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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. [ABSTRACT FROM AUTHOR]

We present a weakly‐compressible two‐phase poroviscoelastic biofilm model based on Smoothed Particle Hydrodynamics (SPH) method. The biofilm is modeled as a mixture of solid and fluid phases interacting via drag forces. Benefiting from the Lagrangian feature of the SPH method, large deformations of the solid structure can be modeled straightforwardly. [ABSTRACT FROM AUTHOR]

An improved coupling method of smoothed particle hydrodynamics (SPH) and element bending group (EBG) is developed for modeling the interaction of viscous flows with free surface and flexible structures with free and fixed ends. SPH and EBG are both particle methods which are appealing in modeling problems with free surfaces, moving interfaces and large deformations. SPH is used to model viscous fluid, while EBG is used to model flexible structure. Structure particles are also used as moving boundary for SPH, and the interaction of flexible structure with fluid is therefore modeled through the interaction of structure particles and fluid particles. A fixed-end treatment is introduced for flexible structures. A free surface treatment and a surface tension model are used for free surface flow. The improved SPH–EBG method is applied to simulate problems of dam break flow on flexible structures. The good agreement of presented numerical results with existing experimental and numerical results clearly demonstrates the effectiveness of the SPH and EBG coupling approach in modeling fluid–flexible structure interactions. [ABSTRACT FROM AUTHOR]

ANFO (ammonium nitrate/fuel oil) is a widely used bulk industrial explosive mixture that is considered to be highly 'non-ideal' with long reaction zones, low detonation energies, and large failure diameters. Thus, its detonation poses great challenge for accurate numerical modeling. Herein, we present a numerical model to simulate ANFO based on improved smoothed particle hydrodynamics (SPH) method, which is a mesh-free Lagrangian method performing well in simulating situations consist of moving interface and large deformation, as happened in high-velocity impact and explosion. The improved three-dimensional SPH method incorporated with JWL++ model is used to simulate the detonation of ANFO. Good agreement is observed between simulation and experiment, which indicates that the proposed method performs well in prediction of behavior of ANFO. [ABSTRACT FROM AUTHOR]

A numerical method based on smoothed particle hydrodynamics with adaptive spatial resolution (SPH-ASR) was developed for simulating free surface flows. This method can reduce the computational demands while maintaining the numerical accuracy. In this method, the spatial resolution changes adaptively according to the distance to the free surface by numerical particle splitting and merging. The particles are split for refinement when they are near the free surface, while they are merged for coarsening when they are away from the free surface. A search algorithm was implemented for identifying the particles at the free surface. A particle shifting technique, considering variable smoothing length, was introduced to improve the particle distribution. The presented SPH-ASR method was validated by simulating various free surface flows, and the results were compared to those obtained using SPH with uniform spatial resolution (USR) and experimental data. [ABSTRACT FROM AUTHOR]

The underwater explosion (UNDEX) phenomenon involves hydrodynamic behaviors with a wide range of spatial scales, from macroscopic cavitation regions to refined areas with fluid-structure interactions around the shock wavefront. Correct description of the refined shock wavefront is important for determining the shock wave position and pressure peak. In this work, the local discontinuous Galerkin (LDG) method for the two-dimensional wave equation, which allows for the local triangular meshes refinement and merging during the shock wave propagation process, is presented to model the UNDEX shock hydrodynamics. This article is an extension of our previous work, where we discretize the UNDEX total wave formulation in the LDG framework and simulate the UNDEX shock wave and cavitation phenomenon. In order to save computational cost (including CPU time and computational storage) and capture the shock wavefront more accurately, the LDG method is extended to be in combination with the mesh adaption technique. The troubled-cell indicator, depending on the local jump of the pressure, is adopted to identify elements which require to be refined or coarsened. Typical numerical examples are tested to assess the capability of the present h -adaptive LDG method for capturing the UNDEX shock wave. The numerical results clearly demonstrate that the mesh adaption technique enables us to dynamically increase the mesh resolution in close proximity to the flow discontinuities with a large pressure jump. The local increase of the mesh resolution results in a substantial increase in the accuracy of the pressure peak. In terms of the computational efficiency, the h -adaptive LDG method can save nearly half of the calculation time in comparison to the non-adaptive LDG method on uniform meshes, whose mesh resolution is the same as that of the maximum level of refinement of the h -adaptive LDG method. • An h -adaptive LDG method is presented for simulating the UNDEX shock hydrodynamics. • The mesh resolution is adaptive with the evolution of the UNDEX shock wavefront. • The present h -adaptive LDG method can well capture the UNDEX pressure peak at a relative small computational cost. [ABSTRACT FROM AUTHOR]

