Navier-Stokes

摘要： In this paper I propose a method for founding solutions of Navier-Stokes equations. Purpose of the research is to solve equations giving form to relations between pressure, velocity and stream. Starting from the fact we do not know the form of functions we give a general representation in Maclaurin Series and prove that with reasonable values of parameters, representation holds and therefore has meaning in continuum. Then we solve the system of equations with respect to the pressure and match equations relation between parameters: matches of equations are possible because of the physical dimensions of equations. Then values of Continuity Equation are verified. The result is a polynomial finite and that coincides with the function in continuum, or is anyway one of its representation. The result under hydrostatic condition returns Stevino formula.

摘要： 文章利用能量方法,通过建立能量不等式,研究了三维可压缩Navier-Stokes方程解对初始数据的连续依赖性。

摘要： Our modeling fluid flow, especially if the fluid is referred to as a gas, is established on mimicking each particle/molecule’s movement and then gathering that movement into macro quantities characterizing the fluid flow. It has resulted in discovering a new principle of the property (mass, momentum, and energy) balance in space. We named it the Ballistic Principle of the Property Balance in Space as described earlier in our publications. This paper uses a different scheme of defining a net rate of total property efflux than our original paper. Using this scheme, we formulated integro-differential forms of mass balance and momentum balance equations adapted to the incompressible fluid flow (gas flow with a mass-flow velocity less than 0.3 Ma) at the non-uniform temperature in the infinite gas space. We also investigated the analytical behavior of the integro-differential equations in the region bounding the point of singularity by applying the Taylor series expansion method to transform the integro-differential mass and momentum balance equations into the corresponding vector differential equations. Then we compared them with the Navier-Stokes equations of mass and momentum conservation for an incompressible fluid. We were surprised to find that the Navier-Stokes momentum balance equation does not describe the fluid flow adequately. Particularly, it does not consider the momentum associated with the part of velocity acquired by each gas particle during its free path traveling in the body force field. Also, the Navier-Stokes momentum balance equation is silent about the influence of the temperature non-uniformity on the momentum balance. Finally, we have demonstrated that the Navier-Stokes equations are not applicable to govern fluid flow on R3 × [0, ∞).

摘要： The lid-driven cavity is an important fluid mechanical system that serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes. These flows are driven by the tangential motion of a bounding wall. The lid-driven cavity serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes. This article presents a complete study of lid-driven cavity flows, with the primary focus being placed on the development of the flow when the Reynolds number was increased. In order to fully comprehend the physics of flow, it is necessary to take into consideration not only pure two-dimensional flows but also flows that are periodic in one space direction and the whole three-dimensional flow.

摘要： This paper discusses a Python interface for the recently published Dune-Fem-DG module which provides highly efcient implementations of the discontinuous Galerkin(DG)method for solving a wide range of nonlinear partial diferential equations(PDEs).Although the C++interfaces of Dune-Fem-DG are highly fexible and customizable,a solid knowledge of C++is necessary to make use of this powerful tool.With this work,easier user interfaces based on Python and the unifed form language are provided to open Dune-Fem-DG for a broader audience.The Python interfaces are demonstrated for both parabolic and frst-order hyperbolic PDEs.

摘要： This work deals with the modeling of the unsteady Newtonian fluid flow associated with an open cylindrical reservoir.This reservoir presents a hole on the right bottom wall.Fluid volume variation,heat and mass transfers are neglected.The unsteady governing equations are based on the conservation of mass and momentum.A finite volume technique is used to solve the non-dimensional equations and related boundary conditions.The algebraic system of equations resulting from the discretization process are solved by means of the THOMAS algorithm.For pressure-velocity coupling,the SIMPLE algorithm(Semi Implicit Method for Pressure Linked Equations)is used.Results for laminar flow(Re<1000),including the pressure and velocities profiles as well as the streamlines in the reservoir are presented.Moreover,the effects of the D/d and H0/D ratios and Reynolds number Re on the fluid flow are discussed.It is shown that the velocities and pressure depend essentially on the reservoir size.To validate the model,the present results have been compared with Zhou et al.’s results,Poiseuille’s and Bernoulli’s exact solution.

