A Bi-fluid Lattice Boltzmann Model for Water Flow in an Irrigation Channel

This paper is devoted to modelling of water flow dynamics in open-channels for the goal of controlling irrigation systems We expose and validate a methodology based on Lattice Boltzmann models as an alternative to the commonly used Saint-Venant equations We adapt a bi-fluid model to the case of a free surface water flow A gravity force is applied to the heaviest fluid as to maintain it at the bottom The considered boundary conditions take into account the control actions provided by the two underflow gates located at the left and right ends of the reach Numerical results for density profiles are given to validate our approach.

[1]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[2]  J. Boon.  The Lattice Boltzmann Equation for Fluid Dynamics and Beyond , 2003 .

[3]  Q. Zou,et al.  On pressure and velocity boundary conditions for the lattice Boltzmann BGK model , 1995, comp-gas/9611001.

[4]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[5]  Qisu Zou,et al.  Analysis and boundary condition of the lattice Boltzmann BGK model with two velocity components , 1995, comp-gas/9507002.

[6]  Bastien Chopard,et al.  Cellular Automata and Lattice Boltzmann Techniques: an Approach to Model and Simulate Complex Systems , 2002, Adv. Complex Syst..

[7]  Shan,et al.  Lattice Boltzmann model for simulating flows with multiple phases and components. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  Jan Schuurmans,et al.  Classification of Canal Control Algorithms , 1995 .

[9]  Matthaeus,et al.  Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[10]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[11]  Khalid Mahmood,et al.  Unsteady flow in open channels , 1975 .

[12]  Shan,et al.  Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Bastien Chopard,et al.  Cellular automata and lattice Boltzmann methods: a new approach to computational fluid dynamics and particle transport , 1999, Future Gener. Comput. Syst..

[14]  Chen,et al.  Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  J. Cunge,et al.  Practical aspects of computational river hydraulics , 1980 .