Visualization of vortical flows in computational fluid dynamics

The concepts and methods of the visual representation of fluid dynamics computations of vortical flows are studied. Approaches to the visualization of vortical flows based on the use of various definitions of a vortex and various tests for its identification are discussed. Examples of the visual representation of solutions to some fluid dynamics problems related to the computation of vortical flows in jets, channels, and cavities and of the computation of separated flows occurring in flows around bodies of various shapes are discussed.     

不可压缩流动的并行数值方法

不可压缩流动的数值模拟是计算流体力学的重要组成部分. 基于有限元离散方法, 本文设计了不可压缩Navier-Stokes (N-S)方程支配流的若干并行数值算法. 这些并行算法可归为两大类: 一类是基于两重网格离散方法, 首先在粗网格上求解非线性的N-S方程, 然后在细网格的子区域上并行求解线性化的残差方程, 以校正粗网格的解; 另一类是基于新型完全重叠型区域分解技巧, 每台处理器用一局部加密的全局多尺度网格计算所负责子区域的局部有限元解. 这些并行算法实现简单, 通信需求少, 具有良好的并行性能, 能获得与标准有限元方法相同收敛阶的有限元解. 理论分析和数值试验验证了并行算法的高效性     

Global attractor for a low order ODE model problem for transition to turbulence

Many researchers have studied simple low order ODE model problems for fluid flows in order to gain new insight into the dynamics of complex fluid flows. We investigate the existence of a global attractor for a low order ODE system that has served as a model problem for transition to turbulence in viscous incompressible fluid flows. The ODE system has a linear term and an energy‐conserving, non‐quadratic nonlinearity. Standard energy estimates show that solutions remain bounded and converge to a global attractor when the linear term is negative definite, that is, the linear term is energy decreasing; however, numerical results indicate the same result is true in some cases when the linear term does not satisfy this condition. We give a new condition guaranteeing solutions remain bounded and converge to a global attractor even when the linear term is not energy decreasing. We illustrate the new condition with examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Mathematical modeling and numerical simulation of two-phase flows using Fourier pseudospectral and front-tracking methods: The proposition of a new method

In the present work, an extension of the Fourier Pseudospectral Method coupled with the Immersed Boudary Method for non-periodic problems (IMERSPEC) applied to numerical simulation of two-phase flow was developed. The proposed method was originally developed for single-phase, incompressible flow. Here, the method is extended to two-phase flows using the front-tracking method (IMERSPEC-FT) to model fluid-fluid interfaces. The proposed method was verified and validated through results involving spurious currents, mass conservation and numerical experiments analysis for rising bubbles. IMERSPEC-FT is shown to be a promising scheme for the two-phase computational fluid dynamics (CFD).     

一维高精度离散GDQ方法

GDQ method is a kind of high order accurate numerical methods developed several years ago, which have been successfully used to simulate the solution of smooth engineering problems such as structure mechanics and incompressible fluid dynamics. In this paper, extending the traditional GDQ method, we develop a new kind of discontinuous GDQ methods to solve compressible flow problems of which solutions may be discontinuous. In order to capture the local features of fluid flows, firstly, the computational domain is divided into many small pieces of subdomains. Then, in each small subdomain, the GDQ method is implementedand some kinds of numerical flux limitation conditions will be required to keep the correct flow direction. At the boundary interface between subdomains, we also use some kind of flux conditions according to the flow direction. The numerical method obtained by the above steps has the advantages of high order accuracy and easy to treat boundary conditions. It can simulate perfectly nonlinear waves such as shock, rarefaction wave and contact discontinuity. Finally, the numerical experiments on one dimensional Burgers equation and Euler equations are given.The numerical results verify the validation of the method.     

Software package for 3D viscous gas flow simulation on multiprocessor computer systems

A parallel software package designed for the numerical simulation of three-dimensional viscous gas flows is presented. The numerical algorithm is based on kinetically consistent difference schemes used on locally refined grids. The software package has been tested in various super-and subsonic flow problems. It provides an opportunity for the direct simulation of turbulent flows. The efficiency of parallelization is analyzed depending on the problem size and the number of processors.     

The Boltzmann equation and its fluid dynamic limits: Numerical studies

We introduce a Boltzmann equation on discrete lattices and demonstrate its applicability for the numerical simulation of flows in the transition regime to fluid dynamics. The application concerns an evaporation condensation where the fluid dynamic flow is ruled by a thin kinetic boundary layer. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some applications of a galerkin-collocation method for boundary integral equations of the first kind

Here we apply the boundary integral method to several plane interior and exterior boundary value problems from conformal mapping, elasticity and fluid dynamics. These are reduced to equivalent boundary integral equations on the boundary curve which are Fredholm integral equations of the first kind having kernels with logarithmic singularities and defining strongly elliptic pseudodifferential operators of order - 1 which provide certain coercivity properties. The boundary integral equations are approximated by Galerkin's method using B-splines on the boundary curve in connection with an appropriate numerical quadrature, which yields a modified collocation scheme. We present a complete asymptotic error analysis for the fully discretized numerical equations which is based on superapproximation results for Galerkin's method, on consistency estimates and stability properties in connection with the illposedness of the first kind equations in L₂. We also present computational results of several numerical experiments revealing accuracy, efficiency and an amazing asymptotical agreement of the numerical with the theoretical errors. The method is used for computations of conformal mappings, exterior Stokes flows and slow viscous flows past elliptic obstacles.     

