Modeling Fluid and Granular Flow using Mesh-free Particle Method

自然流动动力学和制度的有效预测需要对计算流体概念的深入理解。对于简单的瞬变流态，通常采用单相模型来描述复杂的流动现象。大多数自然灾害属于物质相态的混合。为了解决建模框架内流体流动的复杂性，固定空间网格的经典应用，其中在固定位置的物理特性被认为是在模型域中。虽然使用固定网格方法的应用在历史上已经成功地表示流体流动，最近的研究已经突出了一些基于网格的建模方法的缺点。这些基于网格的方法的缺点包括由于复杂的流动边界、界面、自由表面而导致的不准确性，以及其在质量守恒方面的困难。 无网格方法的发展和应用使得复杂流态的精确表示和流体流动问题的数值求解成为可能。移动粒子半隐式（MPS）方法是一种重要的无网格方法。MPS方法使用一组任意分布的粒子，而不是固定的网格布局来求解不同边界和界面的控制方程。每个粒子都有一组场变量，如质量、浓度和动量。尽管对建模工作进行了重大改进，但当需要许多粒子时，流体不可压缩性仍然是原始MPS方法中最耗时的部分。 本研究的重点是改进MPS浅水模式，并发展一个二维MPS与一维浅水方程相结合的混合模式。混合MPS将减少准确表示真实的世界工程应用的计算时间。新开发的模型还将扩展到研究非静水压力下的流动、多孔介质中的流动和复杂颗粒流场景。这些调查的积极成果可用于确定自然灾害的风险。这些模拟结果可以作为工具，以确定潜在的破坏工程基础设施的滑坡，泥石流，雪崩，火山碎屑流，并在建筑和制造业。该计划的第二部分是使用准静态的颗粒材料与MPS模型框架中的流变模型的集成，在开发一个多相模型，更复杂的工程情况。在工程应用和案例研究中，将精度和稳定性的提高纳入MPS模型。该计划的结果将突出MPS方法的各种应用，使其不仅是一种数值方法，而且是一种有用的方法，是补充物理模型。

Effective predictions of natural flow dynamics and regimes require an in-depth understanding of computational fluid concepts. To simply transient flow regimes, single phase modeling is often applied to represent the complex flow phenomena. The majority of the natural hazards belong to the mixture of the phases of matter. To address the complexities of fluid flow within the modeling framework, the classical application of fixed spatial grids where the physical properties at fixed locations are considered in the model domain. Although the application of using fixed mesh approach has been historically successful in representing fluid flow, recent studies have highlighted some of the shortcomings with grid-based modeling methods. The drawbacks of these grid-based approaches include inaccuracies due to complex flow boundaries, interfaces, free surfaces, and its difficulty in mass conservation.     The development and application of mesh-free methods has allowed for accurate representation of complex flow regimes and in solving fluid flow problems numerically. One prominent and promising mesh-free method is the Moving Particle Semi-implicit (MPS) method. The MPS method uses a set of arbitrarily distributed particles as opposed to a fixed mesh grid layout to solve governing equations for diverse boundaries and interfaces. Each particle possesses a set of field variables such as mass, concentration and momentum. Although significant improvements have been made to the modeling efforts, fluid incompressibility remains the most time-consuming part of the original MPS approach when many particles are required.     The initial focus of the research is improvement of MPS shallow water model and development of a hybrid model using 2D MPS with incorporation of a 1D shallow water equation. The hybrid MPS will reduce computation time in accurately representing real world engineering applications. The newly developed model will also be expanded to study flow with non-hydrostatic pressure, flow in porous media and in complex granular flow scenarios. The positive outcomes of these investigations can be used to identify the risks from natural disasters. These simulated outcomes can be used as tools to identify potential damage to engineering infrastructure from landslides, debris flow, avalanches, and pyroclastic flows, and in construction and manufacturing industries. The second part of the program is to use quasi-static state of granular materials with the integration of rheology model in the MPS model framework in developing a multiphase model for more complicate engineering cases. Accuracy and stability improvement will be incorporated into the MPS model in engineering application and case studies. The outcome of the program will highlight the varied applications of the MPS method such that it is not only a numerical method but also a useful approach that is complimentary to physical models.