SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Parallel mesh adaptive techniques for complex flow simulation

Dynamic mesh adaptation on unstructured grids, by localised refinement and derefinement, is a very efficient tool for enhancing solution accuracy and optimise computational time. One of the major drawbacks however resides in the projection of the new nodes created, during the refinement process, onto the boundary surfaces. This can be addressed by the introduction of a library capable of handling geometric properties given by a CAD (Computer Aided Design) description. This is of particular interest also to enhance the adaptation module when the mesh is being smoothed, and hence moved, to then re-project it onto the surface of the exact geometry. However, the above procedure is not always possibly due to either faulty or too complex designs, which require a higher level of complexity in the CAD library. It is therefore paramount to have a built-in algorithm able to place the new nodes, belonging to the boundary, closer to the geometric definition of it. Such a procedure is proposed in this work, based on the idea of interpolating subdivision. In order to efficiently and effectively adapt a mesh to a solution field, the criteria used for the adaptation process needs to be as accurate as possible. Due to the nature of the solution, which is obtained by discretisation of a continuum model, numerical error is intrinsic in the calculation. A posteriori error estimation allows us to somewhat assess the accuracy by using the computed solution itself. In particular, an a posteriori error estimator based on the Zienkievicz Zhu model is introduced. This can be used in the adaptation procedure to refine the mesh in those areas where the local error exceeds a set tolerance, hence further increasing the accuracy of the solution in those regions during the next computational step. Variants of this error estimator have also been studied and implemented. One of the important aspects of this project is the fact that the algorithmic concepts are developed thinking parallel, i.e. the algorithms take into account the possibility of multiprocessor implementation. Indeed these concepts require complex programming if one tries to parallelise them, once they have been devised serially. Another important and innovative aspect of this work is the consistency of the algorithms with parallel processor execution

Methods for Solving Discontinuous-Galerkin Finite Element Equations with Application to Neutron Transport

Cette thèse traite des méthodes d’éléments finis Galerkin discontinus d’ordre élevé pour la résolution d’équations aux dérivées partielles, avec un intérêt particulier pour l’équation de transport des neutrons. Nous nous intéressons tout d’abord à une méthode de pré-traitement de matrices creuses par blocs, qu’on retrouve dans les méthodes Galerkin discontinues, avant factorisation par un solveur multifrontal. Des expériences numériques conduites sur de grandes matrices bi- et tri-dimensionnelles montrent que cette méthode de pré-traitement permet une réduction significative du ’fill-in’, par rapport aux méthodes n’exploitant pas la structure par blocs. Ensuite, nous proposons une méthode d’éléments finis Galerkin discontinus, employant des éléments d’ordre élevé en espace comme en angle, pour résoudre l’équation de transport des neutrons. Nous considérons des solveurs parallèles basés sur les sous-espaces de Krylov à la fois pour des problèmes ’source’ et des problèmes aux valeur propre multiplicatif. Dans cet algorithme, l’erreur est décomposée par projection(s) afin d’équilibrer les contraintes numériques entre les parties spatiales et angulaires du domaine de calcul. Enfin, un algorithme HP-adaptatif est présenté ; les résultats obtenus démontrent une nette supériorité par rapport aux algorithmes h-adaptatifs, à la fois en terme de réduction de coût de calcul et d’amélioration de la précision. Les valeurs propres et effectivités sont présentées pour un panel de cas test industriels. Une estimation précise de l’erreur (avec effectivité de 1) est atteinte pour un ensemble de problèmes aux domaines inhomogènes et de formes irrégulières ainsi que des groupes d’énergie multiples. Nous montrons numériquement que l’algorithme HP-adaptatif atteint une convergence exponentielle par rapport au nombre de degrés de liberté de l’espace éléments finis. ABSTRACT : We consider high order discontinuous-Galerkin finite element methods for partial differential equations, with a focus on the neutron transport equation. We begin by examining a method for preprocessing block-sparse matrices, of the type that arise from discontinuous-Galerkin methods, prior to factorisation by a multifrontal solver. Numerical experiments on large two and three dimensional matrices show that this pre-processing method achieves a significant reduction in fill-in, when compared to methods that fail to exploit block structures. A discontinuous-Galerkin finite element method for the neutron transport equation is derived that employs high order finite elements in both space and angle. Parallel Krylov subspace based solvers are considered for both source problems and $k_{eff}$-eigenvalue problems. An a-posteriori error estimator is derived and implemented as part of an h-adaptive mesh refinement algorithm for neutron transport $k_{eff}$-eigenvalue problems. This algorithm employs a projection-based error splitting in order to balance the computational requirements between the spatial and angular parts of the computational domain. An hp-adaptive algorithm is presented and results are collected that demonstrate greatly improved efficiency compared to the h-adaptive algorithm, both in terms of reduced computational expense and enhanced accuracy. Computed eigenvalues and effectivities are presented for a variety of challenging industrial benchmarks. Accurate error estimation (with effectivities of 1) is demonstrated for a collection of problems with inhomogeneous, irregularly shaped spatial domains as well as multiple energy groups. Numerical results are presented showing that the hp-refinement algorithm can achieve exponential convergence with respect to the number of degrees of freedom in the finite element spac

CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences

This report documents the results of a study to address the long range, strategic planning required by NASA's Revolutionary Computational Aerosciences (RCA) program in the area of computational fluid dynamics (CFD), including future software and hardware requirements for High Performance Computing (HPC). Specifically, the "Vision 2030" CFD study is to provide a knowledge-based forecast of the future computational capabilities required for turbulent, transitional, and reacting flow simulations across a broad Mach number regime, and to lay the foundation for the development of a future framework and/or environment where physics-based, accurate predictions of complex turbulent flows, including flow separation, can be accomplished routinely and efficiently in cooperation with other physics-based simulations to enable multi-physics analysis and design. Specific technical requirements from the aerospace industrial and scientific communities were obtained to determine critical capability gaps, anticipated technical challenges, and impediments to achieving the target CFD capability in 2030. A preliminary development plan and roadmap were created to help focus investments in technology development to help achieve the CFD vision in 2030