NEW METHOD FOR IMPROVED CALCULATIONS OF UNSTEADY COMPLEX FLOWS IN LARGE ARTERIES

Using an improved computational fluid dynamics (CFD) method developed for highly unsteady three-dimensional flows, numerical simulations for oscillating flow cycles and detailed unsteady simulations of the flow and forces on the aortic vessels at the iliac bifurcation, for both healthy and diseased patients, are analyzed. Improvements in computational efficiency and acceleration in convergence are achieved by calculating both an unsteady pressure gradient which is due to fluid acceleration and a good global pressure field correction based on mass flow for the pressure Poisson equation. Applications of the enhanced method to oscillatory flow in curved pipes yield an order of magnitude increase in speed and efficiency, thus allowing the study of more complex flow problems such as flow through the mammalian abdominal aorta at the iliac arteries bifurcation. To analyze the large forces which can exist on stent graft of patients with abdominal aortic aneurysm (AAA) disease, a complete derivation of the force equations is presented. The accelerated numerical algorithm and the force equations derived are used to calculate flow and forces for two individuals whose geometry is obtained from CT data and whose respective blood pressure measurements are obtained experimentally. Although the use of endovascular stent grafts in diseased patients can alter vessel geometries, the physical characteristics of stents are still very different when compared to native blood vessels of healthy subjects. The geometry for the AAA stent graph patient studied in this investigation induced flows that resulted in large forces that are primarily caused by the blood pressure. These forces are also directly related to the flow cross-sectional area and the angle of the iliac arteries relative to the main descending aorta. Furthermore, the fluid flow is significantly disturbed in the diseased patient with large flow recirculation and stagnant regions which are not present for healthy subjects.     

Mixed finite element methods for computing groundwater velocities

Central to the understanding of problems in water quality and quantity for effective management of water resources is the development of accurate numerical models to stimulate groundwater flows and contaminant transfer. We discuss several important difficulties arising in modeling of subsurface flow and present promising numerical procedures for alleviating these problems. Furthermore, we describe mixed-finite element techniques for accurately approximating fluid velocities, and review computational results on a variety of hydrologic problems.     

A relaxation Riemann solver for compressible two-phase flow with phase transition and surface tension

The dynamics of two-phase flows depend crucially on interfacial effects like surface tension and phase transition. A numerical method for compressible inviscid flows is proposed that accounts in particular for these two effects. The approach relies on the solution of Riemann-like problems across the interface that separates the liquid and the vapour phase. Since the analytical solutions of the Riemann problems are only known in particular cases an approximative Riemann solver for arbitrary settings is constructed. The approximative solutions rely on the relaxation technique.The local well-posedness of the approximative solver is proven. Finally we present numerical experiments for radially symmetric configurations that underline the reliability and efficiency of the numerical scheme.     

The theory of regularized traces of operators as applied to approximate computation of eigenvalues and eigenfunctions of fluid dynamics problems

Some results concerning the computation of eigenvalues and eigenfunctions of fluid dynamics problems by applying methods of regularized traces of differential operators are presented. The presentation is focused primarily on the non-self-adjoint fourth-order Orr-Sommerfeld operator, which arises in the hydrodynamic stability theory of viscous flows.     

Performance of turbulence models for flows through rough pipes

The Reynolds-averaged Navier–Stokes (RANS) equations were solved along with turbulence models, namely k–ε, k–ω, Reynolds stress models (RSM), and filtered Navier–Stokes equations along with Large Eddy Simulation (LES) to study the fully-developed turbulent flows in circular pipes roughened by repeated square ribs with various spacings. Solutions of these flows were obtained using the commercial computational fluid dynamics (CFD) software Fluent. The numerical results were validated against experimental measurements and other numerical data published in literature. The performance of the turbulence models was compared and discussed. All the RANS models and LES model were observed to perform equally well in predicting the time-averaged flow statistics. However no instantaneous information can be obtained from the RANS results. Therefore, when a rough overview of the flow process in a pipe roughened by repeated ribs is needed, any one of the RANS models can be of value. On the other hand, the instantaneous as well as time-averaged flows could be studied with more insight using LES, albeit at a cost of CPU effort at least one order higher.     

