Abstract
The pressure equation, generated while solving the incompressible Navier–Stokes equations with the segregated iterative algorithm such as PISO, produces a series of linear equation systems as the time step advances. In this paper, we target at accelerating the iterative solution of these linear systems by improving their initial guesses. We propose a weighted group extrapolation method to obtain a superior initial guess instead of a general one, the solution of the previous linear equation system. In this method, the previous solutions that are used to extrapolate the predicted solutions are carefully organized to address the oscillatory solution on each grid. The proposed method uses a weighted average of the predicted solutions as the new initial guess to avoid over extrapolating. Three numerical test results show that the proposed method can accelerate the iterative solution of most linear equation systems and reduce the simulation time up to 61.3%.
Highlights
The numerical simulation of incompressible flow is a complex nonlinear problem and governed by the Navier–Stokes equations [1,2,3]
The solution of the pressure equation generated in PISO or PIMPLE has dominated the computational cost in the whole simulation
The most time-consuming part is to solve a series of linear equation systems arising from the pressure equation
Summary
The numerical simulation of incompressible flow is a complex nonlinear problem and governed by the Navier–Stokes equations [1,2,3]. In the last few decades, several methods were proposed for choosing a superior initial guess while solving a series of linear equation systems These methods generally fall into two categories, namely the project-based method and the extrapolation-based method. While solving the pressure-velocity coupling, the solution on each cell usually appears to be oscillatory in successive linear equation systems, especially using some iterative algorithms such as PISO, etc. We propose a weighted group extrapolation method to improve the initial guesses for the series of linear equation systems in the incompressible flow. We propose a weighted group extrapolation method for improving the initial guess of the linear equation systems in incompressible flow.
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