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

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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.