Flux Limiter Lattice Boltzmann Scheme Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number

• Published in: Communications in theoretical physics 2011-09, Vol.56 (9), p.490-498
• Main Author: 甘延标 许爱国 张广财 李英骏
• Format: Article
• Language: English
• Subjects: Accuracy; Compressible flow; Couette流动; Finite difference method; Flux; Lattices; Mathematical analysis; Mathematical models; Prandtl number; 可压缩流动; 数值耗散; 普朗特数; 有限差分; 格子Boltzmann; 模型模拟; 通量限制器
• ISSN: 0253-6102
• DOI: 10.1088/0253-6102/56/3/18

We further develop the lattice Boltzmann （LB） model [Physica A 382 （2007） 502] for compressible flows from two aspects. Firstly, we modify the Bhatnagar Gross Krook （BGK） collision term in the LB equation, which makes the model suitable for simulating flows with different Prandtl numbers. Secondly, the flux limiter finite difference （FLFD） scheme is employed to calculate the convection term of the LB equation, which makes the unphysical oscillations at discontinuities be effectively suppressed and the numerical dissipations be significantly diminished. The proposed model is validated by recovering results of some well-known benchmarks, including （i） The thermal Couette flow; （ii） One- and two-dlmenslonal FLiemann problems. Good agreements are obtained between LB results and the exact ones or previously reported solutions. The flexibility, together with the high accuracy of the new model, endows the proposed model considerable potential for tracking some long-standing problems and for investigating nonlinear nonequilibrium complex systems.