论文标题
基于Navier滑动边界条件的虚拟域方法用于模拟流粒子相互作用
The Fictitious Domain Method Based on Navier Slip Boundary Condition for Simulation of Flow-Particle Interaction
论文作者
论文摘要
在本文中，我们开发了一种最小的 - 平方/虚拟域方法，用于直接模拟流体粒子界面处的Navier滑动边界条件的流体颗粒运动。令$ω$和$ b $为$ \ mathbb {r}^{d} $的两个有界域，使得$ \ overline {b} \ subsetω$。固体粒子$ b $的运动受牛顿方程式的约束。我们在这里的目标是开发一种虚拟域方法，其中人们在整个$ω$上解决了原始问题的变体，然后进行井（对$ b $的井校正），以及与粒子的翻译速度和角速度相关的校正。此方法是虚拟控制类型的，并且依赖于最小的 - 平方公式，从而使问题可通过在选择精良的控制空间中运行的共轭梯度算法解决。由于使用牛顿方程式更新粒子运动的完全明确的方案是不稳定的，因此我们提出并实施明确的 - 规范方案，在每个时间步骤中，在每个时间步骤中，显式更新了粒子的位置，并且解决Navier-Stokes方程式的解决方案和粒子速度的解决方案和粒子速度最少通过最少的数字/虚拟级别/虚拟的Domain方法来解决。给出数值结果以验证我们的数值方法。
In this article, we develop a least--squares/fictitious domain method for direct simulation of fluid particle motion with Navier slip boundary condition at the fluid--particle interface. Let $Ω$ and $B$ be two bounded domains of $\mathbb{R}^{d}$ such that $\overline{B} \subset Ω$. The motion of solid particle $B$ is governed by Newton's equations. Our goal here is to develop a fictitious domain method where one solves a variant of the original problem on the full $Ω$, followed by a well--chosen correction over $B$ and corrections related to translation velocity and angular velocity of the particle. This method is of the virtual control type and relies on a least--squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. Since the fully explicit scheme to update the particle motion using Newton's equation is unstable, we propose and implement an explicit--implicit scheme in which, at each time step, the position of the particle is updated explicitly, and the solution of Navier-Stokes equations and particle velocities are solved by the the least--squares/fictitious domain method implicitly. Numerical results are given to verify our numerical method.
