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Material point method applied to multiphase flows

机译：物质点法应用于多相流

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The particle-in-cell method (PIC), especially the latest version of it, the material point method (MPM), has shown significant advantage over the pure Lagrangian method or the pure Eulerian method in numerical Simulations of problems involving large deformations. It avoids the mesh distortion and tangling issues associated with Lagrangian methods and the advection errors associated with Eulerian methods. Its application to multiphase flows or multi-material deformations, however, encounters a numerical difficulty of satisfying continuity requirement due to the inconsistence of the interpolation schemes used for different phases. It is shown in Section 3 that current methods of enforcing this requirement either leads to erroneous results or can Cause significant accumulation of errors. In the present paper, a different numerical method is introduced to ensure that the continuity requirement is satisfied with an error consistent with the discretization error and will not grow beyond that during the time advancement in the calculation. This method is independent of physical models. Its numerical implementation is quite similar to the common method used in Eulerian calculations of multiphase flows. Examples calculated using this method are presented. (C) 2007 Elsevier Inc. All rights reserved.
机译：在涉及大变形的问题的数值模拟中，单元格粒子方法（PIC），尤其是其最新版本的材料点方法（MPM）在纯拉格朗日方法或纯欧拉方法上显示出显着优势。它避免了与拉格朗日方法有关的网格变形和缠结问题以及与欧拉方法有关的对流误差。然而，由于用于不同相的插值方案的不一致性，其在多相流或多材料变形中的应用遇到了满足连续性要求的数值困难。在第3节中显示，当前执行此要求的方法会导致错误的结果，或者会导致大量的错误累积。在本文中，引入了一种不同的数值方法，以确保连续性要求满足与离散化误差一致的误差，并且不会随着计算时间的增长而增长。此方法与物理模型无关。其数值实现与在多相流欧拉计算中使用的通用方法非常相似。给出了使用此方法计算的示例。 （C）2007 Elsevier Inc.保留所有权利。

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