A coupled lattice Boltzmann model for the shallow water-contamination system

作者：Li Yineng; Huang Ping^*

来源：International Journal for Numerical Methods in Fluids, 2009, 59(2): 195-213.

DOI：10.1002/fld.1819

• coupled lattice Boltzmann method
• shallow water equation
• convection with diffusion
• conservation law

A coupled numerical method for the direct simulation of shallow water dynamics and pollutant transport is formulated and implemented. The conservation equations of shallow water dynamics equations and the convection-diffusion equations are solved using the lattice Boltzmann (LB) method. The local equilibrium distribution of the pollutant has no terms of second order in flow velocity. And the relaxation time of the pollutant deviates from a constant for the flows with variable free surface water depth. The numerical tests show that this scheme strictly obeys the conservation law of mass and momentum. Excellent agreement is obtained between numerical predictions and analytical solutions in the pure diffusion problem and convection-diffusion problem. Furthermore, the influences on the accuracy of the lattice size and the diffusivity are also studied. The results indicate that the variation in the free surface water depth cannot affect the conservation of the model, and the model has the ability to simulate the complex topography problem. The comparison shows that the LB scheme has the capacity to solve the complex convection-diffusion problem in shallow water.

• 出版日期2009-1-20
• 单位中山大学