共查询到20条相似文献,搜索用时 0 毫秒
1.
In this paper, we consider the stationary double-diffusive natural convection model, which can model heat and mass transfer phenomena. Based on the fixed point theorem, the existence and uniqueness of the considered model are proved. Moreover, we design three finite element iterative methods for the considered problem. Under the uniqueness condition of a weak solution, iterative method I is stable. Compared with iterative method I, iterative method II is stable with a stronger condition. Moreover, iterative method III is stable with the strongest condition. From the perspective of viscosity, iterative method I displays well in the case of a low viscosity number, iterative method II runs well with slightly low viscosity, and iterative method III can deal with high viscosity. Finally, some numerical experiments are presented for testing the correctness of the theoretic analysis. 相似文献
2.
Two-Level Defect-Correction Method for Steady Navier-Stokes Problem with Friction Boundary Conditions 下载免费PDF全文
In this paper, we present two-level defect-correction finite element method
for steady Navier-Stokes equations at high Reynolds number with the friction boundary
conditions, which results in a variational inequality problem of the second kind.
Based on Taylor-Hood element, we solve a variational inequality problem of Navier-Stokes
type on the coarse mesh and solve a variational inequality problem of Navier-Stokes
type corresponding to Newton linearization on the fine mesh. The error estimates
for the velocity in the $H^1$ norm and the pressure in the $L^2$ norm are derived.
Finally, the numerical results are provided to confirm our theoretical analysis. 相似文献
3.
Error Analysis and Adaptive Methods of Least Squares Nonconforming Finite Element for the Transport Equations 下载免费PDF全文
Huipo Liu Shuanghu Wang & Hongbin Han 《advances in applied mathematics and mechanics.》2016,8(5):871-886
In this paper, we consider a least squares nonconforming finite element of
low order for solving the transport equations. We give a detailed overview on the stability
and the convergence properties of our considered methods in the stability norm.
Moreover, we derive residual type a posteriori error estimates for the least squares
nonconforming finite element methods under $H^{−1}$-norm, which can be used as the error
indicators to guide the mesh refinement procedure in the adaptive finite element
method. The theoretical results are supported by a series of numerical experiments. 相似文献
4.
Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations 下载免费PDF全文
Tianliang Hou & Li Li 《advances in applied mathematics and mechanics.》2016,8(6):1050-1071
In this paper, we investigate the error estimates of mixed finite element
methods for optimal control problems governed by general elliptic equations. The
state and co-state are approximated by the lowest order Raviart-Thomas mixed finite
element spaces and the control variable is approximated by piecewise constant functions.
We derive $L^2$ and $H^{-1}$-error estimates both for the control variable and the state
variables. Finally, a numerical example is given to demonstrate the theoretical results. 相似文献
5.
建立自然对流作用下融化的格子Boltzmann双分布函数模型,根据非线性对流扩散方程的格子Boltzmann模型理论提出一个新的表征融化温度场的分布函数演化方程,并通过变松弛时间方法处理固液两相变热物性传热问题.应用模型对热传导融化及自然对流融化特别固液变热物的融化过程进行模拟.模拟结果与分析解、经典的关联式结果吻合较好,模型的正确性得到了验证.模拟结果表明,自然对流对融化传热过程有着重要的影响,此外固相热传导也对融化传热、融化速率及固液两相温度分布都有一定影响. 相似文献
6.
In this paper, three iterative methods (Stokes, Newton and Oseen iterative methods) based on finite element discretization for the stationary micropolar fluid equations are proposed, analyzed and compared. The stability and error estimation for the Stokes and Newton iterative methods are obtained under the strong uniqueness conditions. In addition, the stability and error estimation for the Oseen iterative method are derived under the uniqueness condition of the weak solution. Finally, numerical examples test the applicability and the effectiveness of the three iterative methods. 相似文献
7.
An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations 下载免费PDF全文
Ying Yang & Benzhuo Lu 《advances in applied mathematics and mechanics.》2013,5(1):113-130
Poisson-Nernst-Planck
equations are a coupled system of nonlinear partial differential
equations consisting of the Nernst-Planck equation and
the electrostatic Poisson equation with delta distribution sources,
which describe the electrodiffusion of ions in a solvated
biomolecular system. In this paper, some error bounds for a piecewise
finite element approximation to this problem are derived. Several numerical
examples including biomolecular problems are shown to support our analysis. 相似文献
8.
