共查询到20条相似文献,搜索用时 159 毫秒
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求解对流扩散方程的紧致修正方法 总被引:1,自引:0,他引:1
提出了求解对流扩散方程的紧致修正方法,该方法是在低阶离散格式的源项中,引入紧致修正项,从而构造高阶紧致修正格式,并进行求解.采用紧致修正方法对典型的对流扩散方程进行计算.结果表明,紧致修正方法虽然与二阶经典差分方法建立在相同的结点数上,但紧致修正方法的精度与紧致方法的精度相同,均具有四阶精度.所以紧致修正方法可以在少网... 相似文献
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用Navier-Stokes方程直接数值模拟平板边界层流动中湍斑的形成和演化过程.发展了模拟湍斑的高精度、高分辨率的高效计算方法,包括推出四阶时间分裂法以提高精度;提出三维耦合差分方法,用于关于压力的泊松方程和关于速度的亥姆霍兹方程的空间离散,建立其四阶三维耦合中心差分格式;并采用四阶紧致迎风差分格式,避免了一般四阶中心差分格式不适用于边界邻域的困难和提高了分辨率;精心地处理各种边界条件,以保持精度和稳定.该方法适用于包含边界邻域的整个区域内的湍斑模拟.通过模拟平板边界层流动中湍斑的复杂演化过程,显示了湍斑的基本特征. 相似文献
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对流扩散方程的指数型摄动差分法 总被引:7,自引:0,他引:7
改进了作者所提出的对流扩散方程四阶指数型摄动差分格式,并阐明其在高Reynolds数适应性和节省计算量方面的显著优点。指数型摄动差分法经改进后具有较为简便的形式,克服了其他紧致高阶格式不能使用于高Reynolds数问题的致命弱点。文中针对计算流体力学的基本困难,作一至三维流动模型方程和自然对流传热问题的精细计算,且以双精制算法检验格式的四阶精度,表明摄动差分法能在较粗的网格下给出相当准确的结果,十分显著地节省计算机时,并对"激波"和"边界层"等高Reynolds数效应有极高的分辨能力。 相似文献
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为研究离散格式对离心泵性能预测精度的影响,本文以自吸式离心泵为计算模型,采用Realizableκ-ε湍流模式进行三维内流场的数值模拟研究,分析了从零流量到最大工作流量下的内部流动和水力性能。建立了考虑内部间隙影响的自吸式离心泵全三维计算模型,分析了动量方程对流项采用一阶差分和二阶差分格式对计算精度的影响,同时分析了压力项的Standard和PRESTO离散格式对计算精度的影响。结果表明,在小流量工况下,采用二阶迎风格式具有较高的计算精度,而在大流量工况下采用一阶迎风格式更为合适。该结果可为准确预测离心泵全工况外特性提供参考依据。 相似文献
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基于中心差分的对流扩散方程四阶紧凑格式 总被引:6,自引:0,他引:6
在经典中心差分格式的基础上,提出对流扩散方程的四阶紧凑差分格式。具体方法是,先就一维情形,将中心差分格式改造为不受网格Reynolds数限制的恒稳二阶格式,再在不增加相关网格点的前提下,通过格式中对流系数和源项的摄动处理,使稳格式的精度提高至四阶。本文并作一、二、三维流动模型方程及高Rayleigh数自然对流传热问题的数值求解,例示本文格式的优良性态。 相似文献
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针对二维非定常半线性扩散反应方程,空间导数项采用四阶紧致差分公式离散,时间导数项采用四阶向后Euler公式进行离散,提出一种无条件稳定的高精度五层全隐格式.格式截断误差为O(τ4+τ2h2+h4),即时间和空间均具有四阶精度.对于第一、二、三时间层采用Crank-Nicolson方法进行离散,并采用Richardson外推公式将启动层时间精度外推到四阶.建立适用于该格式的多重网格方法,加快在每个时间层上迭代求解代数方程组的收敛速度,提高计算效率.最后通过数值实验验证格式的精确性和稳定性以及多重网格方法的高效性. 相似文献
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The object of this paper is to provide a reliable tool to carry out the parametrical studies of post-stall behaviors in multistage axial compression systems. An adapted version of the 1.5D Euler equations with additional source terms is discretized with a finite volume method and are solved in time by a fourth-order Runge–Kutta scheme. The equations are discretized at mid-span both inside the blade rows and the non-bladed regions. The source terms express the blade-flow interactions and are estimated by calculating the velocity triangles for each blade row. Additional source terms are introduced to represent the effects of inlet disturbances on post-stall behaviors and the physical analysis is therefore proposed to explain the phenomenon. 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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The development of a compact fourth-order finite volume method for solutions of the Navier–Stokes equations on staggered grids is presented. A special attention is given to the conservation laws on momentum control volumes. A higher-order divergence-free interpolation for convective velocities is developed which ensures a perfect conservation of mass and momentum on momentum control volumes. Three forms of the nonlinear correction for staggered grids are proposed and studied. The accuracy of each approximation is assessed comparatively in Fourier space. The importance of higher-order approximations of pressure is discussed and numerically demonstrated. Fourth-order accuracy of the complete scheme is illustrated by the doubly-periodic shear layer and the instability of plane-channel flow. The efficiency of the scheme is demonstrated by a grid dependency study of turbulent channel flows by means of direct numerical simulations. The proposed scheme is highly accurate and efficient. At the same level of accuracy, the fourth-order scheme can be ten times faster than the second-order counterpart. This gain in efficiency can be spent on a higher resolution for more accurate solutions at a lower cost. 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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Yongbin Ge 《Journal of computational physics》2010,229(18):6381-6391
A fourth-order compact difference discretization scheme with unequal meshsizes in different coordinate directions is employed to solve a three-dimensional (3D) Poisson equation on a cubic domain. Two multgrid methods are developed to solve the resulting sparse linear systems. One is to use the full-coarsening multigrid method with plane Gauss–Seidel relaxation, which uses line Gauss–Seidel relaxation to compute each planewise solution. The other is to construct a partial semi-coarsening multigrid method with the traditional point or plane Gauss–Seidel relaxations. Numerical experiments are conducted to test the computed accuracy of the fourth-order compact difference scheme and the computational efficiency of the multigrid methods with the fourth-order compact difference scheme. 相似文献