Radial point collocation method (RPCM) for solving convection-diffusion problems
Radial point collocation method (RPCM) for solving convection-diffusion problems
复制标题
解决对流扩散问题的径向点配置法 (RPCM)
DOI：
10.1631/jzus.2006.a1061
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发表时间：
2006
影响因子：
3.2
通讯作者：
中科院分区：
文献类型：
--
作者：
本文将一种无网格方法--径向配点法（RPCM）应用于求解对流扩散问题。该方法的主要特点是采用基于径向基函数的局部支撑区域插值方法。结果表明，该方法是局部的，因此系统矩阵是带状的，这对实际工程问题是非常有吸引力的。在数值试验中，将RPCM应用于求解二维非线性对流扩散Burgers方程。RPCM的计算结果表明了该方法求解瞬态流体动力学问题的准确性和有效性。在Neumann边界条件存在时，采用虚拟点格式提高了求解精度.该方法的无网格特性在求解计算流体问题中具有很大的吸引力。
In this paper, Radial point collocation method (RPCM), a kind of meshfree method, is applied to solve convection-diffusion problem. The main feature of this approach is to use the interpolation schemes in local supported domains based on radial basis functions. As a result, this method is local and hence the system matrix is banded which is very attractive for practical engineering problems. In the numerical examination, RPCM is applied to solve non-linear convection-diffusion 2D Burgers equations. The results obtained by RPCM demonstrate the accuracy and efficiency of the proposed method for solving transient fluid dynamic problems. A fictitious point scheme is adopted to improve the solution accuracy while Neumann boundary conditions exist. The meshfree feature of the present method is very attractive in solving computational fluid problems.