Abstract
An unconditionally stable thermal lattice Boltzmann method (USTLBM) is proposed in this paper for simulating incompressible thermal flows. In USTLBM, solutions to the macroscopic governing equations that are recovered from lattice Boltzmann equation (LBE) through Chapman–Enskog (C-E) expansion analysis are resolved in a predictor–corrector scheme and reconstructed within lattice Boltzmann framework. The development of USTLBM is inspired by the recently proposed simplified thermal lattice Boltzmann method (STLBM). Comparing with STLBM which can only achieve the first-order of accuracy in time, the present USTLBM ensures the second-order of accuracy both in space and in time. Meanwhile, all merits of STLBM are maintained by USTLBM. Specifically, USTLBM directly updates macroscopic variables rather than distribution functions, which greatly saves virtual memories and facilitates implementation of physical boundary conditions. Through von Neumann stability analysis, it can be theoretically proven that USTLBM is unconditionally stable. It is also shown in numerical tests that, comparing to STLBM, lower numerical error can be expected in USTLBM at the same mesh resolution. Four typical numerical examples are presented to demonstrate the robustness of USTLBM and its flexibility on non-uniform and body-fitted meshes.
Highlights
Incompressible thermal flows are frequently encountered in engineering applications [1].much research has been conducted on this topic
Boltzmann method (STLBM) is derived from reconstructing solutions to the macroscopic governing equations recovered from lattice Boltzmann equation and resolved in a predictor–corrector scheme
We present an unconditionally stable thermal lattice Boltzmann method (USTLBM)
Summary
Incompressible thermal flows are frequently encountered in engineering applications [1]. Within LBM framework, one popular approach to interpret such coupling effect is to introduce internal energy distribution function [13] This approach is named as the thermal lattice Boltzmann method (TLBM). Equations (17)–(21) can be reconstructed within the LBM framework to obtain the formulations of simplified thermal lattice Boltzmann method (STLBM). Compared to the standard TLBM, simplified thermal lattice Boltzmann method (STLBM) possesses many advantages It is developed within LBM framework, STLBM directly updates macroscopic variables instead of the distribution functions. In this way, much fewer virtual memories are required in the computation, and physical boundary conditions can be directly and flexibly implemented without transforming into conditions for the distribution functions. In LBM framework, the time interval and the mesh spacing are tied up, low order of accuracy in time may have intrinsic effect on overall accuracy of numerical solution
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
