Mohammadipoor O R, Niazmand H, Mirbozorgi S A
Ferdowsi University of Mashhad, Mechanical Engineering Department, Mashhad, Iran.
University of Birjand, Mechanical Engineering Department, Birjand, Iran.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):013309. doi: 10.1103/PhysRevE.89.013309. Epub 2014 Jan 24.
Since the lattice Boltzmann method originally carries out the simulations on the regular Cartesian lattices, curved boundaries are often approximated as a series of stair steps. The most commonly employed technique for resolving curved-boundary problems is extrapolating or interpolating macroscopic properties of boundary nodes. Previous investigations have indicated that using more than one equation for extrapolation or interpolation in boundary conditions potentially causes abrupt changes in particle distributions. Therefore, a curved-boundary treatment is introduced to improve computational accuracy of the conventional stair-shaped approximation used in lattice Boltzmann simulations by using a unified equation for extrapolation of macroscopic variables. This boundary condition is not limited to fluid flow and can be extended to potential fields. The proposed treatment is tested against several well-established problems and the solutions order of accuracy is evaluated. Numerical results show that the present treatment is of second-order accuracy and has reliable stability characteristics.
由于格子玻尔兹曼方法最初是在规则的笛卡尔网格上进行模拟，弯曲边界通常被近似为一系列阶梯。解决弯曲边界问题最常用的技术是外推或插值边界节点的宏观属性。先前的研究表明，在边界条件中使用多个方程进行外推或插值可能会导致粒子分布的突然变化。因此，引入了一种弯曲边界处理方法，通过使用一个统一的宏观变量外推方程来提高格子玻尔兹曼模拟中使用的传统阶梯形近似的计算精度。这种边界条件不限于流体流动，还可以扩展到势场。针对几个已确立的问题对所提出的处理方法进行了测试，并评估了解的精度阶数。数值结果表明，目前的处理方法具有二阶精度且具有可靠的稳定性特征。
