# Modelling of the turbulent energy decay based on the finite-difference and spectral methods

### Abstract

The work deals with the modeling of turbulent energy using finite-difference and spectral methods. Simulation of the turbulent process is based on the filtered three-dimensional unsteady Navier-Stokes equations, for the closure of the main equation the dynamic model is used. The mathematical model is solved numerically, the equation of motion is solved by a finite-difference method, the equation for pressure is solved by spectral method. Also new algorithm for the numerical solution of the Poisson equation for finding pressure is developed. In the results of simulation, the change of turbulent kineticenergy over the time, the integral length scale, the change of longitudinal-transverse correlation functions are obtained, and longitudinal and transverse one-dimensional spectra are defined.

### References

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7. Wang L.P, Ayala O, Gao H, Andersen C, Mathews K. Study of forced turbulence and its modulation by finite-size solid particles using the lattice Boltzmann approach // Comput. & Math. with Applications. – 2014. – No 67. – P. 363-380.

2. Khintce I.О. Turbulence, its mechanism and theory. – М.:Fizmatgiz, 1963. – 680 p.

3. Ferziger J.H. Large eddy simulation of turbulent flows // AIAA J., 1977. – Vol 15, No 9. – P. 1261-1267.

4. Sagaut P. Large eddy simulation for incompressible flows. – Heidelberg: Springer-Verl., 2002. – 423 p.

5. Samarskii A.A., Nikolaev E.S. Methods for solving grid equations. – M.:Nauka, 1978. – P. 73-120

6. Abdibekov U.S., Zhumagulov B.T., Zhakebayev D.B., Zhubat K.Z. Modelling of the decay of isotropic turbulence by the LES // Mathematical Models and Computer Simulations. Springer. – 2013. – Vol. 5, No 4. – P. 360–370.

7. Wang L.P, Ayala O, Gao H, Andersen C, Mathews K. Study of forced turbulence and its modulation by finite-size solid particles using the lattice Boltzmann approach // Comput. & Math. with Applications. – 2014. – No 67. – P. 363-380.

Published

2016-06-27

How to Cite

ABDIGALIYEVA, A. N..
Modelling of the turbulent energy decay based on the finite-difference and spectral methods.

**International Journal of Mathematics and Physics**, [S.l.], v. 7, n. 1, p. 4-9, june 2016. ISSN 2409-5508. Available at: <http://ijmph.kaznu.kz/index.php/kaznu/article/view/152>. Date accessed: 23 apr. 2018.
Section

Mathematical Modeling

### Keywords

turbulent energy, finite-difference method, spectral method, Poisson equation, cyclic penta- diagonal scheme.