Generation of unstructured grids and Euler solutions for complex geometries

Algorithms are described for the generation and adaptation of unstructured grids in two and three dimensions, as well as Euler solvers for unstructured grids. The main purpose is to demonstrate how unstructured grids may be employed advantageously for the economic simulation of both geometrically as well as physically complex flow fields

Adaptive anisotropic mesh technique for coupled problems: application to welding simulation

International audienceA major problem arising in finite element analysis of coupled problems, such as welding for instance, is the control of the mesh, that is an appropriate mastering of the spatial discretization to get accurate results in a minimum computer time. The present anisotropic adaptation procedure is controlled by a directional error estimator based on local interpolation error and recovery of the second derivatives of different fields involved in the finite element calculation. Error indicators are derived to define an anisotropic mesh metric field, which is an input of the pre existing 3D remeshing procedure. The mesh metric consists of a combination of several metrics, each corresponding to the error estimation associated with a selected field of the solution produced (temperature, phase fraction, stress component). Mesh modifications are used to anisotropically and continuously adapt the mesh. We demonstrate the efficiency of the method by applying it to a coupled thermal-mechanical-metallurgical simulation of arc welding. We demonstrate that the use of an anisotropic adaptive finite element method can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with isotropic meshes

VoroCrust: Voronoi Meshing Without Clipping

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of domains exhibiting arbitrarily curved boundaries and sharp features. In addition, the power of primal-dual mesh pairs, exemplified by Voronoi-Delaunay meshes, has been recognized as an important ingredient in numerous formulations. The VoroCrust algorithm is the first provably-correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume elements. A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks. The algorithm has the flexibility of filling the interior by either structured or random samples, while preserving all sharp features in the output mesh. We demonstrate the capabilities of the algorithm on a variety of models and compare against state-of-the-art polyhedral meshing methods based on clipped Voronoi cells establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf. Supplemental materials available on https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd

Combination of an adaptive remeshing technique with a coupled FEM–DEM approach for analysis of crack propagation problems

The final publication is available at Springer via http://dx.doi.org/10.1007/s40571-019-00306-4This paper presents an enhanced coupled approach between the finite element method (FEM) and the discrete element method (DEM) in which an adaptive remeshing technique has been implemented. The remeshing technique is based on the computation of the Hessian of a selected nodal variable, i.e. the mesh is refined where the curvature of the variable field is greater. Once the Hessian is known, a metric tensor is defined node-wise that serves as input data for the remesher (MmgTools) that creates a new mesh. After remeshing, the mapping of the internal variables and the nodal values is performed and a regeneration of the discrete elements on the crack faces of the new mesh is carried out. Several examples of fracturing problems using the enhanced FEM–DEM formulation are presented. Accurate results in comparison with analytical and experimental solutions are obtained.This work has been supported by the Spanish Government program FPU: FPU16/02697. The authors gratefully acknowledge the received support.Peer ReviewedPostprint (author's final draft

A contribution to the finite element analysis of high-speed compressible flows and aerodynamics shape optimization

