Numerical simulation of the quality of vision around a telescope

Els telescopis astronòmics recullen els raigs de llum procedents dels objectes celests i els transformen en imatges el més nítides possible. No obstant, al travessar l’atmosfera, aquests raigs de llum pateixen tot un seguit de processos que empitjoren la qualitat de la imatge obtinguda. Un dels processos més rellevants és la distorsió del front d’ona. La distorsió del front d’ona pot ésser mesurada i compensada amb els sistemes d’òptica adaptativa que s’incorporen a les instal·lacions dels telescopis. Tant per al dimensionament d’aquests sistemes com per a l’elecció de la ubicació de les instal·lacions o per al disseny de la forma exterior del telescopi és convenient estimar el valor absolut de la distorsió del front d’ona. Els paràmetres que permeten quantificar la distorsió del front d’ona (i la qualitat de la visió) són la distribució del coeficient d’estructura de l’índex de refracció de l’aire (Cn 2), el paràmetre de Fried (r0) i la freqüència de Greenwood (fG). El camp del coeficient d’estructura de l’índex de refracció (Cn 2) es pot estimar a partir dels valors mitjans dels camps de velocitat de l’aire i la seva pressió i temperatura, i de la difusivitat turbulenta, que depèn del grau de turbulència del flux d’aire. Pel que fa al paràmetre de Fried (r0) i la freqüència de Greenwood (fG) es poden obtenir d’integrar el camp del coeficient d’estructura de l’índex de refracció (Cn 2) al llarg d’un raig de llum, i presenten també dependència de la longitud d’ona del raig de llum incident

Variational Multiscale error estimators for solid mechanics adaptive simulations: an Orthogonal Subgrid Scale approach

In this work we present a general error estimator for the finite element solution of solid mechanics problems based on the Variational Multiscale method. The main idea is to consider a rich model for the subgrid scales as an error estimator. The subscales are considered to belong to a space orthogonal to the finite element space (Orthogonal Subgrid Scales) and we take into account their contribution both in the element interiors and on the element boundaries (Subscales on the Element Boundaries). A simple analysis shows that the upper bound for the obtained error estimator is sharper than in other error estimators based on the Variational Multiscale Method. Numerical examples show that the proposed error estimator is an accurate approximation for the energy norm error and can be used both in simple linear constitutive models and in more complex non-linear cases.Peer ReviewedPostprint (author's final draft

Variational Multiscale error estimators for solid mechanics adaptive simulations: an Orthogonal Subgrid Scale approach

In this work we present a general error estimator for the finite element solution of solid mechanics problems based on the Variational Multiscale method. The main idea is to consider a rich model for the subgrid scales as an error estimator. The subscales are considered to belong to a space orthogonal to the finite element space (Orthogonal Subgrid Scales) and we take into account their contribution both in the element interiors and on the element boundaries (Subscales on the Element Boundaries). A simple analysis shows that the upper bound for the obtained error estimator is sharper than in other error estimators based on the Variational Multiscale Method. Numerical examples show that the proposed error estimator is an accurate approximation for the energy norm error and can be used both in simple linear constitutive models and in more complex non-linear cases.Peer ReviewedPostprint (author's final draft

An adaptive fixed-mesh ALE method for free surface flows

In this work we present a Fixed-Mesh ALE method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain. This mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required. Some of the main ingredients of the formulation are the use of an Arbitrary-Lagrangian–Eulerian formulation for computing temporal derivatives, the use of stabilization terms for stabilizing convection, stabilizing the lack of compatibility between velocity and pressure interpolation spaces, and stabilizing the ill-conditioning introduced by the cuts on the background finite element mesh, and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments. Algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved. The method is tested in several numerical examples. The expected convergence rates both in space and time are observed. Smooth solution fields for both velocity and pressure are obtained (as a result of the contribution of the stabilization terms). Finally, a good agreement between the numerical results and the reference experimental data is obtained.Postprint (published version

Interpolation with restrictions between finite element meshes for flow problems in an ALE setting

This is the peer reviewed version of the following article: [Pont, A., Codina, R., and Baiges, J. (2017) Interpolation with restrictions between finite element meshes for flow problems in an ALE setting. Int. J. Numer. Meth. Engng, 110: 1203–1226. doi: 10.1002/nme.5444.], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5444/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The need for remeshing when computing flow problems in domains suffering large deformations has motivated the implementation of a tool that allows the proper transmission of information between finite element meshes. Because the Lagrangian projection of results from one mesh to another is a dissipative method, a new conservative interpolation method has been developed. A series of constraints, such as the conservation of mass or energy, are applied to the interpolated arrays through Lagrange multipliers in an error minimization problem, so that the resulting array satisfies these physical properties while staying as close as possible to the original interpolated values in the L2 norm. Unlike other conservative interpolation methods that require a considerable effort in mesh generation and modification, the proposed formulation is mesh independent and is only based on the physical properties of the field being interpolated. Moreover, the performed corrections are neither coupled with the main calculation nor with the interpolation itself, for which reason the computational cost is very low.Peer ReviewedPostprint (author's final draft

Refficientlib: an efficient load-rebalanced adaptive mesh refinement algorithm for high-performance computational physics meshes