Valentin Roussellet Xiaodong Niu Hiroshi Yamaguchi & Fré dé ric Magoulé s 《advances in applied mathematics and mechanics.》2011,3(1):121-130
In this article, natural convection of a temperature-sensitive magnetic fluid
in a porous media is studied numerically by using lattice Boltzmann method. Results
show that the heat transfer decreases when the ball numbers increase. When the
magnetic field is increased, the heat transfer is enhanced; however, the average
wall Nusselt number increases at small ball numbers but decreases at large ball
numbers due to the induced flow being more likely confined near the bottom walls
with a high number of obstacles. 相似文献
9.
10.
In the present study, mathematical modeling was performed to simulate natural convection of a nanofluid in a square enclosure using the thermal lattice Boltzmann flux solver (TLBFS). Firstly, natural convection in a square enclosure, filled with pure fluid (air and water), was investigated to validate the accuracy and performance of the method. Then, influences of the Rayleigh number, of nanoparticle volume fraction on streamlines, isotherms and average Nusselt number were studied. The numerical results illustrated that heat transfer was enhanced with the augmentation of Rayleigh number and nanoparticle volume fraction. There was a linear relationship between the average Nusselt number and solid volume fraction. and there was an exponential relationship between the average Nusselt number and Ra. In view of the Cartesian grid used by the immersed boundary method and lattice model, the immersed boundary method was chosen to treat the no-slip boundary condition of the flow field, and the Dirichlet boundary condition of the temperature field, to facilitate natural convection around a bluff body in a square enclosure. The presented numerical algorithm and code implementation were validated by means of numerical examples of natural convection between a concentric circular cylinder and a square enclosure at different aspect ratios. Numerical simulations were conducted for natural convection around a cylinder and square in an enclosure. The results illustrated that nanoparticles enhance heat transfer in higher Rayleigh number, and the heat transfer of the inner cylinder is stronger than that of the square at the same perimeter. 相似文献
11.
In this work, two-level stabilized finite volume formulations for the
2D steady Navier-Stokes equations are considered.
These methods are based
on the local Gauss integration technique and the lowest equal-order
finite element pair. Moreover, the two-level
stabilized finite volume methods involve solving one small Navier-Stokes
problem on a coarse mesh with mesh size $H$, a large general Stokes problem for the Simple and
Oseen two-level stabilized finite volume methods on the fine mesh with mesh size $h$=$\mathcal{O}(H^2)$ or a large general Stokes equations for the Newton two-level stabilized finite
volume method on a fine mesh with mesh size $h$=$\mathcal{O}(|\log h|^{1/2}H^3)$.
These methods we studied provide an
approximate solution $(\widetilde{u}_h^v,\widetilde{p}_h^v)$ with the convergence rate of same order
as the standard stabilized finite volume method, which involve solving one large
nonlinear problem on a fine mesh with mesh size $h$. Hence, our methods
can save a large amount of computational time. 相似文献
12.
Ravi P. Agarwal Fatemah Mofarreh Rasool Shah Waewta Luangboon Kamsing Nonlaopon 《Entropy (Basel, Switzerland)》2021,23(8)
This research article is dedicated to solving fractional-order parabolic equations using an innovative analytical technique. The Adomian decomposition method is well supported by natural transform to establish closed form solutions for targeted problems. The procedure is simple, attractive and is preferred over other methods because it provides a closed form solution for the given problems. The solution graphs are plotted for both integer and fractional-order, which shows that the obtained results are in good contact with the exact solution of the problems. It is also observed that the solution of fractional-order problems are convergent to the solution of integer-order problem. In conclusion, the current technique is an accurate and straightforward approximate method that can be applied to solve other fractional-order partial differential equations. 相似文献
13.
14.
