Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

The archetypal feature of a viscoplastic fluid is its yield stress: If the material is not sufficiently stressed, it behaves like a solid, but once the yield stress is exceeded, the material flows like a fluid. Such behavior characterizes materials common in industries such as petroleum and chemical processing, cosmetics, and food processing and in geophysical fluid dynamics. The most common idealization of a viscoplastic fluid is the Bingham model, which has been widely used to rationalize experimental data, even though it is a crude oversimplification of true rheological behavior. The popularity of the model is in its apparent simplicity. Despite this, the sudden transition between solid-like behavior and flow introduces significant complications into the dynamics, which, as a result, has resisted much analysis. Over recent decades, theoretical developments, both analytical and computational, have provided a better understanding of the effect of the yield stress. Simultaneously, greater insight into the material behavior of real fluids has been afforded by advances in rheometry. These developments have primed us for a better understanding of the various applications in the natural and engineering sciences.

Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics

Discrete element models for non-spherical particle systems: From theoretical developments to applications

DEM/CFD-DEM Modelling of Non-spherical Particulate Systems: Theoretical Developments and Applications

Wax formation in oil pipelines: A critical review

In this paper we examine the numerical simulation of isothermal transient flows for a weakly compressible viscoplastic fluid in an axisymmetric pipe geometry. We use the Bingham model to describe the viscoplastic feature of the fluid and the compressibility is introduced in the continuity equation using the isothermal compressibility coefficient. Particular attention is devoted to the velocity-pressure problem in which the "true" (without regularization procedure) viscoplastic model is accounted for by using Lagrange multipliers techniques and augmented Lagrangian/Uzawa methods. The mass, momentum and constitutive equations are discretized using a finite volume method on a staggered grid with a TVD (Total Variation Diminishing) scheme for the convective terms. The resulting numerical method highlights strong and robust convergence properties. Obtained results regarding the transient solution underline the influence of compressibility on the flow pattern, especially in terms of yielded/unyielded regions, pressure and time to restart the flow.

Numerical simulation of weakly compressible Bingham flows: The restart of pipeline flows of waxy crude oils

Grains3D, a flexible DEM approach for particles of arbitrary convex shape — Part I: Numerical model and validations

We investigate the problem of the start up of a compressible flow in a pipeline filled with a viscoplastic and thixotropic material. The objective of this study is to examine the possibility that the flow can restart for a pressure drop below the value predicted by the conservative relation Δ p ˆ = 4 τ ˆ y L ˆ / D ˆ , where τ ˆ y denotes the yield stress, L ˆ the pipe length and D ˆ the pipe diameter, thanks to the combined effects of compressibility and thixotropy. Our numerical model is a compromise between a fully 2D model and a fully 1D model, i.e., a 1.5D model. Only the velocity component in the direction of the pipe axis is assumed non-zero but it is allowed to vary both in axial and radial directions. We show that this intermediate model yields accurate results which are consistent with the predictions of the fully 2D model. The gain in computing time while keeping an equivalent reliability in the numerical predictions enables us to investigate the effects of the compressibility and thixotropy dimensionless numbers at a reasonable cost.

A 1.5D numerical model for the start up of weakly compressible flow of a viscoplastic and thixotropic fluid in pipelines

We present a one-dimensional model of early transients in pipeline restarts of waxy crude oils, which are modelled as compressible yield stress fluids. We show that restart transients are effectively controlled by three dimensionless numbers: a Reynolds number, Re, a compressibility number X ∗ , and the Bingham number B. The first two of these combine to define three different dimensionless timescales, for compressive pressure diffusion, for the propagation of acoustic waves and for viscous damping. The Bingham number governs whether or not the pipeline restarts. We illustrate each qualitatively different regime computationally, and make favourable comparisons against the fully two-dimensional model in [G. Vinay, A. Wachs, J.-F. Agassant, Numerical simulation of weakly compressible Bingham flows: the restart of pipeline flows of waxy crude oils, J. Non-Newtonian Fluid Mech. 136 (2006) 93–105]. Our model is able to explain certain counter-intuitive observations, such as the fact that a pipeline full of more compressible fluid may in certain circumstances restart earlier than the same pipeline filled with a less compressible fluid, see e.g. [M.G. Cawkwell, M.E. Charles, An improved model for start-up of pipelines containing gelled crude oil, J. Pipelines 7 (1987) 41–52].

Start-up transients and efficient computation of isothermal waxy crude oil flows

This paper examines the numerical simulation of transient non-isothermal flows of a viscoplastic fluid in a pipe. The situation considered refers to the waxy crude oils transportation in a pipeline, where the flowing oil is cooled down due to extreme external temperature conditions. The rheological model used is an extension of the classical Bingham model in which plastic viscosity and yield stress are allowed to be temperature-dependent parameters. To solve the governing equations, we propose a decoupled transient solution algorithm. At each time step, the velocity–pressure problem and the temperature problem are solved sequentially. Particular attention is devoted to the velocity–pressure problem in which the “true” (without regularization procedure) Bingham model is accounted for by using Lagrange multipliers techniques and augmented Lagrangian/Uzawa methods. The mass, momentum, constitutive and energy equations are discretized using a Finite Volume method on a staggered grid with a TVD scheme for the convective term. The resulting numerical method highlights strong and robust convergence properties. Obtained results regarding the steady-state solution underline the influence of the temperature changes on the flow pattern, especially in terms of yielded/unyielded regions. In particular, in a pipe flow, as soon as the temperature field varies in the mean flow direction, the fluid is yielded.

Guillaume Vinay

Papers

Numerical simulation of weakly compressible Bingham flows: The restart of pipeline flows of waxy crude oils

Grains3D, a flexible DEM approach for particles of arbitrary convex shape — Part I: Numerical model and validations

A 1.5D numerical model for the start up of weakly compressible flow of a viscoplastic and thixotropic fluid in pipelines

Start-up transients and efficient computation of isothermal waxy crude oil flows

Numerical simulation of non-isothermal viscoplastic waxy crude oil flows