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首页> 外文期刊>SIAM Journal on Scientific Computing >AN IMMERSED INTERFACE METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DISCONTINUOUS VISCOSITY ACROSS THE INTERFACE
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AN IMMERSED INTERFACE METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DISCONTINUOUS VISCOSITY ACROSS THE INTERFACE

机译：界面间具有不连续粘度的不可压缩Navier-Stokes方程的浸入式界面方法

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摘要

We present an immersed interface method for solving the incompressible Navier Stokes equations with discontinuous viscosity across the interface and singular forces. The method is based on the augmented strategy proposed by Li, Ito, and Lai [Comput. Fluids, 36 (2007), pp. 622-635] to decouple the jump conditions of the fluid variables through the introduction of two augmented variables. In the proposed method, the immersed interface is represented by a number of Lagrangian control points, and the augmented interface variables applicable along the interface are solved by the LU method or the GMRES iterative method. In addition, we also derive a new second order accurate bilinear interpolating scheme for the discontinuous velocity and a new jump condition for the normal derivative of the pressure. The jumps in both pressure and velocity and the jumps in their derivatives are related to the augmented interface variables and/or the forces which are interpolated using cubic splines. For a flexible interface, the forces that the interface exerts on the fluid are computed from the constitutive relation of the flexible interface and are applied to the fluid through the jump conditions. The position of the flexible interface is updated implicitly within each time step. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method. The numerical results show that the overall scheme is second order accurate.
机译：我们提出了一种浸入式界面方法，用于求解在界面上具有不连续粘度和奇异力的不可压缩Navier Stokes方程。该方法基于Li，Ito和Lai提出的增强策略。 Fluids，36（2007），pp。622-635]，通过引入两个增强变量来解耦流体变量的跳跃条件。在所提出的方法中，沉浸式界面由多个拉格朗日控制点表示，并且通过LU方法或GMRES迭代方法求解沿界面可应用的扩展界面变量。此外，我们还为不连续速度导出了新的二阶精确双线性插值方案，为压力的正态导数得出了新的跳跃条件。压力和速度的跃变及其导数的跃变与增加的界面变量和/或使用三次样条插值的力有关。对于柔性接口，接口在流体上的作用力是根据柔性接口的本构关系计算的，并通过跳跃条件施加到流体上。灵活接口的位置在每个时间步长内隐式更新。通过二阶精确投影方法，在交错的笛卡尔网格上离散Navier-Stokes方程。数值结果表明，该总体方案是二阶精度的。

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