Application of Lattice Boltzmann Method for Surface Runoff in Watershed

Derived from simplifications of the Saint-Venant equations, the kinematic wave model has the ability to describe the behavior of surface runoff in watersheds. This paper aims to obtain the numerical simulation of the flow routing in a natural watershed, by using lattice Boltzmann method. In the computational model, the surface of the basin will be represented by a V-shaped segmented in two lateral planes and one main channel. The simulation considers the effective precipitation flowing on the watershed per unit of width at the exit of each of the planes that represent the surface of the basin. The water flowing from the planes enters the main channel in the form of lateral contribution. Hydrograms of two rain events are obtained, which present the volume drained in the outlet corresponding to the whole basin in each event. Two equilibrium distribution functions were developed by Chapmann-Enskog expansion at time scales and model D1Q3, one suitable for flow on the basin surface and another for the main channel, in order to obtain the variables of interest in each case. The numerical results obtained were compared with the KINEROS2 hydrological model.Peer Reviewe

Two-dimensional numerical simulation of channel flow with submerged obstacles using the lattice Boltzmann method

Apresenta-se a simulação numérica bidimensional do escoamento de água em um canal retangular com chicanas submersas distribuídas alternadamente nas suas margens. As equações governantes do escoamento são as equações de águas rasas, que serão resolvidas por meio do método do reticulado de Boltzmann (LBM) com múltiplos tempos de relaxamento (MRT). Utilizou-se condições de contorno adequadas para escoamento em canal, vazão e altura da água constante na entrada e saída, respectivamente. Devido às características do problema que pretende-se simular, incorporou-se ao código computacional uma técnica de simulação em grandes escalas (LES - Large Eddy Simulation) a qual permite obter resultados mais próximos do comportamento real do escoamento. Além disso, avalia-se a estabilidade da simulação em todos os pontos da malha para cada passo de tempo e, juntamente com a propriedade da consistência do LBM, obtém-se a convergência da solução. A simulação fornece a profundidade, velocidades nas direções {\textstyle x} e {\textstyle y} , e a magnitude da vorticidade da água.A two-dimensional numerical simulation of the water flow in a rectangular channel with submerged obstacles distributed alternately along its banks is presented. The governing equations of flow are the shallow water equations, which will be solved by the Boltzmann lattice method (LBM) with multiple relaxation times (MRT). The non-slip bounce-back scheme was used on walls and obstacles, constant discharge at the inlet and fixed depth at the outlet of the channel. Due to the characteristics of the problem to be simulated, a large eddy simulation (LES) technique was incorporated into the computational code, which allows to obtain results that are closer to the actual behavior of the flow. In addition, the stability of the simulation at all points of the mesh is evaluated for each step of time and, together with the property of the consistency of the LBM, the convergence of the solution is obtained. The simulation provides the depth, velocities in the x and y directions, and the magnitude of water vorticity.Peer Reviewe

Simulation of the two-dimensional flow of the initiation channel of the Itaipu hydroelectric power plant by the lattice Boltzmann method

Este artigo analisa a capacidade do método do reticulado de Boltzmann (LBM) com múltiplos tempos de relaxamento (MRT) na simulação do escoamento em problemas práticos de engenharia. O estudo de caso abordado refere-se ao primeiro trecho do canal de iniciação, que faz parte do canal da piracema, localizado no Usina Hidrelétrica de Itaipu. O canal de iniciação possui obstáculos submersos distribuídos de uma margem até a outra, com o objetivo de reduzir a velocidade da água e permitir a ocorrência do ciclo da piracema. As equações governantes do escoamento são as equações de águas rasas, que serão resolvidas por meio do LBM-MRT. Utilizou-se condições de contorno adequadas para escoamento em canal, vazão e altura da água constante na entrada e saída, respectivamente. Devido às características do problema que pretende-se simular, incorporou-se ao código computacional uma técnica de simulação em grandes escalas (LES - Large Eddy Simulation) a qual permite obter resultados mais próximos do comportamento real do escoamento. Além disso, avalia-se a estabilidade da simulação em todos os pontos da malha para cada passo de tempo e, juntamente com a propriedade da consistência do LBM, obtém-se a convergência da solução. A simulação fornece a profundidade, velocidades nas direções {\textstyle x} e {\textstyle y} , e a magnitude da vorticidade da água.This paper analyzes the ability of the Lattice Boltzmann method (LBM) with multiple relaxation times (MRT) in the simulation of flow in practical engineering problems. The case study covered refers to the first section of the initiation channel, which is part of the piracema channel, located in the Itaipu Hydroelectric Power Plant. The initiation channel has submerged obstacles distributed from one margin to the other, in order to reduce water velocity and allow the piracema cycle to occur. The governing equations of flow are the shallow water equations, which will be solved through the LBM-MRT. The non-slip bounce-back scheme was used on walls and obstacles, constant discharge at the inlet and fixed depth at the outlet of the channel. Due to the characteristics of the problem to be simulated, a large eddy simulation (LES) technique was incorporated into the computational code, which allows to obtain results that are closer to the actual behavior of the flow. In addition, the stability of the simulation at all points of the mesh is evaluated for each step of time and, together with the property of the consistency of the LBM, the convergence of the solution is obtained. The simulation provides the depth, velocities in the x and y directions, and the magnitude of water vorticity.Peer Reviewe

Simulation of the two-dimensional flow of the initiation channel of the Itaipu hydroelectric power plant by the lattice Boltzmann method

This paper analyzes the ability of the Lattice Boltzmann method (LBM) with multiple relaxation times (MRT) in the simulation of flow in practical engineering problems. The case study covered refers to the first section of the initiation channel, which is part of the piracema channel, located in the Itaipu Hydroelectric Power Plant. The initiation channel has submerged obstacles distributed from one margin to the other, in order to reduce water velocity and allow the piracema cycle to occur. The governing equations of flow are the shallow water equations, which will be solved through the LBM-MRT. The non-slip bounce-back scheme was used on walls and obstacles, constant discharge at the inlet and fixed depth at the outlet of the channel. Due to the characteristics of the problem to be simulated, a large eddy simulation (LES) technique was incorporated into the computational code, which allows to obtain results that are closer to the actual behavior of the flow. In addition, the stability of the simulation at all points of the mesh is evaluated for each step of time and, together with the property of the consistency of the LBM, the convergence of the solution is obtained. The simulation provides the depth, velocities in the x and y directions, and the magnitude of water vorticity

Two-dimensional numerical simulation of channel flow with submerged obstacles using the lattice Boltzmann method

A two-dimensional numerical simulation of the water flow in a rectangular channel with submerged obstacles distributed alternately along its banks is presented. The governing equations of flow are the shallow water equations, which will be solved by the Boltzmann lattice method (LBM) with multiple relaxation times (MRT). The non-slip bounce-back scheme was used on walls and obstacles, constant discharge at the inlet and fixed depth at the outlet of the channel. Due to the characteristics of the problem to be simulated, a large eddy simulation (LES) technique was incorporated into the computational code, which allows to obtain results that are closer to the actual behavior of the flow. In addition, the stability of the simulation at all points of the mesh is evaluated for each step of time and, together with the property of the consistency of the LBM, the convergence of the solution is obtained. The simulation provides the depth, velocities in the x and y directions, and the magnitude of water vorticity