Stochastic level-set method for shape optimisation

We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical programming. The stochastic element of the algorithm is built on the methods of statistical mechanics and is designed so that the system explores a Boltzmann-Gibbs distribution of structures. In non-convex optimisation problems, the deterministic algorithm can get trapped in local optima: the stochastic generalisation enables sampling of multiple local optima, which aids the search for the globally-optimal structure. The method is demonstrated for several simple geometrical problems, and a proof-of-principle calculation is shown for a simple engineering structure.Comment: 17 pages, 10 fig

Lattice Boltzmann - Langevin simulations of binary mixtures

We report a hybrid numerical method for the solution of the model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes are solved using the stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretisation of the order parameter equation. Special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattice level in both cases. The methods are benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytical and numerical results. The Galilean invariance of the model is tested and found to be satisfactory. Thermally induced capillary fluctuations of the interface are captured accurately, indicating that the model can be used to study nonlinear fluctuations

A random projection method for sharp phase boundaries in lattice Boltzmann simulations

Existing lattice Boltzmann models that have been designed to recover a macroscopic description of immiscible liquids are only able to make predictions that are quantitatively correct when the interface that exists between the fluids is smeared over several nodal points. Attempts to minimise the thickness of this interface generally leads to a phenomenon known as lattice pinning, the precise cause of which is not well understood. This spurious behaviour is remarkably similar to that associated with the numerical simulation of hyperbolic partial differential equations coupled with a stiff source term. Inspired by the seminal work in this field, we derive a lattice Boltzmann implementation of a model equation used to investigate such peculiarities. This implementation is extended to different spacial discretisations in one and two dimensions. We shown that the inclusion of a quasi-random threshold dramatically delays the onset of pinning and facetting

OLTARIS: On-Line Tool for the Assessment of Radiation in Space

The On-Line Tool for the Assessment of Radiation In Space (OLTARIS) is a World Wide Web based tool that assesses the effects of space radiation to humans in items such as spacecraft, habitats, rovers, and spacesuits. This document explains the basis behind the interface and framework used to input the data, perform the assessment, and output the results to the user as well as the physics, engineering, and computer science used to develop OLTARIS. The physics is based on the HZETRN2005 and NUCFRG2 research codes. The OLTARIS website is the successor to the SIREST website from the early 2000 s. Modifications have been made to the code to enable easy maintenance, additions, and configuration management along with a more modern web interface. Over all, the code has been verified, tested, and modified to enable faster and more accurate assessments. The next major areas of modification are more accurate transport algorithms, better uncertainty estimates, and electronic response functions. Improvements in the existing algorithms and data occur continuously and are logged in the change log section of the website

Solution of the general dynamic equation along approximate fluid trajectories generated by the method of moments

We consider condensing flow with droplets that nucleate and grow, but do not slip with respect to the surrounding gas phase. To compute the local droplet size distribution, one could solve the general dynamic equation and the fluid dynamics equations simultaneously. To reduce the overall computational effort of this procedure by roughly an order of magnitude, we propose an alternative procedure, in which the general dynamic equation is initially replaced by moment equations complemented with a closure assumption. The key notion is that the flow field obtained from this so-called method of moments, i.e., solving the moment equations and the fluid dynamics equations simultaneously, approximately accommodates the thermodynamic effects of condensation. Instead of estimating the droplet size distribution from the obtained moments by making assumptions about its shape, we subsequently solve the exact general dynamic equation along a number of selected fluid trajectories, keeping the flow field fixed. This alternative procedure leads to fairly accurate size distribution estimates at low cost, and it eliminates the need for assumptions on the distribution shape. Furthermore, it leads to the exact size distribution whenever the closure of the moment equations is exact

High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation

We construct a high order discontinuous Galerkin method for solving general hyperbolic systems of conservation laws. The method is CFL-less, matrix-free, has the complexity of an explicit scheme and can be of arbitrary order in space and time. The construction is based on: (a) the representation of the system of conservation laws by a kinetic vectorial representation with a stiff relaxation term; (b) a matrix-free, CFL-less implicit discontinuous Galerkin transport solver; and (c) a stiffly accurate composition method for time integration. The method is validated on several one-dimensional test cases. It is then applied on two-dimensional and three-dimensional test cases: flow past a cylinder, magnetohydrodynamics and multifluid sedimentation