基于二维紧凑型四阶格子模型的激波管流动模拟

胡开南; 耿少娟; 张宏武

doi:10.13224/j.cnki.jasp.2017.11.027

基于二维紧凑型四阶格子模型的激波管流动模拟

doi: 10.13224/j.cnki.jasp.2017.11.027

1.
中国科学院工程热物理研究所工业燃气轮机实验室,北京 100190；中国科学院大学,北京 100190
2.
中国科学院工程热物理研究所工业燃气轮机实验室,北京 100190

基金项目: 国家重点基础研究发展计划（2016YFB0200901）；国家自然科学基金（51236001）

计量
- 文章访问数: 663
- HTML浏览量: 0
- PDF量: 467
- 被引次数: 0
出版历程
- 收稿日期: 2016-03-30
- 刊出日期: 2017-11-28

Simulating shocktube flow with a twodimensional compact fourth order lattice model

摘要

摘要: 为了提高格子的稳定性，使用Hermite展开方法，构建了新的二维四阶紧凑型格子模型，即D2Q37A。比较了D2Q37A和与Philippi给出的紧凑型格子模型(D2Q37B)的稳定性。在相同的碰撞频率下，与D2Q37B相比，D2Q37A可以模拟初始密度比更高的一维激波管流动。这表明D2Q37A与现有格子模型相比，具有更好的稳定性。详细给出了适用于高阶格子模型的边界条件实现方式。此边界条件实现方式保留了体现LBM（lattice Boltmann method）粒子特性的迁移碰撞机制。用以上给出的格子模型和边界条件处理方式模拟激波管流动，得到的模拟结果和解析解吻合得很好。这表明所给出的边界处理方式是可行的。此边界格式同样可以用于其他类型的流动和边界。
- 格子Boltzmann方法 /
- 四阶格子模型 /
- 迁移碰撞机制 /
- 边界条件 /
- 激波管
Abstract: In order to improve the stability of the lattice model, a new twodimensional compact fourth order lattice model, ie, D2Q37A,was constructed based on the Hermite expansion. The stability of D2Q37A and the one proposed by Philippi (D2Q37B) were compared. Under the same collision frequency, D2Q37A can be applied to the onedimensional shock flow with the higher initial density ratio comparing with D2Q37B.That means D2Q37A was more stable than D2Q37B.An implementation of boundary conditions for high order lattice models was proposed in details. The implementation maintained the streamingcollision mechanism ensuring the particle feature of the LBM（lattice Boltmann method）. This new lattice model and implementation of boundary conditions were applied to onedimensional shock tube problem and the result of simulation was consistent with the analytical solution. The results show the proposed boundary condition scheme is practicable. The proposed boundary scheme can be employed by other type of flow and boundary.
- lattice Boltzmann method /
- fourth order lattice model /
- streamingcollision mechanism /
- boundary condition /
- shock tube

HTML

参考文献(18)

[1]	BENZI R,SUCCI S,VERGASSOLA M.The lattice Boltzmann equation:theory and applications［J］.Physics Reports,1992,222(3):145-197.
[2]	SWIFT M R,ORLANDINI E,OSBORN W,et al.Lattice Boltzmann simulations of liquidgas and binary fluid systems［J］.Physical Review E:Statical Physic Plasmas Fluids and Related Interdisciplinary Topics,1996,54(5):5041-5052.
[3]	QIAN Y H.Simulating thermohydrodynamics with lattice BGK models［J］.Journal of Scientific Computing,1993,8(3):231-242.
[4]	CHEN Y,OHASHI H,AKIYAMA M.Thermal lattice BhatnagarGrossKrook model without nonlinear deviations in macrodynamic equations［J］.Physical Review E：Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics,1994,50(4):2776-2783.
[5]	CHEN Y,OHASHI H,AKIYAMA M.Heat transfer in lattice BGK modeled fluid［J］.Journal of Statistical Physics,1995,81(1/2):71-85.
[6]	SHAN X,YUAN X F,CHEN H.Kinetic theory representation of hydrodynamics:a way beyond the NavierStokes equation［J］.Journal of Fluid Mechanics,2006,550(1):413-441.
[7]	MINORU W,MICHIHISA T.Twodimensional thermal model of the finitedifference lattice Boltzmann method with high spatial isotropy［J］.Physical Review E Statistical Nonlinear and Soft Matter Physics,2003,67(2):210-215.
[8]	GAN Y,XU A,ZHANG G,et al.Twodimensional lattice Boltzmann model for compressible flows with high Mach number［J］.Physica A:Statistical Mechanics and its Applications,2008,387(8/9):1721-1732.
[9]	SHIM J W.Univariate polynomial equation providing onlattice higherorder models of thermal lattice Boltzmann theory［J］.Physical Review E:Statistical Nonlinear and Soft Matter Physics,2013,87(1):417-433.
[10]	SHIM J W.Multidimensional onlattice higherorder models in the thermal lattice Boltzmann theory［J］.Physical Review E:Statistical Nonlinear and Soft Matter Physics,2013,88(5):053310.1-053310.5.
[11]	GUO Z,SHI B,ZHENG C.A coupled lattice BGK model for the Boussinesq equations［J］.International Journal for Numerical Methods in Fluids,2002,39(4):325-342.
[12]	GUO Z,ZHENG C,SHI B,et al.Thermal lattice Boltzmann equation for low Mach number flows:decoupling model［J］.Physical Review E:Statistical Nonlinear and Soft Matter Physics,2007,75(3):036704.1-036704.15.
[13]	MEZRHAB A,BOUZIDI M H,LALLEMAND P.Hybrid latticeBoltzmann finitedifference simulation of convective flows［J］.Computers and Fluids,2004,33(4):623-641.
[14]	VERHAEGHE F,BLANPAIN B,WOLLANTS P.Lattice Boltzmann method for doublediffusive natural convection［J］.Physical Review E:Statistical Nonlinear and Soft Matter Physics,2007,75(2):046705.1-046705.18.
[15]	PHILIPPI P C,HEGELE L A,SANTOS L O E,et al.From the continuous to the lattice Boltzmann equation:the discretization problem and thermal models［J］.Physical Review E:Statistical Nonlinear and Soft Matter Physics.2006,73(2):645-666.
[16]	MENG J,ZHANG Y.Diffuse reflection boundary condition for highorder lattice Boltzmann models with streamingcollision mechanism［J］.Journal of Computational Physics,2014,258(1):601-612.
[17]	SHIM J W.Multidimensional onlattice higherorder models in the thermal lattice Boltzmann theory［J］.Physical Review E:Statistical Nonlinear and Soft Matter Physics,2013,88(5):053310.1-053310.5.
[18]	SOD G A.A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws［J］.Journal of Computational Physics,1978,27(1):1-31.