Analytical Solution For Navier-Stokes Equations In Two Dimensions For Laminar Incompressible Flow
Saeed Otarod, Davar Otarod
将求解描述不可压缩流体的层流的纳维-斯托克斯方程。导出了层流不可压缩流体纳维-斯托克斯方程的不同通解组。
The Navier-Stokes equations describing laminar flow of an incompressible fluid will be solved. Different group of general solutions for Navier stokes equations governing Laminar incompressible fluids will be derived.
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Over the past few years, deep learning methods have proved to be of great interest for the computational fluid dynamics community, especially when used as surrogate models, either for flow reconstruction, turbulence modeling, or for the prediction of aerodynamic coefficients. Overall, exceptional levels of accuracy have been obtained, but the robustness and reliability of the proposed approaches remain to be explored, particularly outside of the confidence region defined by the training dataset. In this contribution, we present a twin auto-encoder network for incompressible laminar flow recons…
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在本文中，在不可压缩流体中的流体压力的确定的问题是解决，特别是参考搜索的算法，允许提前的流体压力，而实际上没有解决数值的泊松方程。基于最近提出的求解不可压纳维-斯托克斯方程的逆动力学方法，我们试图证明可以得到一个精确的发展方程，它使流体压力在时间上自洽地向前推进。新方程易于在拉格朗日CFD模拟代码中数值实现。
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Stochastic Least-Action Principle for the Incompressible Navier-Stokes Equation
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Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier-Stokes equations, based on variations of an integral objective functional, and using traditional gradient-based optimisation strategies. Different approaches for handling the incompressibility condition are considered. The variational methods are applied to the specific case of periodic, two-dimensional Kolmogorov flow and compared against existing Newton iterati…
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本文研究了高雷诺数下不可压缩纳维-斯托克斯流的隐式大涡模拟，采用高阶H(div)-符合有限元方法，在周期域衰减湍流和壁面受限通道流两种情况下进行验证。
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Finite-Time Weak Singularities and the Statistical Structure of Turbulence in 3D Incompressible Navier-Stokes Equations
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Data augmentation for the POD formulation of the parametric laminar incompressible Navier-Stokes equations
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Boundary epsilon regularity for incompressible Navier--Stokes equations via weak-strong uniqueness
本文通过弱-强唯一性方法证明，当解的L^4_tL^4_x范数小于某个仅依赖于域的常数时，不可压缩纳维-斯托克斯方程的有限能量弱解在边界处具有正则性，解决了Albritton等人提出的问题。
The Cahn-Hilliard-Navier-Stokes Framework for Multiphase Fluid Flows: Laminar, Turbulent, and Active
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Existence and properties of the Navier-Stokes equations
纳维-斯托克斯方程解的存在性、唯一性和光滑性的证明是一个实际问题，它的求解对于不同的科学分支都有重要意义。本文研究的主题是求三维Stokes-Navier方程初边值问题的光滑唯一解。分析表明，三维纳维-斯托克斯方程不存在粘性解。其原因是无发散速度场的能力不足。为了得到理想的解，必须对纳维-斯托克斯方程进行修正。修正后的方程描述了粘在物体表面上的不可压缩流体的三维流动。方程的解显示了层流的共振爆破、层流-湍流的过渡、流体分离，这些都为解决磁发电机问题开辟了道路。
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Exact solutions to the Navier-Stokes equation for an incompressible flow from the interpretation of the Schroedinger wave function
速度势的存在是从薛定谔方程导出连续性方程的直接结果。这意味着Cole-Hopf变换适用于不可压缩流的Navier-斯托克斯方程，并允许将Navier-斯托克斯方程简化为Einstein-Kolmogorov方程，其中反应项取决于压力。所得方程的解，以及纳维-斯托克斯方程的解，可以用热方程的格林函数来表示，并以积分映射的形式给出。这种形式的解决方案，使分叉周期加倍可能，即解决方案的过渡和湍流状态，尽管存在的速度潜力。
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