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首页> 外文期刊>Journal of Computational Physics >Random Walks with negative particles for discontinuous diffusion and porosity
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Random Walks with negative particles for discontinuous diffusion and porosity

机译：随机与负粒子一起走，以便不连续扩散和孔隙率

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This study develops a new Lagrangian particle method for modeling flow and transport phenomena in complex porous media with discontinuities. For instance, diffusion processes can be modeled by Lagrangian Random Walk algorithms. However, discontinuities and heterogeneities are difficult to treat, particularly discontinuous diffusion D (x) or porosity theta (x). In the literature on particle Random Walks, previous methods used to handle this discontinuity problem can be characterized into two main classes as follows: "Interpolation techniques", and "Partial reflection methods". One of the main drawbacks of these methods is the small time step required in order to converge to the expected solution, particularly in the presence of many interfaces. These restrictions on the time step, lead to inefficient algorithms. The Random Walk Particle Tracking (RWPT) algorithm proposed here is, like others in the literature, discrete in time and continuous in space (gridless). We propose a novel approach to partial reflection schemes without restrictions on time step size. The new RWPT algorithm is based on an adaptive "Stop&Go" time-stepping, combined with partial reflection/refraction schemes, and extended with a new concept of negative mass particles. To test the new RWPT scheme, we develop analytical and semi-analytical solutions for diffusion in the presence of multiple interfaces (discontinuous multi-layered medium). The results show that the proposed Stop&Go RWPT scheme (with adaptive negative mass particles) fits extremely well the semi-analytical solutions, even for very high contrasts and in the neighborhood of interfaces. The scheme provides a correct diffusive solution in only a few macro-time steps, with a precision that does not depend on their size. (C) 2019 Elsevier Inc. All rights reserved.
机译：本研究发展了一种新的拉格朗日粒子方法，用于模拟具有不连续性的复杂多孔介质中的流动和输运现象。例如，扩散过程可以用拉格朗日随机游动算法建模。然而，不连续性和不均匀性很难处理，尤其是不连续扩散D（x）或孔隙度θ（x）。在关于粒子随机游动的文献中，以前用来处理这种不连续性问题的方法可以分为两大类：“插值技术”和“部分反射方法”。这些方法的主要缺点之一是收敛到预期解所需的时间步长很小，尤其是在存在许多接口的情况下。这些对时间步长的限制，导致算法效率低下。本文提出的随机行走粒子跟踪（RWPT）算法与文献中的其他算法一样，在时间上是离散的，在空间上是连续的（无网格）。我们提出了一种不受时间步长限制的部分反射方案的新方法。新的RWPT算法基于一种自适应的“停-走”时间步进，结合部分反射/折射方案，并扩展为负质量粒子的新概念。为了测试新的RWPT格式，我们开发了多界面（不连续多层介质）中扩散的解析和半解析解。结果表明，所提出的Stop&Go RWPT方案（带有自适应负质量粒子）非常适合半解析解，即使是在非常高的对比度和界面附近。该方案仅在几个宏观时间步内提供了正确的扩散解，其精度不取决于其大小。（C） 2019爱思唯尔公司版权所有。

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