Computer modeling of complex fluid flows usually presents great challenges for conventional grid-based numerical methods. Smoothed particle hydrodynamics (SPH) is a meshfree Lagrangian particle method and has special advantages in modeling complex fluid flows, especially those with large fluid deformations, fluid-structure interactions, and multi-scale physics. In this paper, we review the recent developments of SPH in methodology and applications for modeling complex fluid flows. Specifically, in methodology, some important issues including modified SPH particle approximation schemes for improving discretization accuracy, different particle regularization techniques, and various boundary treatment algorithms for solid boundary, free surface, or multiphase interface are described. More importantly, the SPH method with ideas from the dissipative particle dynamics for complex fluids in macro- or meso-scales is discussed. In applications, different complex fluid flows, including biological flows, microfluidics and droplet dynamics, non-Newtonian fluid flows, free surface flows, multiphase flows, and flows with fluid-structure interaction, are reviewed. Some concluding remarks in SPH modeling of complex fluid flows are provided.

To study the effect of car body-mounted equipment on the car body flexible vibration, a vertical rigid-flexible coupling model of a high-speed vehicle is established, which includes a flexible car body, rigid bodies for two bogie frames, four wheelsets, and the car body-mounted equipment. The car body is approximated by an elastic beam, with dimensions selected to give similar mass and vertical bending frequency to an existing car body. Model validation is then carried out by comparing results from numerical simulation and on-track test. Using frequency response analysis and ride comfort analysis, parametric studies are undertaken in order to investigate the respective effect of equipment mounting systems on the car body flexible vibration and ride comfort perceived by the passenger. It is found that the equipment behaves as a dynamic vibration absorber on account of its elastic connections to the car body. The stiffness, damping, mass, and installing position of the equipment have a significant influence on the car body flexible vibration. The optimal parameters of the dynamic vibration absorber are given, which can contribute much to the vibration absorption of the car body flexible vibration. Finally, extensive tests on a high-speed test vehicle are conducted to represent a part of results obtained in the numerical study, including modal tests on the car body, component tests on rubber springs used in the equipment mounting systems, and roller rig tests on the vibration absorption performance of the equipment. It is shown that the car body flexible vibration can be effectively suppressed by reasonably suspending the car body-mounted equipment.

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SUMMARYThe finite particle method (FPM) is a modified SPH method with high order accuracy while retaining the advantages of SPH in modeling problems with free surfaces, moving interfaces, and large deformations. In both SPH and FPM, kernel gradient is necessary in kernel and particle approximation of a field function and its derivatives. In this paper, a new FPM is presented, which only involves kernel function itself in kernel and particle approximation. The kernel gradient is not necessary in the whole computation, and this approach is thus referred to as a kernel gradient free (KGF) SPH method. This is helpful when a kernel function is not differentiable or the resultant kernel gradient is not sufficiently smooth, and thus it is more general in selecting a kernel function. Moreover, different from the original FPM with an asymmetric corrective matrix, in the new FPM, the resultant corrective matrix is symmetric, and this is advantageous in particle approximations. A series of numerical examples have been conducted to show the efficiencies of KGF-SPH including one-dimensional mathematical tests of polynomial functions with equal or variable smoothing length and two-dimensional incompressible fluid flow of shear cavity. It is found that KGF-SPH is comparable with FPM in accuracy and is flexible as SPH.