共查询到16条相似文献,搜索用时 203 毫秒
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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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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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构造定常对流扩散方程高精度紧致差分格式的新方法 总被引:5,自引:1,他引:4
以一维定常对流扩散方程的高精度差分格式为基础,提出了一种构造二维定常对扩散方程高精度紧致差分格式的新方法,并给出数值例子。 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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本文将非均匀网格直接离散的高阶紧致格式从二维推广到三维,结合附加修正多重网格方法提高了传统迭代方法的收敛效率,并且验证了该格式在不同边界条件的数值表现。结果表明:该方法可以有效的求解NS方程中的压力泊松方程. 相似文献
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Bendiks Jan Boersma 《Journal of computational physics》2011,230(12):4940-4954
In a previous paper we have developed a staggered compact finite difference method for the compressible Navier–Stokes equations. In this paper we will extend this method to the case of incompressible Navier–Stokes equations. In an incompressible flow conservation of mass is ensured by the well known pressure correction method and . The advection and diffusion terms are discretized with 6th order spatial accuracy. The discrete Poisson equation, which has to be solved in the pressure correction step, has the same spatial accuracy as the advection and diffusion operators. The equations are integrated in time with a third order Adams–Bashforth method. Results are presented for a 1D advection–diffusion equation, a 2D lid driven cavity at a Reynolds number of 1000 and 10,000 and finally a 3D fully developed turbulent duct flow at a bulk Reynolds number of 5400. In all cases the methods show excellent agreement with analytical and other numerical and experimental work. 相似文献
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利用余项修正法建立奇异退化扩散反应方程非均匀网格上的高阶紧致差分式,其时间具有二阶精度,空间具有三阶至四阶精度. 利用等分布原理建立时间和空间的网格自适应方法.最后通过具有精确解的数值算例验证方法的可靠性和精确性,并研究一维爆破问题. 相似文献
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CHANG KONG-LIANG 《中国物理C(英文版)》1978,2(3):200-210
Physical processes of the propagation of the solar cosmic rays in the interplanetary space include the diffusion in interplanetary disordered magnetic fields and the convection in solar winds. Dimensional method can be applied to solve those equations convertible into Bessel equation, the results obtained are identical with those solved by the commonly used separate variable method. In order to derive an analytic solution to the diffusion convection equation in an unbounded, uniform medium, two dimensionless parameters reflecting the diffusion and convection characteristics of the particles are introduced. In the diffusion dominated case, the solution is similar in form to the diffusion of a source moving with the convection velocity and is modified by another convection term, which can be expanded into a power series of the convection parameter with coefficients composed of the generalized hypergeometric function series of the diffusion parameter. This solution has a clear physical meaning, and can suitably be used in the discussion of the rise phase characteristics of the solar cosmic rays from medium to high energies (Ep≥101 MeV). 相似文献
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紧致方法对流动换热及静态分岔的模拟 总被引:1,自引:0,他引:1
发展了基于投影法的紧致方法求解流动换热问题,对顶盖驱动流和侧壁加热的方腔内自然对流换热问题进行了数值模拟。与其它传统方法相比,紧致方法能在较少的网格结点下获得精度较高的计算结果。进一步,采用所发展的紧致方法对不同工况下的Rayleigh-Benard对流及其静态分岔现象进行了数值模拟。数值计算结果表明当长宽比变大时,底部努塞尔数会有小幅度增加。当长宽比为8时,用所发展的紧致方法不同的初场可以得出三种不同的流场和温度场。与基于QUICK格式的SIMPLE算法相比,所发展的紧致方法可以多预测一种静态分岔现象。 相似文献