Compute Unified Device Architecture (CUDA) was used to design and implement molecular dynamics (MD) simulations on graphics processing units (GPU). With an NVIDIA Tesla C870, a 20-60 fold speedup over that of one core of the Intel Xeon 5430 CPU was achieved, reaching up to 150 Gflops. MD simulation of cavity flow and particle-bubble interaction in liquid was implemented on multiple GPUs using a message passing interface (MPI). Up to 200 GPUs were tested on a special network topology, which achieves good scalability. The capability of GPU clusters for large-scale molecular dynamics simulation of meso-scale flow behavior was, therefore, uncovered.

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As a fully Lagrangian, particle-based numerical method, the traditional smoothed particle hydrodynamics (SPH) generally suffers from the accuracy problem. To investigate the physical origins of this numerical error, the elastic effect between SPH particles is specifically identified by analogy with physical entities, and a unique non-dimensional number is proposed to evaluate the relative dominance of viscous to elastic effect. Through the simulation of two-dimensional Couette flow, the velocity profile and arrangement of particles are examined for various ratios of viscous to elastic effect. The effective viscosity of SPH particles decreases as this non-dimensional number increases, while the increase of particle number significantly reduces the effective viscosity only at lower ratio of viscous to elastic effect. The disparity among nominal viscous dissipation, total dissipation, and theoretical dissipation further confirms the presence of unphysical dissipation resulting from the elastic effect. In summary, due to the constraints from the Mach number and the ratio of viscous to elastic effect, there exists a critical Reynolds number below which the Newtonian behavior could be approximately obtained through suitable choice of model parameters.smoothed particle hydrodynamics, fluid mechanics, accuracy, Couette flow, particle methods Citation:Zhou G Z, Ge W, Li J H. Theoretical analysis on the applicability of traditional SPH method.

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