The FADE mass-stat:A technique for inserting or deleting particles in molecular dynamics simulations

The emergence of new applications of molecular dynamics (MD) simulation calls for the development of mass-statting procedures that insert or delete particles on-the-fly. In this paper we present a new mass-stat which we term FADE, because it gradually “fades-in” (inserts) or “fades-out” (deletes) molecules over a short relaxation period within a MD simulation. FADE applies a time-weighted relaxation to the intermolecular pair forces between the inserting/deleting molecule and any neighbouring molecules. The weighting function we propose in this paper is a piece-wise polynomial that can be described entirely by two parameters: the relaxation time scale and the order of the polynomial. FADE inherently conserves overall system momentum independent of the form of the weighting function. We demonstrate various simulations of insertions of atomic argon, polyatomic TIP4P water, polymer strands, and C60 Buckminsterfullerene molecules. We propose FADE parameters and a maximum density variation per insertion-instance that restricts spurious potential energy changes entering the system within desired tolerances. We also demonstrate in this paper that FADE compares very well to an existing insertion algorithm called USHER, in terms of accuracy, insertion rate (in dense fluids), and computational efficiency. The USHER algorithm is applicable to monatomic and water molecules only, but we demonstrate that FADE can be generally applied to various forms and sizes of molecules, such as polymeric molecules of long aspect ratio, and spherical carbon fullerenes with hollow interiors

A DSMC investigation of gas flows in micro-channels with bends

Pressure-driven, implicit boundary conditions are implemented in an open source direct simulation Monte Carlo (DSMC) solver, and benchmarked against simple micro-channel flow cases found in the literature. DSMC simulations are then carried out of gas flows for varying degrees of rarefaction along micro-channels with both one and two ninety-degree bends. The results are compared to those from the equivalent straight micro-channel geometry. Away from the immediate bend regions, the pressure and Mach number profiles do not differ greatly from those in straight channels, indicating that there are no significant losses introduced when a bend is added to a micro-channel geometry. It is found that the inclusion of a bend in a micro-channel can increase the amount of mass that a channel can carry, and that adding a second bend produces a greater mass flux enhancement. This increase happens within a small range of Knudsen number (0.02 Knin 0.08). Velocity slip and shear stress profiles at the channel walls are presented for the Knudsen showing the largest mass flux enhancement

Kinetic modelling of non-equilibrium flow of hard-sphere dense gases

A kinetic model is proposed for the nonequilibrium flow of dense gases composed of hard sphere molecules, which significantly simplifies the collision integral of the Enskog equation using the relaxation time approach. The model preserves the most important physical properties of high density gas systems, including the Maxwellian at rest as the equilibrium solution and the equation of state for hard sphere fluids; all the correct transport coefficients, namely, the shear viscosity, thermal conductivity, and bulk viscosity; and inhomogeneous density distribution in the presence of a solid boundary. The collision operator of the model contains a Shakhov model like relaxation part and an excess part in low order spatial derivatives of the macroscopic flow properties; this latter contribution is used to account for the effect arising from the finite size of gas molecules. The density inhomogeneity in the vicinity of a solid boundary in a confined flow is captured by a method based on the density functional theory. Extensive benchmark tests are performed, including the normal shock structure and the Couette, Fourier, and Poiseuille flow at different reduced densities and Knudsen numbers, where the results are compared with the solutions from the Enskog equation and molecular dynamics simulations. It is shown that the proposed kinetic model provides a fairly accurate description of all these nonequilibrium dense gas flows. Finally, we apply our model to simulate forced wave propagation in a dense gas confined between two plates. The inhomogeneous density near the solid wall is found to enhance the oscillation amplitude, while the presence of bulk viscosity causes stronger attenuation of the sound wave. This shows the importance of a kinetic model to reproduce density inhomogeneity and correct transport coefficients, including bulk viscosity