Highly Efficient Lattice Boltzmann Model for Compressible Fluids:Two-Dimensional Case |
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Authors: | CHEN Feng XU Ai-Guo ZHANG Guang-Cai GAN Yan-Biao CHENG Tao LI Ying-Jun |
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Affiliation: | 1.China University of Mining and Technology (Beijing), Beijing 100083, China;2.National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009-26, Beijing 100088, China ;3.North China Institute of Aerospace Engineering, Langfang 065000, China |
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Abstract: | We present a highly efficient lattice Boltzmann model for simulatingcompressible flows. This model is based on the combination of an appropriatefinite difference scheme, a 16-discrete-velocity model [Kataoka andTsutahara, Phys. Rev. E 69 (2004) 035701(R)] and reasonable dispersion anddissipation terms. The dispersion term effectively reduces the oscillationat the discontinuity and enhances numerical precision. The dissipation termmakes the new model more easily meet with the von Neumann stabilitycondition. This model works for both high-speed and low-speed flows witharbitrary specific-heat-ratio. With the new model simulation results for thewell-known benchmark problems get a high accuracy compared with the analytic or experimental ones. The used benchmark tests include (i) Shock tubes such as the Sod, Lax, Sjogreen, Colella explosion wave, and collision of two strong shocks, (ii) Regular and Mach shock reflections, and (iii) Shock wave reaction on cylindrical bubble problems. With a more realistic equation ofstate or free-energy functional, the new model has the potential tostudythe complex procedure of shock wave reaction on porous materials. |
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Keywords: | lattice Boltzmann method compressible flows specific-heat-ratio von Neumann stability analysis |
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