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An implicit-forcing immersed boundary method for simulating viscous flows in irregular domains

机译:模拟不规则域粘性流的隐式强迫沉浸边界方法

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We present a method for solving the incompressible Navier-Stokes equations in irregular domains. These equations are discretized using finite difference method in a uniform Cartesian grid. Stationary rigid boundaries are embedded in the Cartesian grid and singular forces are applied at the rigid boundaries to impose the no-slip conditions. The singular forces are then distributed to the nearby Cartesian grid points using the immersed boundary method. In the present work, the singular forces are computed implicitly by solving a small system of equations at each time step. This system of equations is derived from a second order projection method. The main advantage of this method is that it imposes the no-slip boundary condition exactly and avoids the need for small time step to maintain stability. The ability of the method to simulate viscous flows in irregular domains is demonstrated by applying to 2-dimensional flows past a circular cylinder, multiple rigid obstacles and 3-dimensional flow past a sphere.
机译:我们提出了一种解决不规则域中不可压缩的Navier-Stokes方程的方法。这些方程在有限的笛卡尔网格中使用有限差分法离散化。固定的刚性边界嵌入在笛卡尔网格中,并且在刚性边界处施加奇异力以施加防滑条件。然后使用沉浸边界方法将奇异力分布到附近的笛卡尔网格点。在本工作中,通过在每个时间步求解一个小的方程组来隐式计算奇异力。该方程组是从二阶投影方法得出的。这种方法的主要优点是,它精确地施加了防滑边界条件,并避免了为保持稳定性而花费小时间的步骤。通过应用经过圆柱的二维流,多个刚性障碍物和经过球体的三维流,证明了该方法在不规则区域中模拟粘性流的能力。

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