David Packwood

Add-ons for Lattice Boltzmann Methods: Regularization, Filtering and Limiters

We describe how regularization of lattice Boltzmann methods can be achieved by modifying dissipation. Classes of techniques used to try to improve regularization of LBMs include flux limiters, enforcing the exact correct prod uction of entropy and manip- ulating non-hydrodynamic modes of the system in relaxation. Each of these techniques corresponds to an additional modification of dissipation co mpared with the standard LBGK model. Using some standard 1D and 2D benchmarks including the shock tube and lid driven cavity, we explore the effectiveness of these classes of methods.

A universal preconditioner for simulating condensed phase materials

We introduce a universal sparse preconditioner that accelerates geometry optimisation and saddle point search tasks that are common in the atomic scale simulation of materials. Our preconditioner is based on the neighbourhood structure and we demonstrate the gain in computational efficiency in a wide range of materials that include metals, insulators, and molecular solids. The simple structure of the preconditioner means that the gains can be realised in practice not only when using expensive electronic structure models but also for fast empirical potentials. Even for relatively small systems of a few hundred atoms, we observe speedups of a factor of two or more, and the gain grows with system size. An open source Python implementation within the Atomic Simulation Environment is available, offering interfaces to a wide range of atomistic codes.

A dimer-type saddle search algorithm with preconditioning and linesearch

The dimer method is a Hessian-free algorithm for computing saddle points. We augment the method with a linesearch mechanism for automatic step size selection as well as preconditioning capabilities. We prove local linear convergence. A series of numerical tests demonstrate significant performance gains.

Time Step Expansions and the Invariant Manifold Approach to Lattice Boltzmann Models

The classical method for deriving the macroscopic dynamics of alattice Boltzmann system is to use a combination of different approximations and expansions. Usually aChapman–Enskog analysis is performed, either on the continuous Boltzmann system, or its discrete velocity counterpart. Separately a discrete time approximation is introduced to the discrete velocity Boltzmann system, to achieve a practically useful approximation to the continuous system, for use in computation. Thereafter, with some additional arguments, the dynamics of the Chapman–Enskog expansion are linked to the discrete time system to produce the dynamics of the completely discrete scheme. In this paper we put forward a different route to the macroscopic dynamics. We begin with the system discrete in both velocity space and time. We hypothesize that the alternating steps of advection and relaxation, common to all lattice Boltzmann schemes, give rise to aslow invariant manifold. We perform a time step expansion of the discrete time dynamics using the invariance of the manifold. Finally we calculate the dynamics arising from this system. By choosing the fully discrete scheme as a starting point we avoid mixing approximations and arrive at a general form of the microscopic dynamics up to the second order in the time step. We calculate the macroscopic dynamics of two commonly used lattice schemes up to the first order, and hence find the precise form of the deviation from the Navier–Stokes equations in the dissipative term, arising from the discretization of velocity space.Finally we perform a short wave perturbation on the dynamics of these example systems, to find the necessary conditions for their stability.

A Numerical Analyst’s View of the Lattice Boltzmann Method

The purpose of this paper is to raise the profile of the Lattice Boltzmann method (LBM) as a computational method for solving fluid flow problems. We put forward the point of view that the method need not be seen as a discretisation of the Boltzmann equation, and also propose an alternative route from microscopic to macroscopic dynamics, traditionally taken via the Chapman-Enskog procedure. In that process the microscopic description is decomposed into processes at different time scales, parametrised with the Knudsen number. In our exposition we use the time step as a parameter for expanding the solution. This makes the treatment here more amenable to numerical analysts. We explain a method by which one may ameliorate the inevitable instabilities arising when trying to solve a convection- dominated problem, entropic filtering.

Border Crossings: French Painting and the Public

Robert W. Berger, Public Access to Art in Paris: A Documentary History from the Middle Ages to 1800 Todd P. Olson, Poussin and France: Painting, Humanism and the Politics of Style Humphrey Wine, National Gallery Catalogues: The Seventeenth Century French Paintings

The Sacred and the Profane

Books reviewed in this article: Edgar Wind, The Religious Symbolism of Michelangelo: The Sistine Ceiling Ingrid Rowland, The Culture of the High Renaissance: Ancients and Moderns in Sixteenth-Century Rome