摘要： This paper proposes a novel computationally efficient method of modeling rarefied gas flow in microchannels based on the newly discovered and mathematically proven Ballistic Principle of the Property Balance in Space (BPPBS). The mechanism of influence of the effect of rarefication on the gas flow is specifically investigated. Also, a differential form of the momentum balance equation governing gas flow in the channel between two parallel plates due to the pressure gradient along the channel and its exact implicit solution in the form of an integral equation have been derived. The theory does not use the generalized concept of viscosity based on the variable mean free path (MFP) in the Knudsen layer (KL). Comparing the normalized flow rate as a function of the inverse Knudsen number according to the current theory and the experimental data shows good agreement in the range of the inverse Knudsen number from 0.01 to about 40. The correlation factor is found to be about 0.995. The results show that our approach based on the BPPBS offers substantial and practical advantages in modeling and simulation of rarefied gases. The validity of the widely disseminated claim of the geometry-dependent MFP in the KL was analyzed.

摘要： A meshless and matrix-free fluid dynamics solver(SOMA)is introduced that avoids the need for user generated and/or analyzed grids,volumes,and meshes.Incremental building of the approximation avoids creation and inversion of possibly dense block diagonal matrices and significantly reduces user interaction.Validation results are presented from the application of SOMA to subsonic,compressible,and turbulent flow over an adiabatic flat plate.

摘要： 本文从广义的Navier-Stokes流体方程出发,考虑到流体介质的黏滞性和存在的热传导,导出了更接近实际流体的三维非线性声波动方程.鉴于声传播所涉及的空间和时间尺度的复杂性和多样性,文中针对一维情形下的非线性波动方程进行了求解和分析.由方程的二级近似解可以看出,声压振幅的衰减遵循几何级数规律,而且驱动声波的频率越高声压的衰减就越快.在满足条件ωb? ρ0c20时,基波的衰减系数与驱动频率的平方及耗散系数的乘积成正比;二次谐波的衰减规律更加复杂,与频率的更高次幂相关.对声衰减系数及声压的分布进行数值计算发现,声压的分布还与初始的声压幅值及频率有关,初始的声压与频率越高衰减得越快.另外,当声压高于液体的空化阈值时,液体中就会出现大量的空化泡,文中模拟了单个空化泡的运动,发现随着声压的增大空化泡的振动越剧烈、空化泡所受的黏滞力变大,随着声波作用时间的增大黏滞力的幅值迅速增大并与驱动声压值同阶,因而空化泡的非线性径向运动引起的声衰减不容忽视.结果表明,驱动声压越高在空化区域附近引起的声衰减越快、输出的声压越低.

摘要： This paper is concerned with the Navier-stokes equations with nonlinear perturbation in R^2,which studies the existence of solution,and gets the existence of the attractors.Finally,we discuss with limit-behavior of the Navier-stokes equation4 with nonlinear per-turbation,asα→0.

摘要： 运用人工压缩方法求解不可压二维Navier-Stokes方程,数值研究了模拟鱼类C形起动的尾鳍摆动模型,探讨尾鳍摆动在鱼类典型转弯机动运动中的作用;基于新的实验发现,特别研究了两种尾部弯曲模式(单弯和双弯)对转弯机动的控制机理.对流体动力的变化情况的考察表明,鱼尾鳍的摆动模型产生的流体动力特征与鱼体转弯机动的运动学特征相符.鱼尾的单弯和双弯两种模式对转弯机动的动力学特性起到不同的调节作用,这与鱼类本身的生理和形态特征是相适应的.对比实验测量的定性结果,并结合流动图像解释了尾鳍在鱼类转弯机动中的控制机理.

摘要： 运用人工压缩方法求解不可压二维Navier-Stokes方程,数值研究了模拟鱼类C形起动的尾鳍摆动模型,探讨尾鳍摆动在鱼类典型转弯机动运动中的作用;基于新的实验发现,特别研究了两种尾部弯曲模式(单弯和双弯)对转弯机动的控制机理.对流体动力的变化情况的考察表明,鱼尾鳍的摆动模型产生的流体动力特征与鱼体转弯机动的运动学特征相符.鱼尾的单弯和双弯两种模式对转弯机动的动力学特性起到不同的调节作用,这与鱼类本身的生理和形态特征是相适应的.对比实验测量的定性结果,并结合流动图像解释了尾鳍在鱼类转弯机动中的控制机理.

