Lattice Boltzmann method for overland flow studies and its experimental validation

The negative distribution functions exist when the kinematic wave equation of overland flow is solved using the traditional lattice Boltzmann method. To resolve this shortcoming, an improved lattice Boltzmann method is introduced involving the multi-scale expansion of time coordinate (but not spatial coordinate). Based on the improved multi-scale expansion, a multi-scale analysis method and an undetermined coefficient method are used to gain the equilibrium distribution functions. To validate the proposed approach, special experiments with water flows on the impervious and pervious (with soil macropores) slopes have been conducted. The experimental results show that the improved lattice Boltzmann method is effective in describing overland flows; there are no numerical oscillations, and the distribution functions are positive when the relaxation time is from 0.8 to 2.0.