In this work, a hybrid lattice Boltzmann method (HLBM) is proposed, where the standard lattice Boltzmann implementation based on the Bhatnagar-Gross-Krook (LBGK) approximation is combined together with an unstructured finite-volume lattice Boltzmann model. The method is constructed on an overlapping grid system, which allows the coexistence of a uniform lattice nodes spacing and a coordinate-free lattice structure. The natural adaptivity of the hybrid grid system makes the method particularly suitable to handle problems involving complex geometries.

Hybrid particle-continuum computational frameworks permit the simulation of gas flows by locally adjusting the resolution to the degree of non-equilibrium displayed by the flow in different regions of space and time. In this work, we present a new scheme that couples the direct simulation Monte Carlo (DSMC) with the lattice Boltzmann (LB) method in the limit of isothermal flows.

It is commonly agreed that the most challenging problems in modern science and engineering involve the concurrent and nonlinear interaction of multiple phenomena, acting on a broad and disparate spectrum of scales in space and time. It is also understood that such phenomena lie at the interface between different disciplines, such as physics, chemistry, material science and biology. The multiscale and multi-level nature of these problems commands a paradigm shift in the way they need to be handled, both conceptually and in terms of the corresponding problem-solving computational tools

Overcomplete representations such as wavelets and windowed Fourier expansions have become mainstays of modern statistical data analysis. In the present work, in the context of general finite frames, we derive an oracle expression for the mean quadratic risk of a linear diagonal de-noising procedure which immediately yields the optimal linear diagonal estimator. Moreover, we obtain an expression for an unbiased estimator of the risk of any smooth shrinkage rule.

We focus on the extension of the MLD2P4 package of parallel Algebraic MultiGrid (AMG) preconditioners, with the objective of improving its robustness and efficiency when dealing with sparse linear systems arising from anisotropic PDE problems on general meshes. We present a parallel implemen- tation of a new coarsening algorithm for symmetric positive definite matrices, which is based on a weighted matching approach.

Atmospheric emissions of carbon tetrachloride (CCl4) are regulated by the Montreal Protocol due to its role as a strong ozone-depleting substance. The molecule has been the subject of recent increased interest as a consequence of the so-called "mystery of CCl4", the discrepancy between atmospheric observations and reported production and consumption. Surface measurements of CCl4 atmospheric concentrations have declined at a rate almost 3 times lower than its lifetime-limited rate, suggesting persistent atmospheric emissions despite the ban.

In this paper we propose a method to couple two or more explicit numerical schemes approximating the same time-dependent PDE, aiming at creating a new scheme which inherits advantages of the original ones. We consider both advection equations and nonlinear conservation laws. By coupling a macroscopic (Eulerian) scheme with a microscopic (Lagrangian) scheme, we get a new kind of multiscale numerical method.