Mathematical analysis of large eddy simulation of turbulent flows. (English) Zbl 1081.76002

Świerczewska, Agnieszka

Berichte aus der Mathematik. Aachen: Shaker Verlag; Darmstadt: Univ. Darmstadt, Fachbereich Mathematik (Diss.) (ISBN 3-8322-3583-3/pbk). 86 p. (2004).

The work is a PhD thesis devoted to large eddy simulation of turbulent flows. It consists of six chapters. In Chapter 1, which is an introduction, the theoretical background is given. In Chapter 2, the solutions of the steady-state equation with periodic boundary conditions are analyzed. A theorem which provides a shorter way of showing the convergence of the nonlinear turbulent term is proved in Chapter 3. In Chapter 4, the proof of the existence of a weak solution to the stationary boundary value problem is presented, and in Chapter 5, the same is done for the time-dependent boundary value problem. Finally, in Chapter 6, the existence of solutions is proved for a time-dependent problem with periodic boundary conditions.

Reviewer: Alexander V. Gemintern (Haifa)

MSC:

76-02	Research exposition (monographs, survey articles) pertaining to fluid mechanics
76F65	Direct numerical and large eddy simulation of turbulence
35Q35	PDEs in connection with fluid mechanics

Keywords:

periodic boundary conditions; convergence; existence; weak solution