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首页> 外文期刊>Meccanica: Journal of the Italian Association of Theoretical and Applied Mechanics >A novel non-primitive Boundary Integral Equation Method for three-dimensional and axisymmetric Stokes flows
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A novel non-primitive Boundary Integral Equation Method for three-dimensional and axisymmetric Stokes flows

机译：三维轴对称斯托克斯流的一种新的非本原边界积分方程方法

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摘要

A new Boundary Integral Equation (BIE) formulation for Stokes flow is presented for threedimensional and axisymmetrical problems using nonprimitive variables, assuming velocity field is prescribed on the boundary. The formulation involves the vector potential, instead of the classical stream function, and all three components of the vorticity are implied. Furthermore, following the Helmholtz decomposition, a scalar potential is added to represent the solenoidal velocity field. Firstly, the BIEs for threedimensional flows are formulated for the vector potential and the vorticity by employing the fundamental solutions in free space of vector Laplace and biharmonic equations. The equations for axisymmetric flows are then derived from the three-dimensional formulation in a second step. The outcome is a domain integral free BIE formulation for both three-dimensional and axisymmetric Stokes flows with prescribed velocity boundary condition. Numerical results are included to validate and show the efficiency of the proposed axisymmetric formulation.
机译：假设在边界上指定了速度场，则针对使用非基本变量的三维和轴对称问题，提出了一种针对斯托克斯流的新的边界积分方程（BIE）公式。该公式涉及矢量势，而不是经典的流函数，并且隐含了涡度的所有三个分量。此外，在亥姆霍兹分解之后，添加标量势来表示螺线管速度场。首先，利用矢量拉普拉斯自由空间和双调和方程的基本解，针对矢量势和涡度制定了三维流动的BIE。然后在第二步中从三维公式导出轴对称流的方程。结果是在规定的速度边界条件下，三维和轴对称斯托克斯流都得到了无区域积分的BIE公式。包括数值结果以验证并显示所提出的轴对称公式的效率。

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