摘要： 运用人工压缩方法求解不可压二维Navier-Stokes方程,数值研究了模拟鱼类C形起动的尾鳍摆动模型,探讨尾鳍摆动在鱼类典型转弯机动运动中的作用;基于新的实验发现,特别研究了两种尾部弯曲模式(单弯和双弯)对转弯机动的控制机理.对流体动力的变化情况的考察表明,鱼尾鳍的摆动模型产生的流体动力特征与鱼体转弯机动的运动学特征相符.鱼尾的单弯和双弯两种模式对转弯机动的动力学特性起到不同的调节作用,这与鱼类本身的生理和形态特征是相适应的.对比实验测量的定性结果,并结合流动图像解释了尾鳍在鱼类转弯机动中的控制机理.

摘要： 运用人工压缩方法求解不可压二维Navier-Stokes方程,数值研究了模拟鱼类C形起动的尾鳍摆动模型,探讨尾鳍摆动在鱼类典型转弯机动运动中的作用;基于新的实验发现,特别研究了两种尾部弯曲模式(单弯和双弯)对转弯机动的控制机理.对流体动力的变化情况的考察表明,鱼尾鳍的摆动模型产生的流体动力特征与鱼体转弯机动的运动学特征相符.鱼尾的单弯和双弯两种模式对转弯机动的动力学特性起到不同的调节作用,这与鱼类本身的生理和形态特征是相适应的.对比实验测量的定性结果,并结合流动图像解释了尾鳍在鱼类转弯机动中的控制机理.

摘要： 运用人工压缩方法求解不可压二维Navier-Stokes方程,数值研究了模拟鱼类C形起动的尾鳍摆动模型,探讨尾鳍摆动在鱼类典型转弯机动运动中的作用;基于新的实验发现,特别研究了两种尾部弯曲模式(单弯和双弯)对转弯机动的控制机理.对流体动力的变化情况的考察表明,鱼尾鳍的摆动模型产生的流体动力特征与鱼体转弯机动的运动学特征相符.鱼尾的单弯和双弯两种模式对转弯机动的动力学特性起到不同的调节作用,这与鱼类本身的生理和形态特征是相适应的.对比实验测量的定性结果,并结合流动图像解释了尾鳍在鱼类转弯机动中的控制机理.

摘要： 采用简单迭代法解二维稳态Naier-Stoker问题的非线性边界积分方程组,迭代的每一步皆归结于解非齐次Stokes问题的边界积分方程组,故可用作者在[1]中提供的高精度机械求积方法和外推法得到高精度解.本方法不仅能用外推提高精度,而且省计算.

摘要： 采用简单迭代法解二维稳态Naier-Stoker问题的非线性边界积分方程组,迭代的每一步皆归结于解非齐次Stokes问题的边界积分方程组,故可用作者在[1]中提供的高精度机械求积方法和外推法得到高精度解.本方法不仅能用外推提高精度,而且省计算.

摘要： 采用简单迭代法解二维稳态Naier-Stoker问题的非线性边界积分方程组,迭代的每一步皆归结于解非齐次Stokes问题的边界积分方程组,故可用作者在[1]中提供的高精度机械求积方法和外推法得到高精度解.本方法不仅能用外推提高精度,而且省计算.

摘要： 采用简单迭代法解二维稳态Naier-Stoker问题的非线性边界积分方程组,迭代的每一步皆归结于解非齐次Stokes问题的边界积分方程组,故可用作者在[1]中提供的高精度机械求积方法和外推法得到高精度解.本方法不仅能用外推提高精度,而且省计算.

摘要： 采用简单迭代法解二维稳态Naier-Stoker问题的非线性边界积分方程组,迭代的每一步皆归结于解非齐次Stokes问题的边界积分方程组,故可用作者在[1]中提供的高精度机械求积方法和外推法得到高精度解.本方法不仅能用外推提高精度,而且省计算.