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动力学（SPH）由于其无网格特性，非常适合于各种工程相关的固体场景的数值研究。无网格SPH方法的优点是，除其他事项外，在结构经历极端变形，拓扑结构的显着变化，局部材料失效和/或许多接触的情况下。为了使使用SPH方法的实体模拟更有效，在过去的几年里，人们对一种称为自适应SPH的扩展变体进行了大量的研究。自适应SPH方法通过在运行时分别分裂合并粒子来实现模型某些部分的离散化的动态自适应。为了使这种先进的技术进入工程实践，需要适当的标准，局部决定是否要调整空间离散。到目前为止，只有基本的适应性标准，例如，基于位置的应用。他们需要考虑系统的后期动态是已知的用户已经提前的模拟，什么强烈矛盾的愿景预测SPH simulation.The建议的研究项目的目的是增加自适应SPH技术的适用性，通过开发和面向应用的验证新的自适应标准，是直接基于承诺的空间离散误差。申请人对这一问题的初步调查产生了非常有希望的结果。申请人深入研究了自适应SPH的主题，作为其论文的一部分，因此，存在全面的背景知识以及计划研究活动的重要起点。此外，两个基本的概念，解决基于错误的自适应SPH已经开发出来。它们表明了这类自适应标准的巨大潜力，但受到其适用性的限制。作为拟议的研究金的一部分，现有的方法将被采取和详细分析。在此基础上，将开发SPH的上级基于误差的自适应准则，并证明其适用性。马萨诸塞州理工学院的土木与环境工程系为预期的调查提供了一个理想的环境，因为多年来一直在那里进行关于使用SPH的固体模拟以及自适应SPH方法的高度先进的研究。计划中的研究项目的实现不仅对申请人的预期兴趣非常重要，而且对他未来的学术生涯也非常重要。

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.