*Unlike Fourier’s law, which is built upon the continuum assumption and constitutive equation of energy conservation, kinetic models study the transport phenomena from a more fundamental level and in a more generalized way. The Boltzmann equation (BE), which is one type of kinetic model, is a generalized transport model that can solve any advection-diffusion problem regardless of whether such a problem is advection-dominated or diffusion-dominated. Although the BE has been successfully applied to model fluid transport, which is an advection-dominated process, in this paper, in order to demonstrate the generality of the BE, heat conduction, which is a diffusion-only process, is simulated by two numerical derivatives of the BE: the lattice Boltzmann method (LBM) and the discrete Boltzmann method (DBM). The DBM model presented in this paper is unique in the way that the BE is solved on complete unstructured grids with the finite volume method. Therefore, it is named the finite volume discrete Boltzmann method (FVDBM). Two two-dimensional heat conduction problems with different domain geometries and boundary conditions are simulated by both the LBM and FVDBM and quantitatively compared. From that comparison, it is found that the FVDBM produces a higher level of accuracy than the LBM for problems with curved boundaries, while maintaining the same accuracy as the LBM for problems with flat boundaries. The advantage displayed by the FVDBM approach is the direct result of a more accurate reconstruction of curved boundaries by the utilization of unstructured grids, versus the Cartesian grids necessary for the LBM.*


Numerical Simulation of Heat Conduction Problems With the Lattice Boltzmann Method (Lbm) and Discrete Boltzmann Method (Dbm): A Comparative Study

Division / Sponsors: 
Heat Transfer Division (HTD), Fluids Engineering Division (FED)

Heat Transfer Summer Conference
Paper Proceedings: https://asmedigitalcollection.asme.org/HT/HT2020/volume/83709

18th International Conference on Nanochannels, Microchannels, and Minichannels
Paper Proceedings: https://asmedigitalcollection.asme.org/ICNMM/ICNMM2020/volume/83693

Fluids Engineering Division Summer Meeting
Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2020/volume/83716

HT-ICNMM2020 - Virtual Conference, SHTC - Virtual Conference, FEDSM2020 - Virtual Conference

Supporting the need among researchers worldwide for additional online and multimedia content, ASME now offers the ASME Conference Video Collection. This platform will collect and provide long-term access to conference presentation videos, encompassing all technology areas within ASME's technical conference and events program. About 30,000-40,000 engineers across all mechanical engineering and related disciplines participate in ASME conferences each year. This includes authors of approximately 6,000 to 8,000 technical papers published by ASME, the majority of whom also submit video presentations for our virtual conferences. The video collection will be available as an add-on to existing product packages or as a separate subscription.