Simulation of strong nonlinear waves with vectorial lattice Boltzmann schemes
نویسنده
چکیده
We show that a hyperbolic system with a mathematical entropy can be discretized with vectorial lattice Boltzmann schemes using the methodology of kinetic representation of the dual entropy. We test this approach for the shallow water equations in one and two spatial dimensions. We obtain interesting results for a shock tube, reflection of a shock wave and non-stationary two-dimensional propagation. This contribution shows the ability of vectorial lattice Boltzmann schemes to simulate strong nonlinear waves in non-stationary situations.
منابع مشابه
Stable lattice Boltzmann schemes with a dual entropy approach for monodimensional nonlinear waves
Abstract. We follow the mathematical framework proposed by Bouchut [6] and present in this contribution a dual entropy approach for determining equilibrium states of a lattice Boltzmann scheme. This method is expressed in terms of the dual of the mathematical entropy relative to the underlying conservation law. It appears as a good mathematical framework for establishing a “H-theorem” for the s...
متن کاملSimulation of Micro-Channel and Micro-Orifice Flow Using Lattice Boltzmann Method with Langmuir Slip Model
Because of its kinetic nature and computational advantages, the Lattice Boltzmann method (LBM) has been well accepted as a useful tool to simulate micro-scale flows. The slip boundary model plays a crucial role in the accuracy of solutions for micro-channel flow simulations. The most used slip boundary condition is the Maxwell slip model. The results of Maxwell slip model are affected by the ac...
متن کاملInvestigation of pore-scale random porous media using lattice boltzmann method
The permeability and tortuosity of pore-scale two and three-dimensional random porous media were calculated using the Lattice Boltzmann method (LBM). Effects of geometrical parameters of medium on permeability and tortuosity were investigated as well. Two major models of random porous media were reconstructed by computerized tomography method: Randomly distributed rectangular obstacles in a uni...
متن کاملSome results on energy-conserving lattice Boltzmann models
We consider the problem of “energy conserving” lattice Boltzmann models. A major difficulty observed in previous studies is the coupling between the viscous and thermal waves even at moderate wave numbers. We propose a theoretical framework based on the knowledge of the partial equivalent equations of the lattice Boltzmann scheme at several orders of precision. With the help of linearized model...
متن کاملStructural stability of Lattice Boltzmann schemes
The goal of this work is to determine classes of traveling solitary wave solutions for Lattice Boltzmann schemes by means of an hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurence of such a spurious solitary wave, which exhibits a very long life time, results in a non-vanishing numerical error for arbitra...
متن کامل