This work covers a contribution to two most interesting research elds in aerodynamics, the fi nite element analysis of high-speed compressible flows (Part I) and aerodynamic shape optimization (Part II). The fi rst part of this study aims at the development of a new stabilization formulation based on the Finite Increment Calculus (FIC) scheme for the Euler and Navier-Stokes equations in the context of the Galerkin nite element method (FEM). The FIC method is based on expressing the balance of fluxes in a spacetime domain of nite size. It is tried to prevent the creation of instabilities normally presented in the numerical solutions due to the high convective term and sharp gradients. In order to overcome the typical instabilities happening in the numerical solution of the high-speed compressible flows, two stabilization terms, called streamline term and transverse term, are added through the FIC formulation in space-time domain to the original conservative equations of mass, momentum and energy. Generally, the streamline term holding the direction of the velocity is responsible for stabilizing the spurious solutions produced from the convective term while the transverse term smooths the solution in the high gradient zones. An explicit fourth order Runge-Kutta scheme is implemented to advance the solution in time. In order to investigate the capability of the proposed formulation, some numerical test examples corresponding to subsonic, transonic and supersonic regimes for inviscid and viscous flows are presented. The behavior of the proposed stabilization technique in providing appropriate solutions has been studied especially near the zones where the solution has some complexities such as shock waves, boundary layer, stagnation point, etc. Although the derived methodology delivers precise results with a nearly coarse mesh, the mesh refinement technique is coupled in the solution to create a suitable mesh particularly in the high gradient zones. The comparison of the numerical results obtained from the FIC formulation with the reference ones demonstrates the robustness of the proposed method for stabilization of the Euler and Navier-Stokes equations. It is observed that the usual oscillations occur in the Galerkin FEM, especially near the high gradient zones, are cured by implementing the proposed stabilization terms. Furthermore, allowing the adaptation framework to modify the mesh, the quality of the results improves signi cantly. The second part of this thesis proposes a procedure for aerodynamic shape optimization combining Genetic Algorithm (GA) and mesh re nement technique. In particular, it is investigated the e ect of mesh re nement on the computational cost and solution accuracy during the process of aerodynamic shape optimization. Therefore, an adaptive remeshing technique is joined to the CFD solver for the analysis of each design candidate to guarantee the production of more realistic solutions during the optimum design process in the presence of shock waves. In this study, some practical transonic airfoil design problems using adap- tive mesh techniques coupled to Multi-Objective Genetic Algorithms (MOGAs) and Euler flow analyzer are addressed. The methodology is implemented to solve three practical design problems; the fi rst test case considers a reconstruction design optimization that minimizes the pressure error between a prede ned pressure curve and candidate pressure distribution. The second test considers the total drag minimization by designing airfoil shape operating at transonic speeds. For the final test case, a multi-objective design optimization is conducted to maximize both the lift to drag ratio (L/D) and lift coe cient (Cl). The solutions obtained with and without adaptive mesh re nement are compared in terms of solution accuracy and computational cost. These design problems under transonic speeds need to be solved with a ne mesh, particularly near the object, to capture the shock waves that will cost high computational time and require solution accuracy. By comparison of the the numerical results obtained with both optimization problems, the obtainment of direct bene ts in the reduction of the total computational cost through a better convergence to the final solution is evaluated. Indeed, the improvement of the solution quality when an adaptive remeshing technique is coupled with the optimum design strategy can be judged.El presente trabajo pretende contribuir a dos de los campos de investigaci on m as interesantes en la aerodin amica, el an alisis num erico de flujos compresibles a alta velocidad (Parte I) y la optimizaci on de la forma aerodin amica (Parte II). La primera parte de este estudio se centra en la soluci on num erica de las ecuaciones de Navier-Stokes, que modelan el comportamiento de flujos compresibles a alta velocidad. La discretizaci on espacial se lleva a cabo mediante el m etodo de elementos nitos (FEM) y se pone especial enfasis en el desarrollo de una nueva formulaci on estabilizada basada en la t ecnica de c alculo de Incremento fi nitos (FIC). En este ultima, los t erminos de estabilizaci on convectiva se obtienen de manera natural de las ecuaciones de gobierno a trav es de postulados de conservaci on y equilibrio de flujos en un dominio espacio-tiempo de tamaño nito. Ello lleva a la obtenci on de dos t erminos de estabilizaci on que funcionan de manera complementaria. Uno act ua en direcci on de las lineas de corriente proporcionando la estabilizaci on necesaria para contrarestrar las inestabilidades propias de la forma discreta de Galerkin y el otro t ermino, de tipo shock capturing, act ua de manera transversal a las l neas de corriente y permite mejorar la soluci on num erica alrededor de discontinuidades y otro tipos de fen omenos localizados en el campo de soluci on de problema. La forma discreta de las ecuaciones de gobierno se completa mediante un esquema de integraci on temporal expl icito de tipo de Runge-Kutta de 4to orden. El esquema de soluci on b asico propuesto se complementa con una t ecnica de re namiento adaptativo de malla que permite mejorar autom aticamente la soluci on num erica en zonas localizadas del dominio en que, dadas las caracter sticas del flujo, se necesita una mayor resoluci on espacial. Con el prop osito de investigar el comportamiento de la formulaci on num erica se estudian diferentes casos de an alisis que implican flujos viscosos y no viscosos en r egimen subs onico, trans onico y supers onico y se estudia con especial detalle el funcionamiento de la t ecnica de estabilizaci on propuesta. Los resultados obtenidos demuestran una exactitud satisfactoria y una buena correlaci on con resultados presentes en la literatura, incluso cuando se trabaja con discretizaciones espaciales relativamente gruesas. Adicionalmente, los estudios num ericos realizados demuestran que el empleo del esquema adaptativo de malla es e ficaz para incrementar la exactitud de la soluci on numerica manteniendo un bajo coste computacional. En la segunda parte de este estudio se propone un m etodo para la optimizaci on de formas aerodin amicas que combina algoritmos gen eticos multiobjetivo (MOGAs) y remallado adaptativo con el objetivo de asegurar, con un coste computacional m nimo, la calidad de la soluci on numerica empleada en el proceso de b usqueda de un determinado diseño objetivo, particularmente cuando el flujo presenta discontinuidades y gradientes muy localizados, ti picos de flujos a alta velocidad. La metodolog a se aplica a resolver tres problemas pr acticos de diseño de per les aerodin amicos en flujo trans onico que implican la optimizaci on de la distribuci on de presiones, minimizaci on de la resistencia de onda y maximizaci on conjunta de la sustentaci on y la relaci on sustentaci on/resistencia. Para cada uno de ellos se estudia el efecto del re namiento en la calidad de la soluci on num erica as como tambi en en el coste computacional y la convergencia del problema. Los estudios realizados demuestran la e cacia de la metodolog a propuesta