A new high accuracy method for two-dimensional biharmonic equation with nonlinear third derivative terms: application to Navier–Stokes equations of motion

In this paper, we propose a new compact fourth-order accurate method for solving the two-dimensional fourth-order elliptic boundary value problem with third-order nonlinear derivative terms. We use only 9-point single computational cell in the scheme. The proposed method is then employed to solve Navier–Stokes equations of motion in terms of streamfunction–velocity formulation, and the lid-driven square cavity problem. We describe the derivation of the method in details and also discuss how our streamfunction–velocity formulation is able to handle boundary conditions in terms of normal derivatives. Numerical results show that the proposed method enables us to obtain oscillation-free high accuracy solution.     

Modified alternating direction-implicit iteration method for linear systems from the incompressible Navier–Stokes equations

In order to solve the large sparse systems of linear equations arising from numerical solutions of two-dimensional steady incompressible viscous flow problems in primitive variable formulation, Ran and Yuan [On modified block SSOR iteration methods for linear systems from steady incompressible viscous flow problems, Appl. Math. Comput. 217 (2010), pp. 3050–3068] presented the block symmetric successive over-relaxation (BSSOR) and the modified BSSOR iteration methods based on the special structures of the coefficient matrices. In this study, we present the modified alternating direction-implicit (MADI) iteration method for solving the linear systems. Under suitable conditions, we establish convergence theorems for the MADI iteration method. In addition, the optimal parameter involved in the MADI iteration method is estimated in detail. Numerical experiments show that the MADI iteration method is a feasible and effective iterative solver.     

Third-order temporal discrete scheme for the non-stationary Navier–Stokes equations

In this article, we suggest a new third-order time discrete scheme for the two-dimensional non-stationary Navier–Stokes equations. After presenting the Galerkin finite element approximation for the spatial discretization, we consider an implicit/explicit time discrete scheme for the problem, which is based on the two-step Adams–Moulton scheme (implicit scheme) for the linear term and the three-step Adams–Bashforth scheme (explicit scheme) for the nonlinear term. In this method, we only need to solve a linearized discrete system at each time step, so the scheme can converge fast and the computational cost can be reduced. Moreover, under some assumptions, we deduce the stability and optimal error estimate for the velocity in L ²-norm.     

基于N-S方程和序列二次规划的翼型优化设计

实际工程中的翼型设计通常是对某一性能良好的基本翼型进行局部改进以满足特定的工程要求。中将N—S方程流场分析程序和序列二次规划结合起来，发展了一种实用的翼型优化设计方法，用以提高基本翼型在多个设计点、在多种约束条件下的气动性能。由N—S方程计算得到的升力、阻力等气动参数构成目标函数，数值优化程序对其进行最优化。超临界翼型的设计算例表明，中发展的翼型优化方法设计质量高，所需机时少，易于实施，有较大的工程应用价值。     

Local and parallel finite element methods for the mixed Navier–Stokes/Darcy model

In this paper, the mixed Navier–Stokes/Darcy problem which describes a fluid flow filtrating through porous media is considered. Based on two-grid discretizations, two local and parallel finite element algorithms for solving this mixed model are proposed. Numerical analysis and experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithms.     

线荷载作用下的单向板内力分析

对实际工程计算时通常将线荷载作用下的单向板按单跨(板)梁来计算主方向上的弯矩,而忽视了次方向上的弯矩,导致板底出现次方向上裂缝的情况作了分析,采用纳维叶解法计算并运用MATLAB绘制了受线荷载作用的单向板,并以长宽比为基本参数,讨论了主次方向上弯矩的变化情况,得出了一些结论。     

数值波浪水槽的建立与验证

由于Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程是从动量守恒定律出发，以对不可压缩粘粘性流体不引入地形限制，不考虑水深影响，是真正意义上从流体的运动规律出发的方程，因此本文以Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程为控制方程，用有限元法对它进行离散，建立了它的有限元特征方程，     

Nonlinear eddy viscosity modeling and experimental study of jet spreading rates

Indoor airflow pattern is strongly influenced by turbulent shear and turbulent normal stresses that are responsible for entrainment effects and turbulence‐driven secondary motion. Therefore, an accurate prediction of room airflows requires reliable modeling of these turbulent quantities. The most widely used turbulence models include RANS‐based models that provide quick solutions but are known to fail in turbulent free shear and wall‐affected flows. In order to cope with this deficiency, this study presents a nonlinear k‐ε turbulence model and evaluates it along with linear k‐ε models for an indoor isothermal linear diffuser jet flow measured in two model rooms using PIV. The results show that the flow contains a free jet near the inlet region and a wall‐affected region downstream where the jet is pushed toward the ceiling by entrainment through the well‐known Coanda effect. The CFD results show that an accurate prediction of the entrainment process is very important and that the nonlinear eddy viscosity model is able to predict the turbulence‐driven secondary motions. Furthermore, turbulence models that are calibrated for high Reynolds free shear layer flows were not able to reproduce the measured velocity distributions, and it is suggested that the model constants of turbulence models should be adjusted before they are used for room airflow simulations.     

BIFURCATION AND DYNAMICS OF THIN SLIPPING FILMS UNDER THE INFLUENCE OF INTERMOLECULAR FORCES

1. INTRODUCTION Liquid thin film flows are commonly encountered in nature and numerous practical applications, e.g., chemical engineering, materials process, or microelectronic systems. A great deal of theoretical studies has been performed to understand the stability, dynamics and dewetting of the flows[1]. Since the length scale developed in the spatio-temporal instability of the thin films is much larger than the average thickness of films, long wave or lubrication approximation can be …