# American Institute of Mathematical Sciences

• Previous Article
Exact boundary controllability and observability for first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions
• DCDS Home
• This Issue
• Next Article
Asynchronous time integration for polynomial chaos expansion of uncertain periodic dynamics
March  2010, 28(1): 227-241. doi: 10.3934/dcds.2010.28.227

## Two-point closure based large-eddy simulations in turbulence. Part 2: Inhomogeneous cases

 1 Member of French Academy of Sciences, Laboratory for Geophysical and Industrial Flows, Grenoble, France

Received  September 2009 Revised  November 2009 Published  April 2010

This is the second of two articles dedicated to Roger Temam and Claude-Michel Brauner on turbulence large-eddy simulations using stochastic two-point closures. The first paper [31] has dealt with applications to isotropic turbulence. It has also discussed personal memories of Roger and Claude-Michel, and how we have collaborated on turbulence two-point closures applied to Burgers equation by studying the so-called Burgers-MRCM model. The present paper is basically a review of what can be done with the same models for LES of inhomogeneous turbulence (free-shear and wall-bounded flows) both in incompressible and compressible situations. It borrows results taken from Lesieur and colleagues [28][29][30]. We discuss also simulations obtained with the aid of dynamic multilevel methods (DML) of Dubois, Jauberteau and Temam [19]. Afterwards we consider the incompressible free-shear flows: temporal mixing layers, for which we review the helical-pairing phenomenon both numerically and experimentally, and mixing of a passive scalar in coaxial jets. We study the plane channel with LES and DML calculations. We look at passive control using longitudinal riblets and optimal control as developed by Temam and coworkers. We calculate with DNS and LES channels and mixing layers rotating about a spanwise axis, and demonstrate a universal character of the local Rossby number in anticyclonic regions. Finally we discuss compressible turbulence LES with applications to a subsonic (Mach 0.7) and supersonic (Mach 1.4) round jet.
Citation: Marcel Lesieur. Two-point closure based large-eddy simulations in turbulence. Part 2: Inhomogeneous cases. Discrete & Continuous Dynamical Systems, 2010, 28 (1) : 227-241. doi: 10.3934/dcds.2010.28.227
 [1] Marcel Lesieur. Two-point closure based large-eddy simulations in turbulence, Part 1: Isotropic turbulence. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 155-168. doi: 10.3934/dcdss.2011.4.155 [2] Wen-Chiao Cheng. Two-point pre-image entropy. Discrete & Continuous Dynamical Systems, 2007, 17 (1) : 107-119. doi: 10.3934/dcds.2007.17.107 [3] Feliz Minhós, A. I. Santos. Higher order two-point boundary value problems with asymmetric growth. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 127-137. doi: 10.3934/dcdss.2008.1.127 [4] Wenming Zou. Multiple solutions results for two-point boundary value problem with resonance. Discrete & Continuous Dynamical Systems, 1998, 4 (3) : 485-496. doi: 10.3934/dcds.1998.4.485 [5] Jerry L. Bona, Hongqiu Chen, Shu-Ming Sun, Bing-Yu Zhang. Comparison of quarter-plane and two-point boundary value problems: The KdV-equation. Discrete & Continuous Dynamical Systems - B, 2007, 7 (3) : 465-495. doi: 10.3934/dcdsb.2007.7.465 [6] Xiao-Yu Zhang, Qing Fang. A sixth order numerical method for a class of nonlinear two-point boundary value problems. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 31-43. doi: 10.3934/naco.2012.2.31 [7] Jerry Bona, Hongqiu Chen, Shu Ming Sun, B.-Y. Zhang. Comparison of quarter-plane and two-point boundary value problems: the BBM-equation. Discrete & Continuous Dynamical Systems, 2005, 13 (4) : 921-940. doi: 10.3934/dcds.2005.13.921 [8] Shao-Yuan Huang, Shin-Hwa Wang. On S-shaped bifurcation curves for a two-point boundary value problem arising in a theory of thermal explosion. Discrete & Continuous Dynamical Systems, 2015, 35 (10) : 4839-4858. doi: 10.3934/dcds.2015.35.4839 [9] Hirotoshi Kuroda, Noriaki Yamazaki. Approximating problems of vectorial singular diffusion equations with inhomogeneous terms and numerical simulations. Conference Publications, 2009, 2009 (Special) : 486-495. doi: 10.3934/proc.2009.2009.486 [10] Vakhtang Putkaradze, Stuart Rogers. Numerical simulations of a rolling ball robot actuated by internal point masses. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 143-207. doi: 10.3934/naco.2020021 [11] Carlos Escudero, Fabricio Macià, Raúl Toral, Juan J. L. Velázquez. Kinetic theory and numerical simulations of two-species coagulation. Kinetic & Related Models, 2014, 7 (2) : 253-290. doi: 10.3934/krm.2014.7.253 [12] Florian Schneider, Andreas Roth, Jochen Kall. First-order quarter-and mixed-moment realizability theory and Kershaw closures for a Fokker-Planck equation in two space dimensions. Kinetic & Related Models, 2017, 10 (4) : 1127-1161. doi: 10.3934/krm.2017044 [13] Diego Samuel Rodrigues, Paulo Fernando de Arruda Mancera. Mathematical analysis and simulations involving chemotherapy and surgery on large human tumours under a suitable cell-kill functional response. Mathematical Biosciences & Engineering, 2013, 10 (1) : 221-234. doi: 10.3934/mbe.2013.10.221 [14] M. Mahalingam, Parag Ravindran, U. Saravanan, K. R. Rajagopal. Two boundary value problems involving an inhomogeneous viscoelastic solid. Discrete & Continuous Dynamical Systems - S, 2017, 10 (6) : 1351-1373. doi: 10.3934/dcdss.2017072 [15] K. Q. Lan, G. C. Yang. Optimal constants for two point boundary value problems. Conference Publications, 2007, 2007 (Special) : 624-633. doi: 10.3934/proc.2007.2007.624 [16] Eleftherios Gkioulekas, Ka Kit Tung. On the double cascades of energy and enstrophy in two dimensional turbulence. Part 1. Theoretical formulation. Discrete & Continuous Dynamical Systems - B, 2005, 5 (1) : 79-102. doi: 10.3934/dcdsb.2005.5.79 [17] Luigi C. Berselli, Argus Adrian Dunca, Roger Lewandowski, Dinh Duong Nguyen. Modeling error of $\alpha$-models of turbulence on a two-dimensional torus. Discrete & Continuous Dynamical Systems - B, 2021, 26 (9) : 4613-4643. doi: 10.3934/dcdsb.2020305 [18] Kai-Uwe Schmidt, Jonathan Jedwab, Matthew G. Parker. Two binary sequence families with large merit factor. Advances in Mathematics of Communications, 2009, 3 (2) : 135-156. doi: 10.3934/amc.2009.3.135 [19] François Baccelli, Augustin Chaintreau, Danny De Vleeschauwer, David R. McDonald. HTTP turbulence. Networks & Heterogeneous Media, 2006, 1 (1) : 1-40. doi: 10.3934/nhm.2006.1.1 [20] Luca Bisconti, Davide Catania. Global well-posedness of the two-dimensional horizontally filtered simplified Bardina turbulence model on a strip-like region. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1861-1881. doi: 10.3934/cpaa.2017090

2019 Impact Factor: 1.338