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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
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本文发展了差分法求解流动与换热问题的三维非均分网格7点紧致格式,并利用延迟修正方法将其与SIMPLE算法相结合形成了一种三维紧致修正方法。利用所发展的紧致修正方法对圆筒内同心开缝圆筒的三维自然对流与换热问题进行了数值模拟,所获得的数值结果与实验结果一致。采用Richardson方法证实所发展的三维紧致修正方法大约具有4阶精度。进一步的数值计算表明,在特征参数Ra数大于一定值时,由圆筒内同心开缝圆筒的三维自然对流问题简化的二维模型数值结果与实验结果逐渐加大,用三维模型才能得到比较可靠的结果。 相似文献
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通过泰勒展式系数匹配的方法发展了基于非等距网格的有限容积紧致格式,采用延迟修正的方法建立了基于SIMPLE的紧致方法,,该方法能够得到高精度的数值解,增加迭代求解代数方程组的稳定性。对底部加热的方腔内自然对流换热问题进行数值模拟,结果表明,紧致方法比二阶中心差分方法具有更高的精度。 相似文献
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振荡流共轭换热现象广泛存在于热声热机等工程应用中.基于双分布格子-Boltzmann模型,对平行平板间振荡流共轭换热进行了数值模拟.通过假定共轭界面处流体和固体的未知内能分布函数均为对应的平衡态滑移修正格式,提出了一种处理共轭换热边界的新方法.模拟结果表明,该方法可以保证共轭界面上温度连续和热流连续.分析了不同流体与固体导热系数比情况下振荡流共轭换热的速度场、温度场以及热流分布的特点. 相似文献
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To date, there are very few studies on the transition beyond second Hopf bifurcation in a lid-driven square cavity, due to the difficulties in theoretical analysis and numerical simulations. In this paper, we study the characteristics of the third Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme rectently developed by us. We numerically identify the critical Reynolds number of the third Hopf bifurcation located in the interval of (13944.7021,13946.5333) by the method of bisection. Through Fourier analysis, it is discovered that the flow becomes chaotic with a characteristic of period-doubling bifurcation when the Reynolds number is beyond the third bifurcation critical interval. Nonlinear time series analysis further ascertains the flow chaotic behaviors via the phase diagram, Kolmogorov entropy and maximal Lyapunov exponent. The phase diagram changes interestingly from a closed curve with self-intersection to an unclosed curve and the attractor eventually becomes strange when the flow becomes chaotic. 相似文献
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To date, there are very few studies on the second Hopf bifurcation in a driven square cavity, although there are intensive investigations focused on the first Hopf bifurcation in literature, due to the difficulties of theoretical analyses and numerical simulations. In this paper, we study the characteristics of the second Hopf bifurcation in a driven square cavity by applying a consistent fourth-order compact finite difference scheme recently developed by us. We numerically identify the critical Reynolds number of the second Hopf bifurcation located in the interval of(11093.75, 11094.3604) by bisection. In addition, we find that there are two dominant frequencies in its spectral diagram when the flow is in the status of the second Hopf bifurcation, while only one dominant frequency is identified if the flow is in the first Hopf bifurcation via the Fourier analysis. More interestingly, the flow phase portrait of velocity components is found to make transition from a regular elliptical closed form for the first Hopf bifurcation to a non-elliptical closed form with self-intersection for the second Hopf bifurcation. Such characteristics disclose flow in a quasi-periodic state when the second Hopf bifurcation occurs. 相似文献
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研究了温盐双扩散系统的多组分格子Boltzmann方法.通过对二维方腔的温盐双扩散系统的数值模拟,检验了方法的可行性及有效性,所得到的结果与差分法结果符合良好,继而将此方法推广到三维,建立了三维温盐双扩散系统的格子Boltzmann方法,对三维方腔双扩散问题进行了模拟和分析,并与差分法模拟的结果进行了比较,结果令人满意.最后,分析了格子Boltzmann方法在模拟双扩散对流问题时存在的局限性.
关键词:
格子Boltzmann方法
温盐双扩散
Boussinesq近似
数值模拟 相似文献
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Dingfang Li Xiaofeng Wang & Hui Feng 《advances in applied mathematics and mechanics.》2013,5(1):55-77
A fully higher-order compact (HOC) finite difference scheme on the
9-point two-dimensional (2D) stencil is formulated for solving the
steady-state laminar mixed convection flow in a lid-driven inclined
square enclosure filled with water-$Al_2O_3$ nanofluid. Two
cases are considered depending on the direction of temperature
gradient imposed (Case I, top and bottom; Case II, left and right).
The developed equations are given in terms of the stream
function-vorticity formulation and are non-dimensionalized and then
solved numerically by a fourth-order accurate compact finite
difference method. Unlike other compact solution procedure in
literature for this physical configuration, the present method is
fully compact and fully higher-order accurate. The fluid flow, heat
transfer and heat transport characteristics were illustrated by
streamlines, isotherms and averaged Nusselt number. Comparisons with
previously published work are performed and found to be in excellent
agreement. A parametric study is conducted and a set of graphical
results is presented and discussed to elucidate that significant
heat transfer enhancement can be obtained due to the presence of
nanoparticles and that this is accentuated by inclination of the
enclosure at moderate and large Richardson numbers. 相似文献
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求解Navier-Stokes方程组的组合紧致迎风格式 总被引:1,自引:0,他引:1
给出一种新的至少有四阶精度的组合紧致迎风(CCU)格式,该格式有较高的逼近解率,利用该组合迎风格式,提出一种新的适合于在交错网格系统下求解Navier-Stokes方程组的高精度紧致差分投影算法.用组合紧致迎风格式离散对流项,粘性项、压力梯度项以及压力Poisson方程均采用四阶对称型紧致差分格式逼近,算法的整体精度不低于四阶.通过对Taylor涡列、对流占优扩散问题和双周期双剪切层流动问题的计算表明,该算法适合于对复杂流体流动问题的数值模拟. 相似文献
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采用非结构化网格有限容积法求解了不可压N-S方程组,对流项采用GAMMA格式,扩散项采用二阶中心差分格式建立离散方程,用SOAR算法处理压力与速度的耦合关系,得到了一种求解不可压N-S方程的非结构网格耦合求解器。通过方腔顶盖驱动流、后台阶绕流以及方腔自然对流等几个典型的算例,考察了求解器的计算精度及收敛特性,并与SIMPLE算法进行了比较,结果表明该求解器是有效可行的。 相似文献
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In this paper, a compact finite difference scheme for the fractional sub-diffusion equations is derived. After a transformation of the original problem, the L1 discretization is applied for the time-fractional part and fourth-order accuracy compact approximation for the second-order space derivative. The unique solvability of the difference solution is discussed. The stability and convergence of the finite difference scheme in maximum norm are proved using the energy method, where a new inner product is introduced for the theoretical analysis. The technique is quite novel and different from previous analytical methods. Finally, a numerical example is provided to show the effectiveness and accuracy of the method. 相似文献
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In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection–diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33–53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier–Stokes equations using the stream function–vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature. 相似文献