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A Coupled Approach for Fluid Dynamic Problems Using the PDE Framework Peano

Published online by Cambridge University Press:  20 August 2015

Philipp Neumann ,
Hans-Joachim Bungartz ,
Miriam Mehl ,
Tobias Neckel  and
Tobias Weinzierl
Philipp Neumann*
Affiliation:
Chair of Scientific Computing, Faculty of Informatics, Technische Universität München, Boltzmannstr. 3, 81545 Garching, Germany
Hans-Joachim Bungartz
Affiliation:
Chair of Scientific Computing, Faculty of Informatics, Technische Universität München, Boltzmannstr. 3, 81545 Garching, Germany
Miriam Mehl
Affiliation:
Chair of Scientific Computing, Faculty of Informatics, Technische Universität München, Boltzmannstr. 3, 81545 Garching, Germany
Tobias Neckel
Affiliation:
Chair of Scientific Computing, Faculty of Informatics, Technische Universität München, Boltzmannstr. 3, 81545 Garching, Germany
Tobias Weinzierl
Affiliation:
Chair of Scientific Computing, Faculty of Informatics, Technische Universität München, Boltzmannstr. 3, 81545 Garching, Germany
*
*Corresponding author.Email:neumanph@in.tum.de
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Abstract

We couple different flow models, i.e. a finite element solver for the Navier-Stokes equations and a Lattice Boltzmann automaton, using the framework Peano as a common base. The new coupling strategy between the meso- and macroscopic solver is presented and validated in a 2D channel flow scenario. The results are in good agreement with theory and results obtained in similar works by Latt et al. In addition, the test scenarios show an improved stability of the coupled method compared to pure Lattice Boltzmann simulations.

Keywords

35Q3035Q3576M1076-xxSpatial couplingLattice BoltzmannNavier-StokesPeano

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 1 , July 2012 , pp. 65 - 84
Copyright
Copyright © Global Science Press Limited 2012

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References

[1]Albuquerque, P., Alemani, D., Chopard, B., and Leone., P.A Hybrid Lattice Boltzmann Finite Difference Scheme for the Diffusion Equation. Int. J. Mult. Comp. Eng., 4(2):209–219, 2006.Google Scholar
[2]Berger, M. J. and Collela, P.. Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys., 82:64–84, 1989.Google Scholar
[3]Berger, M. J. and Oliger, J.. Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys, 53:484–512, 1984.Google Scholar
[4]Bhatnagar, P. L., Gross, E. P., and Krook, M.. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev., 94(3):511–525, 1954.Google Scholar
[5]Bungartz, H.-J., Mehl, M., Neckel, T., and Weinzierl., T.The PDE framework Peano applied to fluid dynamics: An efficient implementation of a parallel multiscale fluid dynamics solver on octree-like adaptive Cartesian grids. Comput. Mech., 46(1):103–114,June 2010. Published online.Google Scholar
[6]Chapman, S. and Cowling., T. G.The Mathematical Theory of Nonuniform Gases. Cambridge University Press, London, 1960.Google Scholar
[7]Dünweg, B., Schiller, U. D., and Ladd., A. J.Statistical Mechanics of the Fluctuating Lattice Boltzmann Equation. Phys. Rev. E, 76(036704), 2007.Google Scholar
[8]Geller, S., Krafczyk, M., Tölke, J., Turek, S., and Hron, J.. Benchmark computations based on Lattice-Boltzmann, finite element and finite volume methods for laminar flows. Comput. Fluids, 35(8–9):888–897, 2006. Proceedings of the First International Conference for Meso-scopic Methods in Engineering and Science.CrossRefGoogle Scholar
[9]Karniadakis, G., Beskok, A., and Aluru., N.Microflows and Nanoflows. Fundamentals and Simulation. Springer, New York, 2005.Google Scholar
[10]Ladd., A. J. C.Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech., 271:285–309, 1994.Google Scholar
[11]Latt., J. Technical report: How to implement your DdQq dynamics with only q variables per node (instead of 2q). 2007. Technical report.Google Scholar
[12]Latt, J., Chopard, B., and Albuquerque, P.. Spatial Coupling of a Lattice Boltzmann fluid model with a Finite Difference Navier-Stokes solver, 2005. Published online, http://arxiv.org/pdf/physics/0511243v1.Google Scholar
[13]Mehl, M., Neckel, T., and Neumann., P.Navier-Stokes and Lattice-Boltzmann on octree-like grids in the Peano framework. Int. J. Numer. Meth. Fluids, 65:67–86, 2011.Google Scholar
[14]Neckel, T.. The PDE Framework Peano: An Environment for Efficient Flow Simulations. Verlag Dr. Hut, 2009.Google Scholar
[15]Sagan., H.Space-filling Curves. Springer-Verlag, New York, 1994.Google Scholar
[16]Succi., S.The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press, New York, 2001.Google Scholar
[17]Tij, M., Sabbane, M., and Santos., A.Nonlinear Poiseuille flow in a gas. Phys. Fluids, 10:1021–1027, 1998.CrossRefGoogle Scholar
[18]Uribe, F. J. and Garcia, A. L.. Burnett description for plane Poiseuille flow. Phys. Rev. E, 60(4):4063–4078, Oct 1999.Google Scholar
[19]Weinzierl, T.. A Framework for Parallel PDE Solverson Multiscale Adaptive Cartesian Grids. Verlag Dr. Hut, 2009.Google Scholar
[20]Wolf-Gladrow, D. A.. Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction. Springer, 2000.Google Scholar
[21]Zheng, Y., Garcia, A. L., and Alder, B. J.. Comparison of kinetic theory and hydrodynamics for Poiseuille flow. RAREFIED GAS DYNAMICS: 23rd International Symposium, 663(1):149–156, 2003.Google Scholar
[22]Zou, Q.. and He, X.. On pressure and velocity flow boundary conditions and bounceback for the Lattice Boltzmann BGK model. Phys. Fluids, 9(6):1591–1598, 1997.Google Scholar