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首页> 外文期刊>International Journal of Computational Methods and Experimental Measurements >MODELING MIXED BOUNDARY PROBLEMS WITH THE COMPLEX VARIABLE BOUNDARY ELEMENT METHOD (CVBEM) USING MATLAB AND MATHEMATICA
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MODELING MIXED BOUNDARY PROBLEMS WITH THE COMPLEX VARIABLE BOUNDARY ELEMENT METHOD (CVBEM) USING MATLAB AND MATHEMATICA

机译：使用MATLAB和MATHEMATICA用复杂可变边界元方法（CVBEM）建模混合边界问题

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摘要

The complex variable boundary element method or CVBEM is a numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an approximation function that is derived from the Cauchy integral equation in complex analysis. Given the potential values (i.e. a Dirichlet problem) along the boundary, the typical problem is to use the potential function to solve the governing Laplace equation. In this approach, it is not necessary to know the streamline values on the boundary. The modeling approach can be extended to problems where the streamline function is needed because there are known streamline values along the problem boundary (i.e. a mixed boundary value problem). Two common problems that have such conditions are insulation on a boundary and fluid flow around a solid obstacle. In this paper, five advances in the CVBEM are made with respect to the modeling of the mixed boundary value problem; namely (1) the use of Mathematica and MATLAB in tandem to calculate and plot the flow net of a boundary value problem. (2) The magnitude of the size of the problem domain is extended. (3) The modeling results include direct computation and development of a flow net. (4) The graphical displays of the total flownet are developed simultaneously. And (5) the nodal point location as an additional degree of freedom in the CVBEM modeling approach is extended to mixed boundaries. A demonstration problem of fluid flow is included to illustrate the flownet development capability.
机译：复变边界元法或CVBEM是一种数值技术，可以通过使用从复杂分析中的柯西积分方程派生的逼近函数，为二维或多个维的潜在值问题提供解决方案。给定沿边界的势能值（即Dirichlet问题），典型的问题是使用势能函数求解控制拉普拉斯方程。在这种方法中，不必知道边界上的流线值。建模方法可以扩展到需要流线函数的问题，因为沿问题边界存在已知的流线值（即混合边界值问题）。具有此类条件的两个常见问题是边界处的绝缘和固体障碍物周围的流体流动。本文在混合边界值问题的建模方面取得了五项进展。即（1）串联使用Mathematica和MATLAB来计算和绘制边界值问题的流网。 （2）问题域大小的大小得到了扩展。 （3）建模结果包括直接计算和开发流网。 （4）同时显示总流量网络的图形显示。 （5）在CVBEM建模方法中，作为附加自由度的节点位置扩展到混合边界。包括流体流动的演示问题，以说明流网的开发能力。

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