Cauchy problem for Stokes–Leibenson approximation in a Hele–Shaw corner cellстатья
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Дата последнего поиска статьи во внешних источниках: 8 февраля 2017 г.
Аннотация:The Helmholtz–Kirchhoff transformation gives us a new approach to solve the Hele–Shaw problem. Particularly, we derived a so-called quasi-contour method from which we built a numerical scheme. Following a previous article [1], we propose a way to improve significantly the numerical scheme, which leads to the resolution of a Cauchy problem. The tedious calculation of a surface integral (absent in the physical problem) was replaced with simple integrals along the contour of the fluid. We have then tested the new numerical scheme on the Stokes–Leibenson problem in a corner geometry, highlighting the gain in accuracy of the results. Besides, the existence of a critical manifold in the space of contours is confirmed (see [1]).