Lattice Boltzmann模型在CFD中应用

近年来,格子Boltzmann方法(LBM)已发展为一种模拟流体和物理问题的新颖的、有前景的数值方法,在许多领域的各种数值问题求解上取得很大的成功.文章介绍了一种模拟复杂流动的高效建模数值算法Lattice Boltzmann方法,和它的基本原理及其应用.并通过两个实例数值模拟计算,说明Lattice Boltzmann方法正确、有效,并展示了广阔的应用前景,为今后更深入的研究和广泛应用打下基础.     

On Symmetric Boundary Conditions in the Context of Viscoelastic Fluid Flows

In order to reduce the numerical cost of three dimensional flow problems with geometrical symmetry, the use of symmetric boundary conditions is standard. For Newtonian fluid flow problems this approximation is usually appropriate, particularly when the Reynolds number is small. In the case of viscoelastic fluid flow simulations with stabilization techniques, such as the so-called DEVSS and/or Log-Conformation tensor methods, at high Deborah number flows this implementation is not straightforward, as in the Newtonian case. It is well known that viscoelastic models (e.g. Maxwellian models), show (purely) elastic flow instabilities when the Deborah number is increased above a critical value, even under creeping flow conditions. In this work we present numerical simulations with different stabilization techniques and different differential viscoelastic models at high Deborah number flows. As a test-case, we compare the flow in a full two-dimensional cross-slot geometry to show the asymmetrical behavior of the viscoelastic fluid flow. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-dimensional numerical simulation of the inverse problem of thermal convection using the quasi-reversibility method

Inverse (time-reverse) simulation of three-dimensional thermoconvective flows is considered for a highly viscous incompressible fluid with temperature-dependent density and viscosity. The model of the fluid dynamics is described by the Stokes equations, the incompressibility and heat balance equations subject to the appropriate initial and boundary conditions. To solve the problem backward in time, the quasi-reversibility method is applied to the heat balance equation. The numerical solution is based on the introduction of a two-component vector potential for the velocity of the medium, on the application of the finite element method with a special tricubic spline basis for computing this potential, and on the application of the splitting method and the method of characteristics for computing the temperature. The numerical algorithm is designed to be executed on parallel computers. The proposed numerical algorithm is used to reconstruct the evolution of diapiric structures in the Earth’s upper mantle. The computational efficiency of the algorithm is analyzed on the basis of the appropriate functionals of residuals.     

非牛顿流体非定常旋转流动计算机智能解析理论

计算机符号运算科学是人工智能的前沿方向。计算机软件Macsyma是完成符号运算的有力工具。应用德国Darmstadt大学的计算机软件Macsyma、与数学方法和流变学模型结合,研究了Oldroyd B流体由一类定常状态向另一定常状态转变的非定常流动过程。采用改进的Kantorovich方法和符号运算软件,把该问题的3阶偏微分方程的初、边值问题化为各级近似的2阶常微分方程问题。并给出了1级、2级和3级近似方程的解析形式解答。该研究表明了计算机符号处理解决应用数学和力学问题的潜力,同时指出了由一定常状态向另一定常状态转变的非牛顿流动过程,可以经历无限多途径,这一现象是由于本构方程的非线性性质引起的。     

A simple and efficient implicit direct forcing immersed boundary model for simulations of complex flow

This paper presents an implementation of an implicit immersed boundary (IB) method in a flow solver based on the fractional step method and the finite volume method for complex flows involving moving boundaries and complex geometries. In this implementation, a body force caused by the immersed body is first introduced into the N-S equation to model the effect of immersed boundary. However, the body force is not pre-calculated, but implicitly determined in such a way that the velocity at the immersed boundary interpolated from the corrected velocity field accurately satisfies the no-slip and no-penetration conditions. Then, the large-eddy simulation is applied in the solver, where the subgrid-scale stress is determined by the Smagorinsky–Lilly model. Near the immersed boundaries, the subgrid-scale stress is determined by a wall model where the wall shear stress is directly calculated from the Lagrangian force(which represents the action of fluid on solid) on the immersed boundary. Such treatment makes the simulations of high Reynolds number turbulent flows feasible with the IB method. The accuracy and capability of the present method are demonstrated by simulations of a variety of both two- and three-dimensional simulations, including laminar flow past static and oscillating cylinders, rotating hydrofoil and turbulent flow around a three-dimensional circular cylinder and a sphere. It shows that the present implementation provides an easy-to-use, inexpensive and accurate technique for computational fluid dynamics in industrially relevant problems.     

Two-phase flow modeling for low concentration spherical particle motion through a Newtonian fluid

Models that are used for the simulation of two-phase flows in coastal dynamics make extensive use of empirical data. The main focus of this investigation is to develop models for specific aspects of two-phase flows that are based on physical principles in order to reduce the use of such data. In this study several existing empirically based drag force models are discussed. The motion of spherical or near-spherical solid particles through a Newtonian fluid is investigated and a new method for closure of the drag force, using a Representative Unit Cell is discussed and compared to the existing models as well as to experimental data. The various drag models were also evaluated by numerical simulations, using an in-house developed program based on an adaptation of the SIMPLE procedure.