Multiscale Simulations of Heat Transfer and Fluid Flow Problems

Abstract

The multiscale problems in the thermal and fluid science are classified into two categories: multiscale process and multiscale system. The meanings of the two categories are described. Examples are provided for multiscale process and multiscale system. In this pa-per, focus is put on the simulation of multiscale process. The numerical approaches for multiscale processes have two categories: one is the usage of a general governing equation and solving the entire flow field involving a variation of several orders in characteristic geometric scale. The other is the so-called “solving regionally and coupling at the inter-faces. ” In this approach, the processes at different length levels are simulated by different numerical methods and then information is exchanged at the interfaces between different regions. The key point is the establishment of the reconstruction operator, which transforms the data of few variables of macroscopic computation to a large amount of variables of microscale or mesoscale simulation. Six numerical examples of multiscale simulation are presented. Finally, some research needs are proposed. [DOI: 10.1115/1.4005154

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“…(24) -(25). In this study, the Runge-Kutta-Gill method (Nakayama, 1995) (1) -(4) becomes questionable in these two regime as pointed out by He and Tao (2012). In this case, either higher-order continuum equations (e.g., Burnett equations), should be used there, or molecular modeling should be invoked abandoning the continuum approach altogether.…”

What's going on about geo-process modeling in virtual geographic environments (VGEs)

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A unified coupling scheme between lattice Boltzmann method and finite volume method for unsteady fluid flow and heat transfer

“…The ''Solving problems regionally and coupling at the interface [7]'' is a widely used multiscale strategy, where the computational domain is divided into different sub-regions in which the most proper numerical methods are adopted as shown in Fig. 1.…”

“…An overlapping region where both methods are adopted is located between the sub-regions for information transfer. A compression operator (CO) is employed at the macroscopic boundary for the information transfer from the micro/mesoscale to the macroscale and a reconstruction operator (RO) is adopted at the micro/mesoscopic boundary for the inverse information transfer [7]. Based on this strategy, many coupling methods between different numerical models have been proposed for various multiscale problems, such as molecular dynamic (MD)-continuum [8][9][10][11][12][13], direct simulation of Monte Carlo (DSMC)-continuum [14,15], and lattice Boltzmann method (LBM)-finite volume method (FVM) [16][17][18][19][20][21].…”