Oseen Coupling Method for the Exterior Flow Part I: Oseen Coupling Approximation

Abstract In this paper, we consider the bidimensional exterior unsteady Navier-Stokes equations with nonhomogeneous boundary conditions and present an Oseen coupling problem which approximates the Navier-Stokes problem, obtained by coupling the Navier-Stokes equations in the inner region and the Oseen equations in the outer region. Moreover, we prove the existence, uniqueness and the approximate accuracy of the weak solution of the Oseen coupling equations. Project supported by NSF of China & State Major Key Project of Basic Research     

THE ARTIFICIAL BOUNDARY CONDITION FOR EXTERIOR OSEEN EQUATION IN 2-D SPACE

A finite element method for the solution of Oseen equation in exterior domain is proposed. In this method, a circular artificial boundary is introduced to make the computational domain finite. Then, the exact relation between the normal stress and the prescribed velocity field on the artificial boundary can be obtained analytically. This relation can serve as an boundary condition for the boundary value problem defined on the finite domain bounded by the artificial boundary. Numerical experiment is presented to demonstrate the performance of the method.     

Finite Element Iterative Methods for the 3D Steady Navier–Stokes Equations

In this work, a finite element (FE) method is discussed for the 3D steady Navier–Stokes equations by using the finite element pair Xh×Mh. The method consists of transmitting the finite element solution (uh,ph) of the 3D steady Navier–Stokes equations into the finite element solution pairs (uhn,phn) based on the finite element space pair Xh×Mh of the 3D steady linearized Navier–Stokes equations by using the Stokes, Newton and Oseen iterative methods, where the finite element space pair Xh×Mh satisfies the discrete inf-sup condition in a 3D domain Ω. Here, we present the weak formulations of the FE method for solving the 3D steady Stokes, Newton and Oseen iterative equations, provide the existence and uniqueness of the FE solution (uhn,phn) of the 3D steady Stokes, Newton and Oseen iterative equations, and deduce the convergence with respect to (σ,h) of the FE solution (uhn,phn) to the exact solution (u,p) of the 3D steady Navier–Stokes equations in the H1−L2 norm. Finally, we also give the convergence order with respect to (σ,h) of the FE velocity uhn to the exact velocity u of the 3D steady Navier–Stokes equations in the L2 norm.     

Shape optimization of a body in the Oseen flow

This article is concerned with a numerical simulation of shape optimization of the Oseen flow around a solid body. The shape gradient for shape optimization problem in a viscous incompressible flow is computed by the velocity method. The flow is governed by the Oseen equations with mixed boundary conditions containing the pressure. The structure of continuous shape gradient of the cost functional is derived by using the differentiability of a minimax formulation involving a Lagrange functional with a function space parametrization technique. A gradient type algorithm is applied to the shape optimization problem. Numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

The application of adjoint method for shape optimization in Stokes–Oseen flow

This paper presents a numerical method for shape optimization of a body immersed in an incompressible viscous flow governed by Stokes–Oseen equations. The purpose of this work is to optimize the shape that minimizes a given cost functional. Based on the continuous adjoint method, the shape gradient of the cost functional is derived by involving a Lagrangian functional with the function space parametrization technique. Then, a gradient‐type algorithm is applied to the shape optimization problem. The numerical examples indicate the proposed algorithm is feasible and effective in low Reynolds number flow. Copyright © 2016 John Wiley & Sons, Ltd.     

球栅的Oseen流动及阻力的尾流效应

本文通过大小相同且等距放置的球栅的轴对称Oseen流动研究了阻力的尾流效应。在每个球的球心放置Oseen流子得到了问题的级数解。截断无穷级数并采用配置法解线性代数方程组求出了球栅Oseen流动的近似解及每个球所遭受的阻力。 在不同的球的个数,不同的球的间距以及不同的雷诺数下计算了各个圆球的阻力系数,发现除球栅的遮蔽效应和端缘效应外还存在着尾流效应。研究了上述参数对这些效应的影响并与Stokes流动的结果进行了比较。文章还对方法的收敛性进行了数值研究。     

Two-level defect-correction Oseen iterative stabilized finite element methods for the stationary Navier–Stokes equations

Two-level defect-correction Oseen iterative stabilized finite element methods for the stationary Navier–Stokes equations based on local Gauss integration are considered in this paper. The methods combine the defect-correction method and the two-level strategy with the locally stabilized method. Moreover, the stability and convergence of the presented methods are deduced. Finally, numerical tests confirm the theoretical results of the presented methods.     

Asymptotic properties of the steady fall of a body in viscous fluids

The paper deals with the properties of the steady fall of a body in linear fluids (Oseen and Stokes cases) and in nonlinear fluids (Navier–Stokes fluids) in L^q structure. Copyright © 2004 John Wiley & Sons, Ltd.     

Cyclic polymers swollen in a good solvent dynamic scattering properties

A general formalism for the dynamic scattering properties of cyclic polymers in good solvent conditions is presented. Single-chain dynamics are investigated in the framework of the Oseen tensor model with and without the preaveraging approximation. The chain swelling due to excluded volume interactions is introduced by a renormalization of the internal chain statistics of cyclic polymers. The relaxations of the concentration fluctuations are also described for both ring homopolymers and copolymers. © 1994 John Wiley & Sons, Inc.