Application of the multi distribution function lattice Boltzmann approach to thermal flows
Computer Science Department, University of Geneva, 24 rue du Général Dufour, 1211 Geneva 4, Switzerland
2 Department of Earth and Planetary Science, University of California – Berkeley, 307 McCone Hall 4767, Berkeley, CA, 94720-4767, USA
3 Department of Mathematics, Tufts University, 503 Boston Avenue, Medford, MA, 02155, USA
4 Department of Earth and Space Science, University of Washington, Johnson Hall, Seattle, WA, 98195-1310, USA
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Numerical methods able to model high Rayleigh (Ra) and high Prandtl (Pr) number thermal convection are important to study large-scale geophysical phenomena occuring in very viscous fluids such as magma chamber dynamics (104 < Pr < 107 and 107 < Ra < 1011). The important variable to quantify the thermal state of a convective fluid is a generalized dimensionless heat transfer coefficient (the Nusselt number) whose measure indicates the relative efficiency of the thermal convection. In this paper we test the ability of Multi-distribution Function approach (MDF) Thermal Lattice Boltzmann method to study the well-established scaling result for the Nusselt number (Nu ∝ Ra1/3) in Rayleigh Bénard convection for 104 ≤ Ra ≤ 109 and 101 ≤ Pr ≤ 104. We explore its main drawbacks in the range of Pr and Ra number under investigation: (1) high computational time Nc required for the algorithm to converge and (2) high spatial accuracy needed to resolve the thickness of thermal plumes and both thermal and velocity boundary layer. We try to decrease the computational demands of the method using a multiscale approach based on the implicit dependence of the Pr number on the relaxation time, the spatial and temporal resolution characteristic of the MDF thermal model.
© EDP Sciences, Springer-Verlag, 2009