method, the preconditioning matrix is adjusted automatically from the velocity and/or pressure flow-field by a power-law relation. Attention is directed towards accuracy and convergence of the schemes. The results presented in the paper focus on steady inviscid and laminar flows around sheet-cavitating and fully-wetted bodies including hydrofoils and circular/elliptical cylinder. Excellent agreements are obtained when numerical predictions are compared with other available experimental and numerical results. In addition, it is found that using the power-law preconditioner significantly increases the numerical convergence speed.

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  1. School of Mechanical Engineering, Shahrood University of Technology, Shahrood, 3619995161, Iran

    P. Akbarzadeh

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Akbarzadeh, P. Cavitating/non-cavitating flows simulation by third-order finite volume scheme and power-law preconditioning method. Appl. Math. Mech.-Engl. Ed. 34, 209–228 (2013). https://doi.org/10.1007/s10483-013-1664-7

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