An efficient BEM for numerical solution of the biharmonic boundary value problem

This paper presents an efficient BEM for solving biharmonic equations. All boundary values including geometries are approximated by the universal high order radial basis function networks (RBFNs) rather than the usual low order interpolations. Numerical results show that the proposed BEM is considerably superior to the linear/quadratic-BEM in terms of both accuracy and convergence rate

Solving high-order partial differential equations with indirect radial basis function networks

This paper reports a new numerical method based on radial basis function networks (RBFNs) for solving high-order partial differential equations (PDEs). The variables and their derivatives in the governing equations are represented by integrated RBFNs. The use of integration in constructing neural networks allows the straightforward implementation of multiple boundary conditions and the accurate approximation of high-order derivatives. The proposed RBFN method is verified successfully through the solution of thin-plate bending and viscous flow problems which are governed by biharmonic equations. For thermally driven cavity flows, the solutions are obtained up to a high Rayleigh number

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

Phenomenological model for a novel melt-freeze phase of sliding bilayers

Simulations show that sliding bilayers of colloidal particles can exhibit a new phase, the ``melt-freeze'' phase, where the layers stochastically alternate between solidlike and liquidlike states. We introduce a mean field phenomenological model with two order parameters to understand the interplay of two adjacent layers while the system is in this remarkable phase. Predictions from our numerical simulations of a system in the melt-freeze phase include the tendency of two adjacent layers to be in opposite states (solid and liquid) and the difference between the fluctuation of the order parameter in one layer while the other layer is in the same phase compared to the fluctuation while the other layer is in the opposite phase. We expect this behavior to be seen in future simulations and experiments.Comment: 6 Pages, 6 figure

Three Poems: Charges Against a Newborn; Unanswered; For the First Generation

This creative work features three poems: Charges Against a Newborn, Unanswered, For the First Generation

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

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