使用热格子Boltzmann方法针对圆内开缝圆自然对流的流动与换热进行数值模拟,通过相空间、功率谱等进行非线性动力学特性分析,研究其流动与换热的稳定性.结果表明:随着瑞利数Ra的增加,流场的相图从开始稳定的平衡点经历Hopf分岔后转变为极限环,表明流场进入一个倍周期性振荡状态;随着瑞利数进一步增加,稳定的极限环分岔为二维环面,系统相空间结构复杂化;当瑞利数Ra大于某一临界值时,二维环面分岔突变进入混沌状态,系统在相空间中出现非常复杂的轨线结构.总体上,通过系统不同瑞利数所对应的非线性动力学特性的表现形式,表明系统经过Ruelle-Takens道路到达混沌,展现出自然对流从稳定的流动和换热发展到非线性运动特征的混沌历程. 相似文献
15.
为提升高热流密度下LED灯具的自然对流散热性能,以一款基于热电制冷(TEC)的单颗LED小型灯具模组为研究对象,在采用实验测量和回归拟合准确获得TEC性能参数的基础上,建立了有无TEC参与散热的等效热路模型,并选择合理的数学公式对其进行性能描述,进而遵循本文设计的计算流程快速得到各种散热性能数据。LED模组的散热分析表明:在恒定的LED热功率下,施加最佳的TEC电流可获得最高的散热性能;LED热功率越低,安装TEC的散热性能越比常规方法优异。经遗传算法优化前后的性能对比分析表明:优化后结构中TEC的合理工作区明显增大,能满足LED更高功率的散热需求;当LED为0.493 W时,优化后结构的最佳结温仅为15.66℃,远低于30℃的环境温度。基于TEC实验数据建立的等效热路模型,能为装配TEC的LED模组提供快速完整的散热设计分析与结构优化的合理方案。 相似文献
16.
采用SIMPLE算法,QUICK差分格式,对底部加热三维长方体腔内空气的自然对流进行了数值模拟。根据模拟结果,探讨了方腔内流体流动与换热的静态分岔与振荡等非线性现象。数值结果显示,在固定的几何尺寸和不同Ra的情况下,当初始场不同时,会出现若干不同的解,即存在解的静态分岔;在固定的几何尺寸和相同的初始场情况下,低Ra时流动和换热处于稳态,当Ra超过某一临界值时,流动和换热就会随时间振荡,并通过倍周期分岔过渡到混沌;当方腔的几何尺寸不同时,分岔点的特征值Ra也发生变化。 相似文献
17.
In this article, we mainly consider a first order penalty finite element method (PFEM) for the 2D/3D unsteady incompressible magnetohydrodynamic (MHD) equations. The penalty method applies a penalty term to relax the constraint “”, which allows us to transform the saddle point problem into two smaller problems to solve. The Euler semi-implicit scheme is based on a first order backward difference formula for time discretization and semi-implicit treatments for nonlinear terms. It is worth mentioning that the error estimates of the fully discrete PFEM are rigorously derived, which depend on the penalty parameter , the time-step size , and the mesh size h. Finally, two numerical tests show that our scheme is effective. 相似文献
18.
Natural Convection in a Concentric Annulus: A Lattice Boltzmann Method Study with Boundary Condition-Enforced Immersed Boundary Method 下载免费PDF全文
Yang Hu Xiao-Dong Niu Shi Shu Haizhuan Yuan & Mingjun Li 《advances in applied mathematics and mechanics.》2013,5(3):321-336
In this paper, a boundary condition-enforced IBM is introduced into the LBM
in order to satisfy the non-slip and temperature boundary conditions, and natural
convections in a concentric isothermal annulus between a square outer cylinder and a
circular inner cylinder are simulated. The obtained results show that the boundary
condition-enforced method gives a better solution for the flow field and the complicated
physics of the natural convections in the selected case is correctly captured. The
calculated average Nusselt numbers agree well with the previous studies. 相似文献
19.
20.
Posteriori Error Estimation for an Interior Penalty Discontinuous Galerkin Method for Maxwell's Equations in Cold Plasma 下载免费PDF全文
Jichun Li 《advances in applied mathematics and mechanics.》2009,1(1):107-124
In this paper, we develop a residual-based a posteriori error
estimator for the time-dependent Maxwell's equations in the cold
plasma. Here we consider a semi-discrete interior penalty
discontinuous Galerkin (DG) method for solving the governing
equations. We provide both the upper bound and lower bound analysis
for the error estimator. This is the first posteriori error analysis
carried out for the Maxwell's equations in dispersive media. 相似文献