A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems

Radial basis function networks (RBFNs) have been widely used in solving partial differential equations as they are able to provide fast convergence. Integrated RBFNs have the ability to avoid the problem of reduced convergence-rate caused by differentiation. This paper is concerned with the use of integrated RBFNs in the context of control-volume discretisations for the simulation of fluid-flow problems. Special attention is given to (i) the development of a stable high-order upwind scheme for the convection term and (ii) the development of a local high-order approximation scheme for the diffusion term. Benchmark problems including the lid-driven triangular-cavity flow are employed to validate the present technique. Accurate results at high values of the Reynolds number are obtained using relatively-coarse grids

A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows

A numerical computation of continuum-microscopic model for visco-elastic flows based on the Integrated Radial Basis Function (IRBF) Control Volume and the Stochastic Simulation Techniques (SST) is reported in this paper. The macroscopic flow equations are closed by a stochastic equation for the extra stress at the microscopic level. The former are discretised by a 1D-IRBF-CV method while the latter is integrated with Euler explicit or Predictor-Corrector schemes. Modelling is very efficient as it is based on Cartesian grid, while the integrated RBF approach enhances both the stability of the procedure and the accuracy of the solution. The proposed method is demonstrated with the solution of the start-up Couette flow of the Hookean and FENE dumbbell model fluids

Imposition of physical parameters in dissipative particle dynamics

In the mesoscale simulations by the dissipative particle dynamics (DPD), the motion of a fluid is modelled by a set of particles interacting in a pairwise manner, and it has been shown to be governed by the Navier–Stokes equation, with its physical properties, such as viscosity, Schmidt number, isothermal compressibility, relaxation and inertia time scales, in fact its whole rheology resulted from the choice of the DPD model parameters. In this work, we will explore the response of a DPD fluid with respect to its parameter space, where the model input parameters can be chosen in advance so that (i) the ratio between the relaxation and inertia time scales is fixed; (ii) the isothermal compressibility of water at room temperature is enforced; and (iii) the viscosity and Schmidt number can be specified as inputs. These impositions are possible with some extra degrees of freedom in the weighting functions for the conservative and dissipative forces. Numerical experiments show an improvement in the solution quality over conventional DPD parameters/weighting functions, particularly for the number density distribution and computed stresses

BEM-RBF approach for viscoelastic flow analysis

A new BE-only method is achieved for the numerical solution of viscoelastic flows. A decoupled algorithm is chosen where the fluid is considered as being composed of an artificial Newtonian component and the remaining component is accordingly defined from the original constitutive equation. As a result the problem is viewed as that of solving for the flow of a Newtonian liquid with the non-linear viscoelastic effects acting as a pseudo body force. Thus the general solution is obtained by adding a particular solution to the homogeneous one. The former is obtained by a BEM for the base Newtonian fluid and the latter is obtained analytically by approximating the pseudo body force in terms of suitable radial basis functions (RBFs). Embedded in the approximation of the pseudo body force is the calculation of the polymer stress. This is achieved by solving the constitutive equation using RBF networks (RBFNs). Both the calculations of the particular solution and the polymer stress are therefore meshless and the resultant BEM-RBF method is a BE-only method. The complete elimination of any structured domain discretisation is demonstrated with a number of flow problems involving the Upper Convected Maxwell (UCM) and the Oldroyd-B fluids

A note on dissipative particle dynamics (DPD) modelling of simple fluids

In this paper, we show that a Dissipative Particle Dynamics (DPD) model of a viscous Newtonian fluid may actually produce a linear viscoelastic fluid. We demonstrate that a single set of DPD particles can be used to model a linear viscoelastic fluid with its physical parameters, namely the dynamical viscosity and the relaxation time in its memory kernel, determined from the DPD system at equilibrium. The emphasis of this study is placed on (i) the estimation of the linear viscoelastic effect from the standard parameter choice; and (ii) the investigation of the dependence of the DPD transport properties on the length and time scales, which are introduced from the physical phenomenon under examination. Transverse-current auto-correlation functions (TCAF) in Fourier space are employed to study the effects of the length scale, while analytic expressions of the shear stress in a simple small amplitude oscillatory shear flow are utilised to study the effects of the time scale. A direct mechanism for imposing the particle diffusion time and fluid viscosity in the hydrodynamic limit on the DPD system is also proposed

Production, income, and expenditure in commercial sexual activity as a measure of GDP in the UK national accounts

Executive summary: This paper reports the economic activity of sex workers for its inclusion into gross domestic product (GDP) for the UK National Accounts. Markets in consenting but nonetheless illicit activities, including commercial sexual activity and drugs, were incorporated into figures for the UK National Accounts for the first time in 2014. This was to ensure comparability of the Gross National Income (GNI) measurements across EU countries. We evaluate the methods and data used to calculate prostitution in the first ONS (2014) analysis and explore the constraints and limitations in the calculation of prostitution data. We provide an updated figure for the number of sex workers using monitoring data from NHS specialist services and a using a standard methodology that has been employed by HIV prevention organisations across Europe to supply estimates of the number of sex workers in the UK as well as income and expenditure in various sex work markets in which both parties are voluntary participants. The London and regional markets are sectored separately to take account of the denser market in the capital, and to reflect the composition and differential pricing and working practices of sex workers in different sectors based on location and gender. Trying to estimate informal covert markets and activities presents an immense methodological challenge. Not surprisingly there have been few attempts to estimate this hidden part of the UK economy in the peer-reviewed literature or from quality sources. To date only Kinnell (1999), and Cusick, Kinnell, Brooks-Gordon and Campbell (2009) have attempted it in the UK. There remain significant limitations and levels of uncertainty, but we provide a model that is based on primary and secondary data from national and regional governmental and NGO services, to develop a model of the non-observed economy (NOE) which is scalable, simple, and with more explanatory power than previous attempts, to create a framework for the future calculation of this activity in the UK National Accounts

EMaP: Explainable AI with Manifold-based Perturbations

In the last few years, many explanation methods based on the perturbations of input data have been introduced to improve our understanding of decisions made by black-box models. The goal of this work is to introduce a novel perturbation scheme so that more faithful and robust explanations can be obtained. Our study focuses on the impact of perturbing directions on the data topology. We show that perturbing along the orthogonal directions of the input manifold better preserves the data topology, both in the worst-case analysis of the discrete Gromov-Hausdorff distance and in the average-case analysis via persistent homology. From those results, we introduce EMaP algorithm, realizing the orthogonal perturbation scheme. Our experiments show that EMaP not only improves the explainers' performance but also helps them overcome a recently-developed attack against perturbation-based methods.Comment: 29 page