Numerical and analytical spatial coupling of a lattice Boltzmann model and a partial differential equation

Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena

Volumn , Issue , 2006, Pages 423-441

  Van Leemput, P ^a   Vanroose, W ^a   Roose, D ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

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EID: 77953789398     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/3-540-35888-9_19     Document Type: Chapter

References (18)

1. P. Albuquerque, D. Alemani, B. Chopard, P. Leone: Coupling a lattice Boltzmann and a finite difference scheme. In: International Conference on Computational Science - ICCS 2004, vol. 3039 of Lecture Notes in Computer Science, ed. by M. Bubak, G. D. van Albada, P. M. Sloot, J. Dongarra, pages 540-547 (Springer, Berlin Heidelberg New York 2004).
2. F.J. Alexander, A.L. Garcia, D.M. Tartakovsky: Algorithm refinement for stochastic partial differential equations: I. Linear diffusion. J. Comput. Phys. 182, 47-66 (2002).
3. B. Chopard, A. Dupuis, A. Masselot, P. Luthi: Cellular automata and lattice Boltzmann techniques: An approach to model and simulate complex systems. Adv. Complex Systems 5 (2/3), 103-246 (2002).
4. D. Dab, J.-P. Boon, Y.-X. Li: Lattice-gas automata for coupled reactiondiffusion equations. Phys. Rev. Lett. 66 (19), 2535-2538 (1991).
5. S.P. Dawson, S. Chen, G.D. Doolen: Lattice Boltzmann computations for reaction-diffusion equations. J. Chem. Phys. 98 (2), 1514-1523 (1993).
6. A.L. Garcia, J.B. Bell, W.Y. Crutchfield, B.J. Alder: Adaptive mesh and algorithm refinement using direct simulation Monte Carlo. J. Comput. Phys. 154, 134-155 (1999).
7. C. W. Gear, T. J. Kaper, I. G. Kevrekidis, A. Zagaris: Projecting to a slow manifold: Singularly perturbed systems and legacy codes. SIAM J. Appl. Dynamical Systems 4 (3), 711-732 (2005).
8. C.W. Gear, I.G. Kevrekidis: Constraint-defined manifolds: A legacy code approach to low-dimensional computation. J. Scientific Computing 25 (1), 17-28 (2005) Preprint available at physics/0312094.
9. I. Ginzbourg, P.M. Adler: Boundary flow condition analysis for the threedimensional lattice Boltzmann model. J. Phys. II France 4, 191-214 (1994).
10. N.G. Hadjiconstantinou. Hybrid atomistic-continuum formulations and the moving contact-line problem. J. Comput. Phys. 154, 245-265 (1999).
11. P. Le Tallec, F. Mallinger: Coupling Boltzmann and Navier-Stokes equations by half fluxes. J. Comput. Phys. 136, 51-67 (1997).
12. P. Le Tallec, M.D. Tidriri: Convergence analysis of domain decomposition algorithms with full overlapping for the advection-diffusion problems. Math. of Computation 68 (226), 585-606 (1999).
13. Y.H. Qian, D. D'Humieres, P. Lallemand: Lattice BGK models for Navier-Stokes equation. Europhys. Lett 17 (6), 479-484 (1992).
14. Y.H. Qian, S.A. Orszag: Scalings in diffusion-driven reaction A + B - C: Numerical simulations by lattice BGK models. J. Stat. Phys. 81 (1/2), 237-253 (1995).
15. S. Tiwari, A. Klar: An adaptive domain decomposition procedure for Boltzmann and Euler equations. J. Comput. & Appl. Math. 90, 223-237 (1998).
16. P. Van Leemput, K. Lust, I.G. Kevrekidis: Coarse-grained numerical bifurcation analysis of lattice Boltzmann models. Physica D: Nonlinear Phenomena 210 (1-2), 58-76 (2005).
17. P. Van Leemput, W. Vanroose, D. Roose: Initialization of a lattice Boltzmann model with constrained runs. Technical Report TW 444, Katholieke Universiteit Leuven, Department of Computer Science, December 2005.Submitted to J. Comput. Phys.
18. W. Vanroose. Analysis of a lattice Boltzmann model for planar streamer fronts. in preparation, (2006).