Navier-Stokes equations/ Navier-Stokes equation solutionunstructured triangular mesheslow Mach number modelnumerical methodfinite volume methodunstructured finite elementsfinite difference schemegeneralized coordinate transformationsA low Mach number model of the Navier–Stokes equations has been developed for ...
纳维-斯托克斯方程（N-S方程）是描述黏性流体运动的偏微分方程，由法国物理学家克劳德-路易·纳维和爱尔兰数学家、物理学家乔治·加布里埃尔·斯托克斯爵士的工作发展而来。它基于牛顿第二定律推导，描述了牛顿流体的动量和质量守恒，考虑了压强、温度和密度等因素。该方程在流体力学中极为重要，可用于模拟天气、洋流和气流...
3. Dou, H.-S., No existence and smoothness of solution of the Navier-Stokes equation, Entropy...
The lack of the superposition principal makes it extremely difficult to construct a generalized solution of Navier-Stokes equation. In fact, three-dimensional Navier-Stokes existence and smoothness has been listed as one of the millennium prize problems by Clay Mathematics Institute. Equation of incompr...
^Schöwe, A., 2014. Global strong solution for large data to the hyperbolic Navier-Stokes equation. arXiv preprint arXiv:1409.7797. ^Schöwe, A., 2012. A quasilinear delayed hyperbolic Navier-Stokes system: global solution, asymptotics and relaxation limit. Methods and Applications of Analysis...
Existence and smoothness of solution of the Navier-Stokes equation are exactly disproved for the first time by using two different approaches: Energy gradient theory and Poisson equation method. At a higher Reynolds number, the velocity profile in laminar flow is distorted under a disturbance and ve...
L. Ross, "Numerical Solution of the Navier-Stokes Equation for Flow Past Spheres: Part I. Viscous Flow around Spheres with and without Radial Mass Efflux," AlChE J., 13, 212 ( 1967).Hamielec, A., Johnson, A., Houghton, W.: Numerical solution of the Navier-Stokes equation for flow ...
Ω, we would need to introduce the Stokes operator − ∆ and the associate semi-group. Note that Ker = {u | ∃φ such that u = ∇φ}. Using , (1) becomes the evolution equation ∂u ∂t = ∆u − ∇· (u ⊗u), ∇· u = 0, u(x, 0) = u 0 (x). ...
在求解不可压缩流体问题时，利用Navier-Stokes方程描述流场，通过PINN方法可以实现对流场参数的求解。实验结果显示，PINN能够准确预测流场中的速度分量u和v以及压力p，验证了其在复杂流体动力学问题求解方面的有效性和实用性。通过训练和优化，PINN不仅能够解决正问题，还能处理逆问题，为物理系统建模和参数识别...
^Tosio Kato. Strong Lp-solutions of the Navier-Stokes equation in Rm, with appli- cations to weak solutions. Math. Z., 187(4):471–480, 1984.^F. Planchon. Global strong solutions in Sobolev or Lebesgue spaces to the in- compressible Navier-Stokes equations in R3. Ann. Inst. H. ...