Modelling of turbulence energy decay based on hybrid methods

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.

Mathematical formulation F large eddy simulation using hybrid finite difference methods and poisson equations

“…The intermediate velocity field is solved using the Adams Bashforth scheme combined with a five-point sweep method. The numerical algorithm for solving incompressible MHD turbulence without considering large eddy simulation is considered (Abdibekova et al, 2018). Let's consider the velocity component u 1 in the horizontal direction at the spatial location (i + 1/2,j,k):…”

Modelling the Influence of Electron Concentration on MHD Turbulence by Les

“…For approximation of the convective and diffusion terms of the intermediate velocity field a finite-difference method in combination with penta-diagonal matrix is used, which allowed to increase the order of accuracy in space. The numerical algorithm for the solution of incompressible MHD turbulence without large eddy simulation is considered at [15]. The intermediate velocity field is solved using the Adams-Bashfort scheme in combination with the five-point sweep method.…”

“…The Poisson equation is transformed from the physical space into the spectral space by using a Fourier transform. To solve the three-dimensional Poisson equation, the spectral conversion in combination with matrix sweeping algorithm is developed [15]. The resulting pressure field in the third stage is used to recalculate the final velocity field [16].…”

The HFD method for large eddy simulation of MHD turbulence decay

“…The intermediate velocity field is solved by using the Adams-Bashforth scheme in combination with a five-point sweep method. The numerical algorithm for the solution of incompressible MHD turbulence without taking into account large eddy simulation is considered at [1]. Let's consider the velocity component u 1 in the horizontal direction at the spatial location (i + 1/2, j, k):…”

“…Therefore, Equation ( 7) is actually an order O (∆t 4 ) approximation to equation (6), rather than an order O (∆t 3 ) approximation as stated in [13] without proof. Since the difference between q * i+ 1 2 jk and q i+ 1 2 jk is of higher order, we shall return to the same notation and just use q i+ 1 2 jk . To determine q i+ 1 2 jk , equation ( 7) is solved in 3 stages in sequence as follows:…”