关于不可压缩纳维-斯托克斯方程的无网格GFDM求解器
On Meshfree GFDM Solvers for the Incompressible Navier-Stokes Equations
AI总结：
本文研究了传统无网格GFDM方案在求解拉格朗日不可压缩纳维-斯托克斯方程时的不足，提出改进方案以提高速度散度条件的逼近精度，并通过数值比较验证了其优越性。
摘要：
对于不可压缩纳维-斯托克斯方程的无网格求解方案，通常基于有限体积方法中常用的算法，如投影法、SIMPLE和PISO算法。然而，这些算法在无网格方法中特有的缺点往往被忽视。本文研究了传统无网格广义有限差分法（GFDM）方案在求解拉格朗日不可压缩纳维-斯托克斯方程时的不足，包括操作分裂方案和整体方案。大多数这些方案的主要缺点是对质量守恒条件的局部近似不准确。进一步，我们提出了一种新的改进方案，克服了这些问题并显示出对速度散度条件更好的逼近。我们随后进行了数值比较，证明了新的整体方案比现有方案更准确。
英文摘要：
Meshfree solution schemes for the incompressible Navier--Stokes equations are usually based on algorithms commonly used in finite volume methods, such as projection methods, SIMPLE and PISO algorithms. However, drawbacks of these algorithms that are specific to meshfree methods have often been overlooked. In this paper, we study the drawbacks of conventionally used meshfree Generalized Finite Difference Method~(GFDM) schemes for Lagrangian incompressible Navier-Stokes equations, both operator splitting schemes and monolithic schemes. The major drawback of most of these schemes is inaccurate local approximations to the mass conservation condition. Further, we propose a new modification of a commonly used monolithic scheme that overcomes these problems and shows a better approximation for the velocity divergence condition. We then perform a numerical comparison which shows the new monolithic scheme to be more accurate than existing schemes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
