Application of the multi distribution function lattice Boltzmann approach to thermal flows

• Published in: The European physical journal. ST, Special topics Vol. 171; no. 1; pp. 37 - 43
• Main Authors: Parmigiani, A., Huber, C., Chopard, B., Latt, J., Bachmann, O.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.04.2009; EDP Sciences
• Subjects: Atomic; Classical and Continuum Physics; Classical statistical mechanics; Condensed Matter Physics; Exact sciences and technology; Materials Science; Measurement Science and Instrumentation; Molecular; Optical and Plasma Physics; Physics; Physics and Astronomy; Statistical mechanics of classical fluids; Statistical physics, thermodynamics, and nonlinear dynamical systems; Lattice Node; Rayleigh Number; European Physical Journal Special Topic; Lattice Boltzmann Method; Nusselt Number; Prandtl number; Multiscale method; Digital simulation; Rayleigh number; Viscous fluids; Convection; Boundary layers; Heat transfer; Distribution functions
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjst/e2009-01009-7

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 (10 4 < Pr < 10 7 and 10 7 < Ra < 10 11 ). 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 ∝ Ra 1/3 ) in Rayleigh Bénard convection for 10 4 ≤ Ra ≤ 10 9 and 10 1 ≤ Pr ≤ 10 4 . We explore its main drawbacks in the range of Pr and Ra number under investigation: (1) high computational time N c 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.