Modelling of turbulence energy decay based on hybrid methods. Issue 5 (2nd July 2018) - Abdibekova, Aigerim; Zhakebayev, Dauren; Abdigaliyeva, Akmaral; Zhubat, Kuanysh
Abstract : Purpose: The purpose of this study is to present an exact and fast-calculated algorithm for the modelling of turbulent energy decay based on two different methods: finite-difference and spectral methods. Design/methodology/approach: The filtered three-dimensional non-stationary Navier–Stokes equation is used for simulating the turbulent process. The problem is solved using hybrid methods, where the equation of motion is solved using finite difference methods in combination with cyclic penta-diagonal matrix, which allowed to reach high order of accuracy, and Poisson equation is solved using the spectral methods, which is proposed to speed up the solution procedure. For validation of the given algorithm, the turbulent characteristics were compared with the exact solution of the classical Taylor and Green vortex problem, showing good agreement. Findings: The proposed method shows high computational efficiency and good estimation quality. A numerical algorithm for solving non-stationary three-dimensional Navier–Stokes equations for modelling of isotropic turbulence decay using hybrid methods was developed. The simulation's turbulence characteristics show good agreements with analytical solution. The developed numerical algorithm can be used for simulation of turbulence decay with different values of viscosity. Originality/value: An efficient algorithm for simulation of turbulence processes depending on the properties of the viscosity was developed.