Xingwang Chen, Old Dominion University


Simulation of Hartmann Flow by Using Lattice Boltzmann Equation

Abstract: We use the lattice Boltzmann equation (LBE) to study magnetohydrodynamics (MHD). In particular, we use an LBE model to simulate the steady Hartmann flow in three dimensions. The configuration of the Hartmann flow is the following. The flow is through a square duct. A magnetic field is applied in the direction perpendicular to the flow direction. The duct walls either perpendicular or parallel to the magnetic field are called the Hartmann wall or side wall, respectively. The walls can be either conductive or insulated.  We assume all the walls are insulated in our study.  In this work we use a lattice Boltzmann model with two sets of distribution functions for the flow and the magnetic field. We use the multiple-relaxation-time model in our simulation. We solve the flow in different Hartmann number, which is the ratio of magnetic and viscous forces, and validate our model by comparing the numerical solutions with the analytic once.
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Advisor:  Li-Shi Luo (ODU)