明渠水流-水质模型的格子Boltzmann方法

建立了一个明渠水流-水质的格子Boltzmann模型(LBM),经过Chapman-Enskog展开可以得出守恒形式的二维明渠浅水动力学方程组和对流扩散方程。对于浓度场,针对各向异性的紊动扩散系数提出改进的简化LBM模型,即松弛时间在纵向和横向不一致以及平衡分布函数不含流速的二阶项,更符合宏观方程。数值模拟了污染物的非对称扩散稳态和对流扩散输送的二维稳态问题,并与理论解进行了对比,相对误差在3%以下。对于二维恒定流下事故瞬时排放污染物的动态扩散输送问题,结果较好的反映了下游取水口处浓度增值随时间变化的高斯分布,和一阶迎风有限体积通量向量分裂法(FVS)的计算结果对比相对误差不大于1.8%。本模型具有很好的并行计算性能,在环境污染模拟与预测的数值计算领域有着广阔的发展前景。

A Lattice Boltzmann Model for the Open Channel Shallow Water and Contaminant Transport Equations

A lattice Boltzmann model (LBM) for the open channel shallow water and pollutant transport equations is developed. The model can recover the conservation equations of shallow water dynamics via Chapman-Enskog expansion. A modified LBM is proposed for the anisotropic turbulent dispersion coefficient in the pollutant field. In the modified LBM the relaxation time is different in the x-direction and the y-direction and the local equilibrium has no terms of second order in flow velocity. The numerical tests show that this model strictly obeys the conservation law of mass and momentum. In the numerical test the asymmetric pure diffusion problem and the 2-D steady state convection-diffusion of pollutant problem are simulated. Good agreement is obtained between numerical predictions and analytical solutions and the relative error is less than 3%. Furthermore, the pollutant transport with instantly let source in 2-D steady flow is simulated. The results reflect the Gaussian distribution of concentration at the intake in the down river. And the agreement is good with the results of the one order unwind finite volume flux vector splitting scheme (FVS). The relative error is less then 1.8% between the two methods at the intake. The model is good at parallel computation and it is a very competitive method for simulation of environmental contamination.