کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4967574 1449379 2017 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A finite difference method for a conservative Allen-Cahn equation on non-flat surfaces
ترجمه فارسی عنوان
یک روش متمایز محدود برای معادله آلن کوه محافظه کار در سطوح غیرتقاضی
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
چکیده انگلیسی
We present an efficient numerical scheme for the conservative Allen-Cahn (CAC) equation on various surfaces embedded in a narrow band domain in the three-dimensional space. We apply a quasi-Neumann boundary condition on the narrow band domain boundary using the closest point method. This boundary treatment allows us to use the standard Cartesian Laplacian operator instead of the Laplace-Beltrami operator. We apply a hybrid operator splitting method for solving the CAC equation. First, we use an explicit Euler method to solve the diffusion term. Second, we solve the nonlinear term by using a closed-form solution. Third, we apply a space-time-dependent Lagrange multiplier to conserve the total quantity. The overall scheme is explicit in time and does not need iterative steps; therefore, it is fast. A series of numerical experiments demonstrate the accuracy and efficiency of the proposed hybrid scheme.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 334, 1 April 2017, Pages 170-181
نویسندگان
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