Stokes流的边界正则化积分方程（BRIEF）
Boundary regularized integral equation formulation (BRIEF) of Stokes flow
摘要：
具有规定边界条件的单相Stokes流问题可以用边界正则化积分方程来表示，该积分方程完全没有传统公式中存在的奇异性。通过减去相关的辅助流场$\boldsymbol{w}$，消除了在常规边界积分法中使用基本解时产生的常见数学奇异性，该辅助流场可以从斯托克斯方程的许多已知基本解中的一个构造。这种方法是精确的，并且不需要引入额外的截止参数。这种边界正则化积分方程公式的数值实现提供了相当大的节省编码工作，提高数值精度。即使在部分边界几乎接触的问题中，也保留了该公式的高精度。
英文摘要：
Single-phase Stokes flow problems with prescribed boundary conditions can be formulated in terms of a boundary regularized integral equation that is completely free of singularities that exist in the traditional formulation. The usual mathematical singularities that arise from using the fundamental solution in the conventional boundary integral method are removed by subtracting a related auxiliary flow field, $\boldsymbol{w}$, that can be constructed from one of many known fundamental solutions of the Stokes equation. This approach is exact and does not require the introduction of additional cutoff parameters. The numerical implementation of this boundary regularized integral equation formulation affords considerable savings in coding effort with improved numerical accuracy. The high accuracy of this formulation is retained even in problems where parts of the boundaries may almost be in contact.
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