Abstract: The natural convection in triangular enclosures occurs widely in the fields of electronic device cooling, solar energy collector and so on. The two-dimensional impressible lattice Boltzmann model is built in this work for its simulation. On the basis of D2G9 model, coupling with the two-dimensional thermal lattice Boltzmann model TD2Q5 and non-equilibrium extrapolation boundary scheme, the temperature field in Couette flow is simulated. The predicted results of Couette flow agree well with the analytical solution when the Eckert number varies from 5 to 100, which shows that the present thermal model TD2Q5 is accurate and numerically stable. The velocity and temperature fields of natural convection in a triangular enclosure are solved at different Rayleigh number values. The predicted results coincide very well with that reported in the literature, indicating the present numerical models may be extended for thermal flows in triangular enclosures with higher Rayleigh number.

Key words: lattice Boltzmann method, impressible fluid, thermal model, numerical simulation, cavity flow

摘要： 建立了二维不可压缩D2G9格子Boltzmann模型，耦合二维TD2Q5热格子Boltzmann模型，在非平衡态外推的边界条件下，首先对不同Eckert数(Ec)和Prandtl数(Pr)时Couette流的温度场进行数值模拟，计算结果与解析解吻合良好，且在Ec变化很大的条件下，计算结果仍与解析解相符，验证了模型的准确性和稳定性. 然后对封闭三角空腔内不同Rayleigh数(Ra)下的自然对流流场和温度场进行了数值模拟，结果与文献计算值吻合良好，说明格子Boltzmann方法的TD2Q5热模型可用于高Ra时的空腔热流动模拟.

关键词: 格子Boltzmann方法, 不可压缩, 热模型, 数值模拟, 空腔流