On the formulation and implementation of the stress-free boundary condition over deformed bathymetry using a spectral-element-method-based incompressible Navier–Stokes equations solver
On the formulation and implementation of the stress-free boundary condition over deformed bathymetry using a spectral-element-method-based incompressible Navier–Stokes equations solver
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使用基于谱元方法的不可压缩纳维斯托克斯方程求解器来制定和实现变形测深的无应力边界条件
DOI：
10.1016/j.ocemod.2021.101834
复制
发表时间：
2021
期刊：
影响因子：
3.2
通讯作者：
Stastna, Marek
中科院分区：
文献类型：
--
作者：
Diamantopoulos, Theodoros;Diamessis, Peter J.;Stastna, Marek
提出了各种策略，强制执行无应力的变形域边界条件，使用弱形式为基础的离散化在笛卡尔参考系。由于计算区域的不规则性和边界条件的特殊性，引入了笛卡尔速度分量之间的耦合。因此，与用于方程的标量未知量的计算内核相比，需要不同的计算内核用于相关联的矢量亥姆霍兹方程的数值解。提出了三种方法，旨在实现精确或近似实现零切向应力（牵引力）在变形边界，同时确保解耦的矢量亥姆霍兹方程的解决方案中的速度分量。其中两个战略，那些近似的自由滑动边界条件，被施加到一个内部孤立波（ISW）的传播的抑郁症超过变形测深。的空间结构和幅度的伪牵引，这是准确预测的一个简单的缩放估计，探索作为一个函数的ISW为基础的雷诺数，R e。对于考虑的R e值，相对于相应的无滑移切向剪应力，伪牵引力可以忽略不计。伪牵引引起的，时间积分损失的ISW能量被发现是显着弱于相关的粘性耗散在内部水柱。虽然，在实验室规模或海洋R e，一个近似的自由滑动边界条件被发现产生可以忽略不计的伪牵引力，这可能不是这样的情况下，当一个升高的涡流粘度在这种情况下使用作为一个替代品无滑移湍流底部边界层动力学。
Various strategies are proposed for enforcing stress-free boundary conditions on deformed domains using a weak-form-based discretization in a Cartesian frame of reference. Due to the irregularity of the computational domain and the particular type of boundary condition, a coupling between the Cartesian velocity components is introduced. As such, a different computational kernel is required for the numerical solution of the associated vector Helmholtz equation, as contrasted to what is used for the scalar unknowns of the equations. Three approaches are presented, aimed towards the exact or approximate implementation of zero tangential stress (traction) at the deformed boundary while ensuring a decoupling of the velocity components in the solution of the vector Helmholtz equation. Two of these strategies, those which approximate the free slip boundary condition, are applied to the propagation of an internal solitary wave (ISW) of depression over a deformed bathymetry. The spatial structure and amplitude of the resultant pseudo-traction, which is accurately predicted by a simple scaling estimate, are explored as a function of the ISW-based Reynolds number, R e. For the R e values considered, the pseudo-traction is negligible with respect to the corresponding no-slip tangential shear stress. The pseudo-traction-induced, time-integrated loss of ISW energy is found to be significantly weaker than the associated viscous dissipation in the interior water column. Although, at laboratory-scale or oceanic R e, an approximate free-slip boundary condition is found to yield negligible pseudo-traction, this might not be the case when an elevated eddy viscosity is used in this context as a surrogate for no-slip turbulent bottom boundary layer dynamics.
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