Numerical investigation on a new local preconditioning method for solving the incompressible inviscid, non-cavitating and cavitating flows

A locally power-law preconditioning algorithm is developed. This is applied to compute incompressible inviscid, steady-state, non-cavitating and cavitating flows. The preconditioning parameters are adapted automatically from the pressure of computational domain. This method suggests better convergence rates rather than the standard artificial compressibility and the standard preconditioning method. Single-fluid Euler equations, cast in their conservative form, along with the barotropic cavitation model are employed. The cell-centred Jameson's finite volume discretization technique is used to solve the preconditioned governing equations. The stabilization is achieved via the second and fourth, order artificial dissipation scheme. Explicit four-stage Runge-Kutta time integration is applied to find the steady-state condition. In this paper, the method is assessed through simulations of incompressible inviscid, steady-state, non-cavitating and cavitating flows over a 2D NACA0012 and a 2D NACA66(MOD)+a=0.8 hydrofoil section. The results show satisfactory agreement with others numerical and experimental works in pressure distribution and hydrodynamic forces. Using the power-law preconditioner decreases the convergence rate significantly. In addition, information such as the effects of the new locally power-law preconditioner, the effects of the artificial dissipation terms, and the effects of the artificial compressibility parameter, on convergence speed and solution accuracy is highlighted.