Catálogo de publicaciones - libros

In this paper we introduce an extension of the Fast Marching Method introduced by Sethian [6] for the eikonal equation modelling front evolutions in normal direction. The new scheme can deal with a velocity without . This scheme is then used for solving dislocation dynamics problems in which the velocity of the front depends on the position of the front itself and its sign is not restricted to be positive or negative.

We study the problem of time-step adaptation in semi-Lagrangian schemes for the approximation of the level-set equation of Mean Curvature Motion. We try to present general principles for time adaptivity strategies applied to geometric equations and to make a first attempt based on local truncation error. The efficiency of the proposed technique on classical benchmarks is discussed in the last section.

The Heterogeneous Multiscale Method (HMM) applied to elliptic homogenization problems has been analyzed for simplicial elements in [E, Ming, Zhang, J. Amer. Math. Soc. 18, pp. 121–156, 2005] and [Abdulle, SIAM, Multiscale Model. Simul., Vol. 4, No 2, pp.195–220, 2005.]. In this paper we discuss and analyze the use of quadrilateral (hexahedral) finite elements for the HMM applied to elliptic homogenization problem. We give and a priori estimates and discuss a strategy to recover the microscopic information. Numerical examples confirm our error estimates.

This work concerns the derivation of new stabilized finite element methods for the Stokes problem. Starting from pairs of spaces which are not stable, they are made stable by enriching them with multiscale functions, i.e., functions which are local, but not bubble-like, arising from the solution of local problems at the element level. This general methodology is applied to stabilize the non-stable ℙ/ℙ pair.

The main objective of this work is to study the ability of a multiresolution method based on wavelet approximation to predict unsteady shocked flows. A correct prediction of shock wave phenomena is often crucial in flow simulations for many industrial configurations such as in air intakes of supersonic vehicles or shock tube facilities where moving shock waves interact with shear layers. To capture these very fine and localized structures, many shock capturing schemes have been developed in the last decades that work with adequat robustness. However, shock wave/shear layer interactions generate unsteady vortical flows with separation that need adaptive multiresolution technics to achieve correct predictions.

The local projection stabilization for the Stokes system is formulated for anisotropic quadrilateral meshes. Stability is proven and an error analysis is given.

In this paper we present a framework using C° interior penalty methods for computations of the Navier-Stokes equations at high Reynolds number. The method is motivated by a formal scale separation argument and then justified by a priori error estimates. As a possible measure of solution quality we propose to monitor the ratio between the artificial dissipation induced by the numerical method and the computed physical dissipation. We prove that for our method the artificial dissipation serves as an a posteriori error estimator.

In this article, variational multiscale large eddy simulation based on multigrid scale-separating operators is presented. Two different scale-separating operators, which are basically applicable within both a finite element and a finite volume method, are proposed for separating large resolved scales and small resolved scales. One of these operators is a projector. Using the multigrid operators for scale separation, dynamic and non-dynamic subgrid-scale modeling approaches are applied to the challenging test case of turbulent flow in a diffuser. Variational multiscale large eddy simulation using a projective multigrid scale-separating operator provides remarkable results already in combination with a simple non-dynamic subgrid-scale modeling approach. Furthermore, this methodical combination turns out to be very efficient with regard to the important aspect of computational cost.

The mathematical foundations of Large Eddy Simulation (LES) for three-dimensional turbulent incompressible viscous flows are discussed and the notion of suitable approximations is introduced.

Nonstationary incompressible flow problems can be split into auxiliary problems of Oseen type. We present the analysis of conforming stabilized Galerkin methods of SUPG/PSPG-type with equal-order interpolation of velocity/pressure and with emphasis on anisotropic mesh refinement in boundary layers. We prove a modified inf-sup condition with a constant independent of the viscosity and of critical parameters of the mesh. Numerical tests confirm the results.