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A novel method for modeling Neumann and Robin boundary conditions in smoothed particle hydrodynamics

机译:平滑粒子流体动力学中Neumann和Robin边界条件建模的新方法

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摘要

We present a novel smoothed particle hydrodynamics (SPH) method for diffusion equations subject to Neumann and Robin boundary conditions. The Neumann and Robin boundary conditions are common to many physical problems (such as heat/mass transfer), and can prove challenging to implement in numerical methods when the boundary geometry is complex. The new method presented here is based on the approximation of the sharp boundary with a diffuse interface and allows an efficient implementation of the Neumann and Robin boundary conditions in the SPH method. The paper discusses the details of the method and the criteria for the width of the diffuse interface. The method is used to simulate diffusion and reactions in a domain bounded by two concentric circles and reactive flow between two parallel plates and its accuracy is demonstrated through comparison with analytical and finite difference solutions. To further illustrate the capabilities of the model, a reactive flow in a porous medium was simulated and good convergence properties of the model are demonstrated.
机译:我们为受Neumann和Robin边界条件约束的扩散方程式提出了一种新颖的平滑粒子流体动力学(SPH)方法。诺伊曼和罗宾边界条件是许多物理问题(例如热/质量传递)所共有的,并且当边界几何形状复杂时,在数值方法中实现具有挑战性。此处介绍的新方法基于具有扩散界面的尖锐边界的逼近,并允许在SPH方法中有效地实现Neumann和Robin边界条件。本文讨论了该方法的详细信息以及漫反射界面宽度的标准。该方法用于模拟由两个同心圆界定的区域中的扩散和反应以及两个平行板之间的反应流,并通过与解析解和有限差分法进行比较证明了其准确性。为了进一步说明该模型的功能,模拟了多孔介质中的反应流,并证明了该模型的良好收敛性。

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