Shape calculus for vortex patch equilibria and its application to lattice configurations
Shape calculus for vortex patch equilibria and its application to lattice configurations
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DOI：
10.1016/j.cam.2017.10.023
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发表时间：
2018-04
期刊：
影响因子：
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通讯作者：
Tomoki Uda
中科院分区：
文献类型：
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作者：
Tomoki Uda
提出了一个新的对数核奇异围道积分的形导数公式。这个公式给出了一个计算涡斑平衡的简单数值格式。由于它的简单性，任何点涡的定常构形都可以推广到涡斑的定常构形。作为一个测试问题，一个双周期阵列的涡补丁被认为是显示新公式的效率。几个非平凡家庭的固定涡补丁晶格也提出。
A new shape derivative formula for singular contour integrals with logarithmic kernels is proposed. This formula yields a simple numerical scheme for computing vortex patch equilibria. Owing to its simplicity, any steady configuration of point vortices can be extended to that of vortex patches. As a test problem, a doubly periodic array of vortex patches is considered to show the efficiency of the new formula. Several non-trivial families of stationary vortex patch lattices are also presented.