用格子Boltzmann方法模拟流场中
Lattice boltzmann method for simulating the displacement of deformable membrane in fluid
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摘要: 采用格子Boltzmann方法模拟可变形膜与周围流体的相互作用. 分析了格子Boltzmann方法中的边界处理方法和边界受力的计算方法，并且用此方法计算流场中可变形膜的受力.可将离散化后的膜看作一系列的质点，从而得到膜的动力学方程. 将可变形膜在流场中受到的力引入方程中，可以计算膜的变形. 求解了几种不同情况下，膜的形状随时间的变化.发现，如果可变形膜非常软或者非常硬，经过足够长的时间后，膜的形状会接近一条直线，即回到初始状态. 模拟过程是二阶精度的.Abstract: A lattice Boltzmann method is employed to simulate theinteraction between the deformable membraneand surrounding fluids. The boundary condition and the force exerting on themembrane are handled based on the lattice Boltzmann method. Interactionbetween the membrane and surrounding fluids may cause the membrane tovibrate. The membrane is discretized into segments. Each segment issimplified to a mass particle and connected to its neighbors. The Newtoniandynamic simulation is applied to each segment. The dynamic equation of thedeformable membrane can be simulated according to the force acting on it.The hydrodynamic forces acting on the membrane are obtained by thecomputation of fluid flow stress at the moving boundary using the latticeBoltzmann momentum-exchange method. It can simulate the curved shape withsecond-order accuracy. The fluid flow and membrane deformable equations arecoupled. The membrane as a moving boundary affects the fluid flow, and thedeformation of the membrane is the result of the hydrodynamic force actingon it. In this paper, the configurations of membranes at corresponding timeunder different conditions are computed. In the numerical test, both ends ofthe membrane are fixed and its initial shape is set to be a straight line,its initial vibrant velocity normal to the membrane surface is given to bevaried at different position. The flow is simulated by the lattice Boltzmannmethod with second-order accuracy, and the deformation of the membrane iscomputed using the Newtonian dynamic equation. The results show that theconfiguration of the membrane is closed to its initial straight line in asufficient long time if the membrane is relatively soft or stiff, and theresults agree well with the other published results.
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