• A new weakly-compressible SPH model is proposed to simulate the multi-phase flows with large density ratios. • The SPH model removes unnecessary contributions from different phases for immiscible multi-phase flows. • The SPH model improves both the stability and accuracy across the multi-phase interfaces. • The SPH model allows the use of larger CLF numbers to greatly improve computational efficiency. The discontinuity across interface of multi-phase flows with large density ratios usually poses great challenges for numerical simulations. The smoothed particle hydrodynamics (SPH) is a meshless method with inherent advantages in dealing with multi-phase flows without the necessity of tracking the moving interfaces. In this paper, we develop a new weakly-compressible SPH model for multi-phase flows with large density ratios while allowing large CFL numbers. In the present SPH model, the continuity equation is first modified by eliminating the influence from particles of different phases based on the simple fact that different phases will not contribute when calculating the density for immiscible multi-phase flows; thus, the modified continuity equation will only consider the influence from neighboring particles of the same phase. The pressure and density of the particles of other phases are then re-initialized by using the Shepard interpolation function. The present multi-phase SPH model has been tested by four numerical examples, including the two-phase hydrostatic water, standing waves, liquid sloshing, and dam breaking. It has been demonstrated that the present multi-phase SPH model can obtain satisfactory results stably, even at large CFL numbers, and this means that large time steps can be employed. Therefore, the present multi-phase SPH model can significantly save computational cost through using large time steps, especially for large-scale problems with a large number of particles. [ABSTRACT FROM AUTHOR]

• Four integrated SPH models are presented and compared for simulating natural convection. • The most suitable SPH model for natural convection is provided. • Natural convection for R a = 10 9 and Pr = 0.71 is successfully modeled for the first time by using the SPH method. • Mechanisms of the natural convection in a square cavity at different Rayleigh numbers are discussed. This paper conducts the simulation of natural convection in a differentially heated square cavity at high Rayleigh numbers by using the smoothed particle hydrodynamics (SPH) method. Due to the decrease of the accuracy and stability, it is challenging for the SPH method to simulate natural convection at high Rayleigh numbers, and there are few reported SPH literatures of natural convection at R a > 10 6 for air (Pr = 0.71). In this study, four integrated SPH models are presented to simulate the natural convection and their accuracy and stability are assessed. These four SPH models are associated with Kernel Gradient Correction (KGC) to improve approximation accuracy and Particle Shifting Technology (PST) to regularize particle distribution while they are different in treating density diffusion and calculating the pressure term. The numerical results show that SPH model_4 (KGC, PST, δ -SPH and asymmetric pressure approximation) is the most suitable for simulating the closed natural convection problems, especially at high Rayleigh numbers. Good agreements with reference solutions are obtained by SPH model_4 for the natural convection at 10 4 ≤ R a ≤ 10 8. Furthermore, the simulation of natural convection at R a = 10 9 is conducted by SPH model_4. The evolutions of thermal convection are described in detail. It is found that dynamics characteristic reveals that the dominant force is the pressure gradient, rather than the buoyancy force before the quasi-steady state. In addition, the chaotic motion at R a = 10 9 has significant influence to the heat transfer characteristic in the vertical boundary layers. [ABSTRACT FROM AUTHOR]

Predicting the propagation and transformation of the solitary wave is very important in coastal engineering. This paper presents a numerical investigation of the solitary wave breaking over a slope by using a finite particle method (FPM), which is an enhanced smoothed particle hydrodynamics (SPH). We firstly conduct a comparative study on SPH and FPM in modelling solitary wave and it is demonstrated that FPM performs better than SPH qualitatively and quantitatively. A modified particle shifting technique (PST) is integrated into FPM to avoid possible ill corrective matrix due to extremely disordered particle distribution. We find that the artificial viscous coefficient can greatly influence the wave run-up and propose an empirical equation to quickly determine the optimal value of the artificial viscous coefficient used in the FPM simulations. The solitary wave breaking is then modelled for scenarios with relative wave heights and slopes, and three typical breaking types, including surging breaker (SU), plunging breaker (PL) and spilling breaker (SP), are analyzed. The result indicates that SP affects the pressure field more extensive than PL and SU. When the breaker type transits from SP to SU, the breaker tends to break at a narrower region close to the shoreline, the breaking depth decreases, the breaking index gradually turns into an unstable value, and the relative run-up height of breaking waves becomes larger. Although the wave celerity at breaking has no clear relationship with breaker types, the wave celerity at breaking increases with the increase of the relative wave height and slightly decreases with a steeper slope. • For simulations of the solitary wave breaking over slopes, FPM performs better than SPH in terms of stability and accuracy. • An empirical equation is proposed to decide the artificial viscous coefficient for simulating wave transformation by FPM. • The spilling breaker affects the pressure field more extensive than plunging breaker and surging breaker. • The wave celerity at breaking has no clear relationship with breaker types. • The wave dissipation turns into lower when wave breaking types change from spilling breaker to surging breaker. [ABSTRACT FROM AUTHOR]