A smooth dissipative particle dynamics method for domains with arbitrary-geometry solid boundaries

Abstract

A smooth dissipative particle dynamics method with dynamic virtual particle allocation (SDPD-DV) for modeling and simulation of mesoscopic fluids in wall-bounded domains is presented. The physical domain in SDPD-DV may contain external and internal solid boundaries of arbitrary geometries, periodic inlets and outlets, and the fluid region. The SDPD-DV method is realized with fluid particles, boundary particles, and dynamically allocated virtual particles. The internal or external solid boundaries of the domain can be of arbitrary geometry and are discretized with a surface grid. These boundaries are represented by boundary particles with assigned properties. The fluid domain is discretized with fluid particles of constant mass and variable volume. Conservative and dissipative force models due to virtual particles exerted on a fluid particle in the proximity of a solid boundary supplement the original SDPD formulation. The dynamic virtual particle allocation approach provides the density and the forces due to virtual particles. The integration of the SDPD equations is accomplished with a velocity-Verlet algorithm for the momentum and a Runge–Kutta for the entropy equation. The velocity integrator is supplemented by a bounce-forward algorithm in cases where the virtual particle force model is not able to prevent particle penetration. For the incompressible isothermal systems considered in this work, the pressure of a fluid particle is obtained by an artificial compressibility formulation for liquids and the ideal gas law for gases. The self-diffusion coefficient is obtained by an implementation of the generalized Einstein and the Green–Kubo relations. Field properties are obtained by sampling SDPD-DV outputs on a post-processing grid that allows harnessing the particle information on desired spatiotemporal scales. The SDPD-DV method is verified and validated with simulations in bounded and periodic domains that cover the hydrodynamic and mesoscopic regimes for isothermal systems. Verification of the SDPD-DV is achieved with simulations of transient, Poiseuille and Couette isothermal flow of liquid water between plates with heights of 10−5 m and 10−3 m. The velocity profiles from the SDPD-DV simulations are in very good agreement with analytical estimates and the field density fluctuation near solid boundaries is shown to be below 5%. Verification of SDPD-DV applied to domains with internal curved solid boundaries is accomplished with the simulation of a body-force driven, low-Reynolds number flow of water over a cylinder of radius R=0.02 m. The SDPD-DV field velocity and pressure compare favorably with those obtained by FLUENT. The results from these benchmark tests show that SDPD-DV is effective in reducing the density fluctuations near solid walls, enforces the no-slip condition, and prevents particle penetration. Scale-effects in SDPD-DV are examined with an extensive set of SDPD-DV isothermal simulations of liquid water and gaseous nitrogen in mesoscopic periodic domains. For the simulations of liquid water the mass of the fluid particles is varied between 1.24 and 3.3×107 real molecular masses and their corresponding size is between 1.08 and 323 physical length scales. For SDPD-DV simulations of gaseous nitrogen the mass of the fluid particles is varied between 6.37×103 and 6.37×106 real molecular masses and their corresponding size is between 2.2×102 and 2.2×103 physical length scales. The equilibrium states are obtained and show that the particle speeds scale inversely with particle mass (or size) and that the translational temperature is scale-free. The self-diffusion coefficient for liquid water is obtained through the mean-square displacement and the velocity auto-correlation methods for the range of fluid particle masses (or sizes) considered. Various analytical expressions for the self-diffusivity of the SDPD fluid are developed in analogy to the real fluid. The numerical results are in very good agreement with the SDPD-fluid analytical expressions. The numerical self-diffusivity is shown to be scale dependent. For fluid particles approaching asymptotically the mass of the real particle the self-diffusivity is shown to approach the experimental value. The Schmidt numbers obtained from the SDPD-DV simulations are within the range expected for liquid water.