Development and Validation of Novel, Discretization-Error-Based Adaptivity Criteria for Smoothed Particle Hydrodynamics

基于粒子的空间离散技术光滑粒子流体力学(SPH)由于其无网格的特性，非常适合于各种与工程相关的固体场景的数值研究。在结构经历极端变形、拓扑结构显著变化、局部材料破坏和/或许多接触的情况下，无网格SPH方法具有明显的优势。为了使使用SPH方法的实体模拟更有效，在过去的几年中，人们对一种被称为自适应SPH的扩展变体进行了大量的研究工作。自适应SPH方法通过在运行时分别拆分合并的粒子来实现对模型的某些部分的离散化的动态适应。为了将这种先进的技术应用到工程实践中，需要适当的标准来确定是否要调整空间离散化。到目前为止，只使用基本的适应性标准，例如基于位置的标准。他们要求用户在模拟之前就知道被考虑系统的后期动态，这与预测性SPH模拟的愿景强烈冲突。提出的研究项目的目的是通过开发和面向应用的验证直接基于承诺的空间离散化误差的新的适应性准则来增加自适应SPH技术的适用性。首先，申请人就这一问题进行的调查产生了非常有希望的结果。作为论文的一部分，申请者深入研究了适应性SPH的主题，因此，对于计划中的研究活动，有全面的背景知识和重要的起点。此外，已经开发了两个基本概念来解决SPH的基于误差的自适应性。它们表明了这类适应性标准的巨大潜力，但在适用性方面受到限制。作为拟议的研究金的一部分，将采用和详细分析现有的办法。在此基础上，将为SPH制定更好的基于误差的适应性标准，并将证明它们的适用性。麻省理工学院土木工程与环境工程系为计划中的调查提供了理想的环境，因为在使用SPH进行实体模拟以及特别是自适应SPH方法的主题上已经进行了多年的高级研究。计划中的研究项目的实现不仅对申请者的预期适应能力非常重要，而且对他未来的学术生涯也是非常重要的。

Due to its meshfree character, the particle-based spatial discretization technique Smoothed Particle Hydrodynamics (SPH) is well-suited for the numerical investigation of a variety of engineering-relevant solid scenarios. Advantages with the meshless SPH method are seen, among other things, in the case of structures experiencing extreme deformations, significant changes in topology, local material failure and/or many contacts. To make solid simulations using the SPH method more efficient, a great research effort towards an extended variant that is known as adaptive SPH has been spent over the last few years. The adaptive SPH method enables a dynamic adaptation of the discretization of certain parts of a model by splitting respectively merging particles at runtime. In order that this advanced technique find its way into the engineering practice, adequate criteria that locally decide if the spatial discretization is to be adjusted are needed. Up to now, solely elementary adaptivity criteria, e.g., position-based ones, are employed. They require that the later dynamics of the considered system is known to the user already in advance of the simulation, what strongly contradicts the vision of predictive SPH simulations.The aim of the proposed research project is to increase the applicability of the adaptive SPH technique through the development and application-oriented validation of novel adaptivity criteria that are directly based on the committed spatial discretization error. First investigations by the applicant concerning this matter led to highly promising results. The applicant intensively worked on the topic of adaptive SPH as part of his dissertation, and, hence, comprehensive background knowledge as well as important starting points for the planned research activities exist. Furthermore, two fundamental concepts addressing error-based adaptivity for SPH have already been developed. They indicate the enormous potential of this class of adaptivity criteria but are subjected to limitations regarding their applicability. As part of the proposed research fellowship, the existing approaches are to be taken up and analyzed in detail. Based on this, superior error-based adaptivity criteria for SPH will be developed and their suitability will be proven. The Department of Civil and Environmental Engineering at the Massachusetts Institute of Technology offers an ideal environment for the intended investigations since highly advanced research on the topic of both solid simulation using SPH in general as well as the adaptive SPH method in particular has been conducted there for years. The realization of the planned research project will not only be of high importance to the intended habilitation of the applicant but also his future career in academics.