The Navier–Stokes equations are the fundamental equations governing fluid motions. Due to the excellent properties of memory and heredity of the time fractional derivative involved in the equations, the time fractional Navier–Stokes equations (TFNSE) have been applied to describe various phenomena including turbulence, non-uniform flows and viscoelasticity. In this paper, we develop a new method combining the finite difference method (FDM) with Kansa’s meshfree approach to solve the TFNSE with initial and boundary conditions. The proposed method not only avoids the procedure of mesh generation, but also can effectively solve problem on complex domain. Finally, several numerical examples are given to validate the feasibility of the proposed method.

中文翻译：

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时间分数阶纳维-斯托克斯方程的无网格方法


纳维-斯托克斯方程是控制流体运动的基本方程。由于方程中涉及的时间分数阶导数具有良好的记忆性和遗传性，时间分数纳维-斯托克斯方程（TFNSE）已被应用于描述湍流、非均匀流和粘弹性等各种现象。在本文中，我们开发了一种将有限差分法 (FDM) 与 Kansa 无网格方法相结合的新方法，用于求解具有初始和边界条件的 TFNSE。该方法不仅避免了网格生成的过程，而且可以有效解决复杂领域的问题。最后，给出了几个数值例子来验证所提方法的可行性。