# American Institute of Mathematical Sciences

• Previous Article
Global existence of weak solution to the free boundary problem for compressible Navier-Stokes
• KRM Home
• This Issue
• Next Article
Propagation of chaos for the spatially homogeneous Landau equation for Maxwellian molecules
March  2016, 9(1): 51-74. doi: 10.3934/krm.2016.9.51

## Asymptotic preserving scheme for a kinetic model describing incompressible fluids

 1 Inria Rennes Bretagne Atlantique (team IPSO) and IRMAR, University of Rennes 1, Campus de Beaulieu, 35042 Rennes, France 2 CNRS and IRMAR, University of Rennes 1, Campus de Beaulieu, 35042 Rennes, France 3 Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India 4 National Mathematics Initiative, Indian Institute of Science, Bangalore, India 5 Department of Civil Engineering, Indian Institute of Science, Bangalore, India

Received  September 2014 Revised  July 2015 Published  October 2015

The kinetic theory of fluid turbulence modeling developed by Degond and Lemou in [7] is considered for further study, analysis and simulation. Starting with the Boltzmann like equation representation for turbulence modeling, a relaxation type collision term is introduced for isotropic turbulence. In order to describe some important turbulence phenomenology, the relaxation time incorporates a dependency on the turbulent microscopic energy and this makes difficult the construction of efficient numerical methods. To investigate this problem, we focus here on a multi-dimensional prototype model and first propose an appropriate change of frame that makes the numerical study simpler. Then, a numerical strategy to tackle the stiff relaxation source term is introduced in the spirit of Asymptotic Preserving Schemes. Numerical tests are performed in a one-dimensional framework on the basis of the developed strategy to confirm its efficiency.
Citation: Nicolas Crouseilles, Mohammed Lemou, SV Raghurama Rao, Ankit Ruhi, Muddu Sekhar. Asymptotic preserving scheme for a kinetic model describing incompressible fluids. Kinetic & Related Models, 2016, 9 (1) : 51-74. doi: 10.3934/krm.2016.9.51
##### References:

show all references

##### References:
 [1] Nicolas Vauchelet. Numerical simulation of a kinetic model for chemotaxis. Kinetic & Related Models, 2010, 3 (3) : 501-528. doi: 10.3934/krm.2010.3.501 [2] Nicolai Sætran, Antonella Zanna. Chains of rigid bodies and their numerical simulation by local frame methods. Journal of Computational Dynamics, 2019, 6 (2) : 409-427. doi: 10.3934/jcd.2019021 [3] Ching-Shan Chou, Yong-Tao Zhang, Rui Zhao, Qing Nie. Numerical methods for stiff reaction-diffusion systems. Discrete & Continuous Dynamical Systems - B, 2007, 7 (3) : 515-525. doi: 10.3934/dcdsb.2007.7.515 [4] Petr Bauer, Michal Beneš, Radek Fučík, Hung Hoang Dieu, Vladimír Klement, Radek Máca, Jan Mach, Tomáš Oberhuber, Pavel Strachota, Vítězslav Žabka, Vladimír Havlena. Numerical simulation of flow in fluidized beds. Discrete & Continuous Dynamical Systems - S, 2015, 8 (5) : 833-846. doi: 10.3934/dcdss.2015.8.833 [5] Alina Chertock, Changhui Tan, Bokai Yan. An asymptotic preserving scheme for kinetic models with singular limit. Kinetic & Related Models, 2018, 11 (4) : 735-756. doi: 10.3934/krm.2018030 [6] Casimir Emako, Farah Kanbar, Christian Klingenberg, Min Tang. A criterion for asymptotic preserving schemes of kinetic equations to be uniformly stationary preserving. Kinetic & Related Models, 2021, 14 (5) : 847-866. doi: 10.3934/krm.2021026 [7] Yue Qiu, Sara Grundel, Martin Stoll, Peter Benner. Efficient numerical methods for gas network modeling and simulation. Networks & Heterogeneous Media, 2020, 15 (4) : 653-679. doi: 10.3934/nhm.2020018 [8] Jeffrey R. Haack, Cory D. Hauck. Oscillatory behavior of Asymptotic-Preserving splitting methods for a linear model of diffusive relaxation. Kinetic & Related Models, 2008, 1 (4) : 573-590. doi: 10.3934/krm.2008.1.573 [9] Thomas Blanc, Mihai Bostan, Franck Boyer. Asymptotic analysis of parabolic equations with stiff transport terms by a multi-scale approach. Discrete & Continuous Dynamical Systems, 2017, 37 (9) : 4637-4676. doi: 10.3934/dcds.2017200 [10] Dieter Armbruster, Christian Ringhofer, Andrea Thatcher. A kinetic model for an agent based market simulation. Networks & Heterogeneous Media, 2015, 10 (3) : 527-542. doi: 10.3934/nhm.2015.10.527 [11] Alina Chertock, Alexander Kurganov, Mária Lukáčová-Medvi${\rm{\check{d}}}$ová, Șeyma Nur Özcan. An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions. Kinetic & Related Models, 2019, 12 (1) : 195-216. doi: 10.3934/krm.2019009 [12] Lijin Wang, Pengjun Wang, Yanzhao Cao. Numerical methods preserving multiple Hamiltonians for stochastic Poisson systems. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021095 [13] Ana I. Muñoz, José Ignacio Tello. Mathematical analysis and numerical simulation of a model of morphogenesis. Mathematical Biosciences & Engineering, 2011, 8 (4) : 1035-1059. doi: 10.3934/mbe.2011.8.1035 [14] Rolf Rannacher. A short course on numerical simulation of viscous flow: Discretization, optimization and stability analysis. Discrete & Continuous Dynamical Systems - S, 2012, 5 (6) : 1147-1194. doi: 10.3934/dcdss.2012.5.1147 [15] Giacomo Albi, Lorenzo Pareschi, Mattia Zanella. Opinion dynamics over complex networks: Kinetic modelling and numerical methods. Kinetic & Related Models, 2017, 10 (1) : 1-32. doi: 10.3934/krm.2017001 [16] Guoliang Ju, Can Chen, Rongliang Chen, Jingzhi Li, Kaitai Li, Shaohui Zhang. Numerical simulation for 3D flow in flow channel of aeroengine turbine fan based on dimension splitting method. Electronic Research Archive, 2020, 28 (2) : 837-851. doi: 10.3934/era.2020043 [17] Hung-Wen Kuo. Effect of abrupt change of the wall temperature in the kinetic theory. Kinetic & Related Models, 2019, 12 (4) : 765-789. doi: 10.3934/krm.2019030 [18] Yoshikazu Giga, Hiroyoshi Mitake, Hung V. Tran. Remarks on large time behavior of level-set mean curvature flow equations with driving and source terms. Discrete & Continuous Dynamical Systems - B, 2020, 25 (10) : 3983-3999. doi: 10.3934/dcdsb.2019228 [19] Eleonora Messina. Numerical simulation of a SIS epidemic model based on a nonlinear Volterra integral equation. Conference Publications, 2015, 2015 (special) : 826-834. doi: 10.3934/proc.2015.0826 [20] John V. Shebalin. Theory and simulation of real and ideal magnetohydrodynamic turbulence. Discrete & Continuous Dynamical Systems - B, 2005, 5 (1) : 153-174. doi: 10.3934/dcdsb.2005.5.153

2020 Impact Factor: 1.432

## Metrics

• HTML views (0)
• Cited by (1)

• on AIMS