Mesh adaptation in fluid mechanics

The development, application and impact of mesh adaptation procedures in the field of computational fluid mechanics (CFD) are reviewed. The discussion is restricted to unstructured (i.e. unordered) grids, such as those commonly encountered in finite element applications

Research in computerized structural analysis and synthesis

Computer applications in dynamic structural analysis and structural design modeling are discussed

Reduced-basis methods applied to problems in elasticity : analysis and applications

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2003.Includes bibliographical references (p. 177-180).Modern engineering problems require accurate, reliable, and efficient evaluation of quantities of interest, the computation of which often requires solution of a partial differential equation. We present a technique for the prediction of linear-functional outputs of elliptic partial differential equations with affine parameter dependence. The essential components are: (i) rapidly convergent global reduced-basis approximations - projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space (Accuracy); (ii) a posteriori error estimation - relaxations of the error-residual equation that provide inexpensive bounds for the error in the outputs of interest (Reliability); and (iii) off-line/on-line computational procedures - methods which decouple the generation and projection stages of the approximation process (Efficiency). The operation count for the on-line stage depends only on N (typically very small) and the parametric complexity of the problem. We present two general approaches for the construction of error bounds: Method I, rigorous a posteriori error estimation procedures which rely critically on the existence of a "bound conditioner" - in essence, an operator preconditioner that (a) satisfies an additional spectral "bound" requirement, and (b) admits the reduced-basis off-line/on-line computational stratagem; and Method II, a posteriori error estimation procedures which rely only on the rapid convergence of the reduced-basis approximation, and provide simple, inexpensive error bounds, albeit at the loss of complete certainty. We illustrate and compare these approaches for several simple test problems in heat conduction, linear elasticity, and (for Method II) elastic stability.(cont.) Finally, we apply our methods to the "static" (at conception) and "adaptive" (in operation) design of a multifunctional microtruss channel structure. We repeatedly and rapidly evaluate bounds for the average deflection, average stress, and buckling load for different parameter values to best achieve the design objectives subject to performance constraints. The output estimates are sharp - due to the rapid convergence of the reduced-basis approximation; the performance constraints are reliably satisfied - due to our a posteriori error estimation procedure; and the computation is essentially real-time - due to the off-line/on-line decomposition.by Karen Veroy.Ph.D

Snapshot-Based Methods and Algorithms

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

Development of reduced numeric models to aero-thermal flows in buildings

Esta tesis se enmarca dentro de la resoluci_on num_erica de modelos que simulan el comportamiento de ujos turbulentos mediante t_ecnicas de orden reducido y bajo coste computacional. En particular, desarrollamos t_ecnicas de bases reducidas que permiten reducir dr_asticamente el c_alculo de una soluci_on a estos modelos. El objetivo es desarrollar modelos matem_aticos orientados al dise~no de edi_cios eco-e_cientes, lo que conlleva a la resoluci_on de modelos complejos donde las inc_ognitas del problema aparecen acopladas. La modelizaci_on de orden reducido proporciona reducciones de varios _ordenes de magnitud en el coste computacional de la simulaci_on num_erica de estos procesos y problemas de dise~no, haciendo cada vez m_as abordable su resoluci_on efectiva en tiempo real. Normalmente los modelos de orden reducido requieren de cientos de grados de libertad en lugar de millones como frecuentemente necesita el modelo de orden completo. En este trabajo consideramos diferentes modelos de complejidad creciente, desarrollando las t_ecnicas de orden reducido aplicadas a dichos modelos. Realizamos un estudio de estabilidad para dichos m_etodos num_ericos y se completa con simulaciones num_ericas que permiten validar los resultados te_oricos obtenidos. En primer lugar consideramos el modelo de turbulencia para ujos de aire conocido como modelo de Smagorinsky. Se trata de un modelo b_asico de turbulencia, que corresponde a las ecuaciones de Navier-Stokes donde la viscosidad es una viscosidad turbulenta, que matem_atica es una funci_on no lineal de la inc_ognita. Para la aproximaci_on de este t_ermino utilizamos t_ecnicas de Interpolaci_on Emp__rica, desarrollando un estimador de error a posteriori de acuerdo con la Teor__a de Brezzi-Rappaz-Raviart. Para este modelo en su versi_on bidimensional, realizamos distintos test num_ericos obteniendo que el tiempo de c_alculo para la velocidad del ujo se divide por mil cuando utilizamos t_ecnicas de orden reducido. A continuacion nos ocupamos de una modi_caci_on del modelo de Smagorinsky donde consideramos que la viscosidad turbulenta act_ua s_olo sobre las peque~nas escalas resueltas, y adem_as consideramos una estabilizaci_on local de proyecci_on para el c_alculo de la presi_on. El considerar esta estabilizaci_on de la presion nos permite evitar el enriquecimiento del espacio de velocidades para obtener un m_etodo estable. Para este modelo hemos comprobado num_ericamente que el tiempo de c_alculo se reduce m_as que en el modelo original de Smagorinsky. Por _ultimo consideramos un modelo acoplado de tipo Boussinesq obtenido mediante t_ecnicas de multiescala variacional. El modelo est_a formado por las ecuaciones del modelo de Smagorinsky junto a la ecuaci_on de la temperatura. Estas ecuaciones est_an acopladas mediante los t_erminos de otabilidad. El estudio realizado para este modelo se centra en aplicar t_ecnicas de orden reducido para dos tipos de par_ametros: f__sico y geom_etrico. El tratamiento para cada uno de estos par_ametros es distinto desde el punto de vista matem_atico. Para este problema desarrollamos de nuevo un estimador de error a posteriori y lo validamos mediante simulaciones num_ericas sencillas que representan el estudio del ujo de aire y la temperatura en habitaciones de geometr__a sencilla