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首页> 外文期刊>Journal of Computational Physics >Partially implicit motion of a sharp interface in Navier-Stokes flow
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Partially implicit motion of a sharp interface in Navier-Stokes flow

机译：Navier-Stokes流中尖锐界面的部分隐式运动

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摘要

We develop a numerical method for the coupled motion of Navier-Stokes flow with an elastic interface of zero thickness which exerts tension and bending forces on the fluid. The interface motion is made partially implicit by approximating a backward Euler step in the high wavenumbers as in the small scale decomposition method of Hou, Lowengrub and Shelley. This modified step is combined with the method of Beale and Layton [J.T. Beale, A.T. Layton, A velocity decomposition approach for moving interfaces in viscous fluids, J. Comput. Phys. 228 (2009) 3358-67]; the fluid velocity is found by computing the Stokes velocity and a more regular remainder. The resulting scheme is second order in space and first order in time; it can be made second order in time by extrapolation. The discontinuities in the pressure and velocity gradient are preserved. The partially implicit method allows much larger time steps than an explicit method with negligible added effort. The formulas in the Fourier transform for the implicit approximation in high wavenumbers are similar to those derived in Hou and Shi [T.Y. Hou, Z. Shi, An efficient semi-implicit immersed boundary method for the Navier-Stokes equations, J. Comput. Phys. 227 (2008) 9138-69] in a different context.
机译：我们开发了一种Navier-Stokes流耦合运动的数值方法，该方法具有零厚度的弹性界面，该界面对流体施加张力和弯曲力。像Hou，Lowengrub和Shelley的小规模分解方法一样，通过在高波数上近似向后的Euler阶跃，使界面运动部分隐含。这个修改过的步骤与Beale和Layton [J.T.比尔（A.T.） Layton，一种在粘性流体中移动界面的速度分解方法，J。Comput。物理228（2009）3358-67];通过计算斯托克斯速度和更规则的余数可以找到流体速度。生成的方案在空间上是二阶，在时间上是一阶。可以通过外推使其及时成为二阶。压力和速度梯度的不连续性得以保留。与显式方法相比，与隐式方法相比，部分隐式方法所耗费的时间要大得多。高波数中隐式逼近的傅里叶变换公式与侯和史[T.Y. Hou，Shi。Shi，Navier-Stokes方程的一种有效的半隐式边界法，J。Comput。物理227（2008）9138-69]。

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