Numerical Monte-Carlo analysis of the influence of pore-scale dispersion on macrodispersion in heterogeneous porous media

Macrodispersion is the result of molecular diffusion and hydrodynamic dispersion. Molecular diffusion comes from the random motion of molecules. Hydrodynamic dispersion comes from the spreading of solutes due to the heterogeneous flow. From pore scale to Darcy scale, dispersion is modeled by fixed dispersivities. At larger scales, dispersion comes both from the smaller scale dispersion and from the fluctuations of flow issued by the heterogeneous permeability. In this study, we investigate the influences of pore-scale dispersion and heterogeneous permeability on the macrodispersion

Numerical assessment of 3D macrodispersion in heterogeneous porous media

Hydrodynamic dispersion is a key controlling factor of solute transport in heterogeneous porous media that critically depends on dimensionality. It has been shown that the transverse macrodispersion (asymptotic dispersion transverse to the mean velocity direction) vanishes only in 2D and not in 3D. Using classical Gaussian correlated permeability fields with a lognormal distribution of variance σ²y, we determine numerically the longitudinal and transverse dispersivities as functions of heterogeneity and dimensionality. We show that the transverse macrodispersion steeply increases with σ²y underlying the essential role of flow lines braiding, a mechanism specific to 3D systems. The transverse macrodispersion remains however at least two orders of magnitude smaller than the longitudinal macrodispersion, which increases even more steeply with σ²y. At moderate to high levels of heterogeneity, the transverse dispersion also converges much faster to its asymptotic regime than do the longitudinal dispersion. Braiding cannot be thus taken as the sole mechanism responsible for the high longitudinal macrodispersions. It could be either supplemented or superseded by stronger velocity correlations in 3D than in 2D. This assumption is supported by the much larger longitudinal macrodispersions obtained in 3D than in 2D, up to a factor of 7 for σ²y = 7.56

Preconditioning Newton-Krylov Methods in Non-Convex Large Scale Optimization

We consider an iterative preconditioning technique for non-convex large scale optimization. First, we refer to the solution of large scale indefinite linear systems by using a Krylov subspace method, and describe the iterative construction of a preconditioner which does not involve matrices products or matrices storage. The set of directions generated by the Krylov subspace method is used, as by product, to provide an approximate inverse preconditioner. Then, we experience our preconditioner within Truncated Newton schemes for large scale unconstrained optimization, where we generalize the truncation rule by Nash–Sofer (Oper. Res. Lett. 9:219–221, 1990) to the indefinite case, too. We use a Krylov subspace method to both approximately solve the Newton equation and to construct the preconditioner to be used at the current outer iteration. An extensive numerical experience shows that the proposed preconditioning strategy, compared with the unpreconditioned strategy and PREQN (Morales and Nocedal in SIAM J. Optim. 10:1079–1096, 2000), may lead to a reduction of the overall inner iterations. Finally, we show that our proposal has some similarities with the Limited Memory Preconditioners (Gratton et al. in SIAM J. Optim. 21:912–935, 2011)

Digital game elements, user experience and learning

The primary aim of this paper is to identify and theoretically validate the relationships between core game design elements and mechanics, user motivation and engagement and consequently learning. Additionally, it tries to highlight the moderating role of player personality traits on learning outcomes and acceptance and suggest ways to incorporate them in the game design process. To that end, it outlines the role of narrative, aesthetics and core game mechanics in facilitating higher learning outcomes through intrinsic motivation and engagement. At the same time, it discusses how player goal orientation, openness to experience, conscientiousness, sensation seeking and need for cognition influence the translation of the gameplay experience into valuable learning outcomes and user acceptance of the technology

Least-Squares Polynomial Filters for Ill-Conditioned Linear Systems

An important problem which arises in several applications is to find the solution of an ill-conditioned Symmetric Semi-Positive Definite linear system whose right-hand side is perturbed by noise. In this situation, it is desirable for the solution to be accurate in the directions of eigenvectors associated with large eigenvalues, and to have small components in the space associated with smallest eigenvalues. A method is presented to satisfy these requirements, which is based on constructing a polynomial filter using least-squares techniques. Key words: Polynomial filters, least-squares polynomials, ill-conditioned systems, regularization, Tychonov regularization, image recovery, Chebyshev bases. AMS subject classifications: 65F10, 65F50, 65N22