No separate or additional fees are collected for access to or distribution of the work.In this paper we present a novel algorithm for adaptive mesh refinement in computational physics meshes in a distributed memory parallel setting. The proposed method is developed for nodally based parallel domain partitions where the nodes of the mesh belong to a single processor, whereas the elements can belong to multiple processors. Some of the main features of the algorithm presented in this paper are its capability of handling multiple types of elements in two and three dimensions (triangular, quadrilateral, tetrahedral, and hexahedral), the small amount of memory required per processor, and the parallel scalability up to thousands of processors. The presented algorithm is also capable of dealing with nonbalanced hierarchical refinement, where multirefinement level jumps are possible between neighbor elements. An algorithm for dealing with load rebalancing is also presented, which allows us to move the hierarchical data structure between processors so that load unbalancing is kept below an acceptable level at all times during the simulation. A particular feature of the proposed algorithm is that arbitrary renumbering algorithms can be used in the load rebalancing step, including both graph partitioning and space-filling renumbering algorithms. The presented algorithm is packed in the Fortran 2003 object oriented library \textttRefficientLib, whose interface calls which allow it to be used from any computational physics code are summarized. Finally, numerical experiments illustrating the performance and scalability of the algorithm are presented.Peer ReviewedPostprint (published version

A variational multiscale stabilized finite element formulation for Reissner–Mindlin plates and Timoshenko beams

The theories for thick plates and beams, namely Reissner–Mindlin’s and Timoshenko’s theories, are well known to suffer numerical locking when approximated using the standard Galerkin finite element method for small thicknesses. This occurs when the same interpolations are used for displacement and rotations, reason for which stabilization becomes necessary. To overcome this problem, a Variational Multiscale stabilization method is analyzed in this paper. In this framework, two different approaches are presented: the Algebraic Sub-Grid Scale formulation and the Orthogonal Sub-Grid Scale formulation. Stability and convergence is proved for both approaches, explaining why the latter performs much better. Although the numerical examples show that the Algebraic Sub-Grid Scale approach is in some cases able to overcome the numerical locking, it is highly sensitive to stabilization parameters and presents difficulties to converge optimally with respect to the element size in the L 2 norm. In this regard, the Orthogonal Sub-Grid Scale approach, which considers the space of the sub-grid scales to be orthogonal to the finite element space, is shown to be stable and optimally convergent independently of the thickness of the solid. The final formulation is similar to approaches developed previously, thus justifying them in the frame of the Variational Multiscale concept.This work was supported by Vicerrectoría de Investigación, Chile, Desarrollo e Innovación (VRIDEI) of the Univeridad de Santiago de Chile, and the National Agency for Research and Development (ANID) Doctorado Becas Chile/2019 - 72200128 of the Government of Chile. R. Codina acknowledges the support received from the ICREA Acadèmia Research Program of the Catalan Government, Spain .Peer ReviewedPostprint (published version

A fractional step method for computational aeroacoustics using weak imposition of Dirichlet boundary conditions

In this work we consider the approximation of the isentropic Navier–Stokes equations. The model we present is capable of taking into account acoustic and flow scales at once. After space and time discretizations have been chosen, it is very convenient from the computational point of view to design fractional step schemes in time so as to permit a segregated calculation of the problem unknowns. While these segregation schemes are well established for incompressible flows, much less is known in the case of isentropic flows. We discuss this issue in this article and, furthermore, we study the way to weakly impose Dirichlet boundary conditions via Nitsche’s method. In order to avoid spurious reflections of the acoustic waves, Nitsche’s method is combined with a non-reflecting boundary condition. Employing a purely algebraic approach to discuss the problem, some of the boundary contributions are treated explicitly and we explain how these are included in the different steps of the final algorithm. Numerical evidence shows that this explicit treatment does not have a significant impact on the convergence rate of the resulting time integration scheme. The equations of the formulation are solved using a subgrid scale technique based on a term-by-term stabilization.Peer ReviewedPostprint (author's final draft

Solution of low Mach number aeroacoustic flows using a Variational Multi-Scale finite element formulation of the compressible Navier–Stokes equations written in primitive variables

In this work we solve the compressible Navier–Stokes equations written in primitive variables in order to simulate low Mach number aeroacoustic flows. We develop a Variational Multi-Scale formulation to stabilize the finite element discretization by including the orthogonal, dynamic and non-linear subscales, together with an implicit scheme for advancing in time. Three additional features define the proposed numerical scheme: the splitting of the pressure and temperature variables into a relative and a reference part, the definition of the matrix of stabilization parameters in terms of a modified velocity that accounts for the local compressibility, and the approximation of the dynamic stabilization matrix for the time dependent subscales. We also include a weak imposition of implicit non-reflecting boundary conditions in order to overcome the challenges that arise in the aeroacoustic simulations at low compressibility regimes. The order of accuracy of the method is verified for two- and three-dimensional linear and quadratic elements using steady manufactured solutions. Several benchmark flow problems are studied, including transient examples and aeroacoustic applications.Peer ReviewedPostprint (author's final draft

Variational multiscale error estimators for the adaptive mesh refinement of compressible flow simulations

This article investigates an explicit a-posteriori error estimator for the finite element approximation of the compressible Navier–Stokes equations. The proposed methodology employs the Variational Multi-Scale framework, and specifically, the idea is to use the variational subscales to estimate the error. These subscales are defined to be orthogonal to the finite element space, dynamic and non-linear, and both the subscales in the interior of the element and on the element boundaries are considered. Another particularity of the model is that we define some norms that lead to a dimensionally consistent measure of the compressible flow solution error inside each element; a scaled -norm, and the calculation of a physical entropy measure, are both studied in this work. The estimation of the error is used to drive the adaptive mesh refinement of several compressible flow simulations. Numerical results demonstrate good accuracy of the local error estimate and the ability to drive the adaptative mesh refinement to minimize the error through the computational domain.Peer ReviewedPostprint (author's final draft