کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
519447 | 867665 | 2013 | 24 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: A small-scale decomposition for 3D boundary integral computations with surface tension A small-scale decomposition for 3D boundary integral computations with surface tension](/preview/png/519447.png)
An efficient, non-stiff boundary integral method for the initial value problem for interfacial Darcy flow (which is a model of porous media flow) in three space dimensions is presented. We consider a ‘doubly-periodic’ interface separating two fluids, with surface tension present at the boundary. Surface tension introduces high order (i.e., high derivative) terms in the governing equation, and this imposes a severe stability constraint on explicit time-integration methods. Furthermore, the high order terms appear in a nonlocal operator, which makes it difficult to design an efficient implicit method. The stiffness is removed by developing a small-scale decomposition in the spirit of prior work in the two-dimensional problem by Hou, Lowengrub, and Shelley. In order to develop this small-scale decomposition, we formulate the problem using a generalized isothermal parameterization of the free surface. An additional difficulty is the efficient calculation of the Birkhoff–Rott integral for the velocity of the interface. We present a new algorithm, based on Ewald summation, to compute this in O(NlogN)O(NlogN) operations, where N is the number of interface grid points. Our non-stiff method is expected to apply widely to problems for doubly-periodic interfacial flow with surface tension which have a boundary integral formulation.
Journal: Journal of Computational Physics - Volume 247, 15 August 2013, Pages 168–191