A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method
AbstractAn 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. View Full-Text
Scifeed alert for new publicationsNever miss any articles matching your research from any publisher
- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
- Define your Scifeed now
Chen, Z.; Shu, C.; Tan, D.S. A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method. Appl. Sci. 2017, 7, 277.
Chen Z, Shu C, Tan DS. A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method. Applied Sciences. 2017; 7(3):277.Chicago/Turabian Style
Chen, Zhen; Shu, Chang; Tan, Danielle S. 2017. "A Truly Second-Order and Unconditionally Stable Thermal Lattice Boltzmann Method." Appl. Sci. 7, no. 3: 277.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.