共查询到18条相似文献,搜索用时 46 毫秒
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基于变分原理的二维热传导方程差分格式 总被引:5,自引:3,他引:2
研究二维热传导方程的差分数值模拟.用变分原理在不规则结构网格上建立热流通量形式的差分格式.将热流通量作为未知函数求泛函极值,并与温度函数联立求解.克服通常九点格式用插值方法计算网格边界上的热传导系数和网格结点上的温度所引入的误差. 相似文献
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讨论抛物型方程的离散差分格式的构造,对九点差分格式进行了适用范围的讨论,并在此基础上提出辅助网格差分方法,用于处理因网格长宽比大且扭曲较大的网格引起的计算精度与计算效率降低的问题,该方法从守恒方程出发,将九点差分格式应用于按某种合适的方式进行重分之后的网格上,减少由于网格正则性差以及网格节点上的物理量采用周围网格量的加权平均等原因所引起的计算误差,得到一个新的但其解仍然逼近原来网格上的物理量的方程组.所构造的方法便于实施,且更适合于对实际物理模型的模拟,能比较好地适应流体大变形导致的网格扭曲,数值试验表明它有较好的数值精度和稳定性. 相似文献
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热传导方程是一种偏微分方程。对于有界热传导齐次方程的混合问题,用分离变量法求解往往很复杂,也很抽象。为了更好的理解方程的解,更直观的看出它的物理意义,本文用Maple软件将方程的解用图像表示出来。先用pdsolve函数求解方程,再用PlotSd函数进行绘图,通过改变边界条件,比较了图形的变化情况。从结果可以看出Manle软件对于热传导方程求解和绘图十分简便,也很直观。在物理教学中可以得到很好的应用。 相似文献
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研究二维散乱点集上数值求解非线性扩散方程的有限方向差分方法。利用五个邻点信息构造具有最小模板的离散格式,并且离散系数具有显式表达式。另外,利用五点公式获得了间断问题物质界面的离散格式,该格式对界面流的计算具有近似二阶精度。不同计算区域及不同类型的离散点集上的计算结果验证了方法的有效性。 相似文献
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Three Boundary Meshless Methods for Heat Conduction Analysis in Nonlinear FGMs with Kirchhoff and Laplace Transformation 下载免费PDF全文
Zhuo-Jia Fu Wen Chen & Qing-Hua Qin 《advances in applied mathematics and mechanics.》2012,4(5):519-542
This paper presents three boundary meshless methods for solving problems of steady-state and transient heat conduction in nonlinear functionally graded materials (FGMs). The three methods are, respectively, the method of fundamental solution (MFS), the boundary knot method (BKM), and the collocation Trefftz method (CTM) in conjunction with Kirchhoff transformation and various variable transformations. In the analysis, Laplace transform technique is employed to handle the time variable in transient heat conduction problem and the Stehfest numerical Laplace inversion is applied to retrieve the corresponding time-dependent solutions. The proposed MFS, BKM and CTM are mathematically simple, easy-to-programming, meshless, highly accurate and integration-free. Three numerical examples of steady state and transient heat conduction in nonlinear FGMs are considered, and the results are compared with those from meshless local boundary integral equation method (LBIEM) and analytical solutions to demonstrate the efficiency of the present schemes. 相似文献
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A. Tadeu C. S. Chen J. Antόnio & Nuno Simõ es 《advances in applied mathematics and mechanics.》2011,3(5):572-585
Fourier transform is applied to remove the time-dependent variable in the
diffusion equation. Under non-harmonic initial conditions this gives rise to a
non-homogeneous Helmholtz equation, which is solved by the method of
fundamental solutions and the method of particular solutions. The particular
solution of Helmholtz equation is available as shown in [4, 15].
The approximate solution in frequency domain is then inverted
numerically using the inverse Fourier transform algorithm. Complex frequencies
are used in order to avoid aliasing phenomena and to allow the computation of
the static response. Two numerical examples are given to illustrate the
effectiveness of the proposed approach for solving 2-D diffusion equations. 相似文献
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Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson’s equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method (RKPM). A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples. 相似文献
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提出一种求解二维功能梯度材料(FGMs)稳态热传导问题的重心Lagrange插值配点法.基于Chebyshev节点构造二维重心Lagrange插值函数及其偏导数,然后基于配点法将其直接代入FGMs热传导问题的控制方程和边界条件,得到系统离散方程.重心Lagrange插值配点法是一种真正的无网格方法,很好地融合了重心Lagrange插值和配点格式的优势,具有高效、稳定、高精度和易于数值实现的优点.采用重心Lagrange插值配点法分别对指数型、二次型和三角型FGMs热传导问题进行数值模拟.结果表明:该方法具有较高的计算效率和计算精度,对材料梯度参数的变化不敏感.可以进一步拓展到FGMs瞬态问题和FGMs的热力耦合分析. 相似文献
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提出双曲传热反问题热物性参数和边界条件多宗量联合反演的一般数值求解模式,考虑了非均质和分布参数的影响,时域上采用时域精细算法进行离散,建立了便于敏度分析的有限元正演模型.由最小二乘原理建立反演模型,应用共轭梯度法进行求解.探讨了时间步长和测量误差对反演结果的影响,并进行了数值验证. 相似文献
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In this paper, we propose a new positivity-preserving finite volume scheme with fixed stencils for the nonequilibrium radiation diffusion equations on distorted meshes. This scheme is used to simulate the equations on meshes with both the cell-centered and cell-vertex unknowns. The cell-centered unknowns are the primary unknowns, and the element vertex unknowns are taken as the auxiliary unknowns, which can be calculated by interpolation algorithm. With the nonlinear two-point flux approximation, the interpolation algorithm is not required to be positivity-preserving. Besides, the scheme has a fixed stencil and is locally conservative. The Anderson acceleration is used for the Picard method to solve the nonlinear systems efficiently. Several numerical results are also given to illustrate the efficiency and strong positivity-preserving quality of the scheme. 相似文献