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The continuum surface force (CSF) model in conjunction with the smoothed particle hydrodynamics (SPH) method is commonly used in the simulation of multi-phase flows with surface tension effect. However, it cannot be directly applied for modeling free-surface flows since the normalization requirement, which states that the integral of the surface delta function through the interface should be equal to one, is violated due to the particle deficiency issue. In this work, we propose an improved CSF model based on the SPH method with the aim of recovering the normalization requirement. The particle deficiency issue at the free surface is tackled by introducing the jump in color function into the calculation of the surface delta function. As a result, the accuracy of the surface tension measurement is significantly improved without using the virtual particles. Besides, this improved CSF model also allows an accurate and efficient implementation of the Robin boundary condition which is frequently encountered in heat transfer problems. Several benchmark problems are investigated to validate the performance of the proposed method. The numerical results verify that the improved CSF model in SPH method is well capable of simulating free-surface flows and heat transfer problems. [ABSTRACT FROM AUTHOR]

Abstract Particulate flow has a wide range of industrial applications and is frequently modeled with coupled CFD–DEM approaches. Herein, we first identified a simulation gap between the resolved CFD–DEM and unresolved CFD–DEM through a size effect study. Then we analyzed the error sources of the conventional unresolved CFD–DEM when modeling particulate flows with comparable mesh size and particle diameter. We finally developed a semi-resolved CFD–DEM model, which combines the advantages of both resolved and unresolved CFD–DEM models. The semi-resolved CFD–DEM uses a drag force model to characterize particle–fluid interaction, while the relative velocity in the drag force model is corrected through kernel-based approximations on the neighboring fluid cells rather than simply taking values in the local cell containing the concerned particle, and the void fraction in the force model is corrected as well. In order to improve the computational efficiency, a Hilbert curve based searching strategy is used to identify the fluid cells covered by the influencing area of the kernel function. A number of numerical simulations have been conducted and numerical results from different CFD–DEM approaches are compared together with experimental data. It is shown that the presented semi-resolved CFD–DEM bridges the simulation gap between the resolved CFD–DEM and unresolved CFD–DEM while it is as efficient as the conventional unresolved CFD–DEM and as accurate as the resolved CFD–DEM. [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]

• An indirect ALE DG model on moving triangular meshes with mesh topological adaptability is developed. • The best features of the Lagrangian description, DG method and adaptive topology optimization strategy are incorporated. • The present scheme can handle hydrodynamics problems which involve complex deformations, large distortions and strong shock. • The new indirect ALE DG scheme is more accurate and stable than the conventional Lagrangian DG scheme. In this paper, we present a novel cell-centered indirect Arbitrary-Lagrangian-Eulerian (ALE) discontinuous Galerkin (DG) scheme on moving unstructured triangular meshes with mesh topological adaptability, aiming to deal with the strong distortions and large deformation flow problems. The scheme combines the explicit time marching Lagrangian DG methodology with the adaptive mesh topology optimization technique. The scheme consists of the following three steps. Firstly, we utilize the Runge-Kutta DG method to solve the compressible Euler equation in Lagrangian framework, and employ a nodal solver to obtain the nodal velocity and numerical fluxes across element boundaries. The physical variable and nodal position are updated in this step. Secondly, the adaptive mesh topology optimization technique, which includes the mesh refinement, edge collapse operation and mesh regularization, is implemented to eliminate the highly distorted elements and improve the mesh quality. Thirdly, the conservative remapping algorithm is employed, which can maintain the conservative interpolation of the Lagrangian solution onto the remeshed grid. The present indirect ALE DG scheme can ensure the high quality of the mesh by optimizing the topology connectivity, so that the present scheme can successfully simulate complex vortical flow problems for a sufficient simulation time. Due to the inherent Lagrangian nature, the present scheme can naturally track the multi-material flow interface, rather than using algorithms with interface reconstruction or diffuse interfaces. The scheme is validated with several benchmark flow problems. It is demonstrated that the present indirect ALE DG scheme with topological adaptability can accurately simulate flow problems with large fluid deformations and distortions. It can achieve remarkable improvements compared with the conventional Lagrangian DG method with fixed topological connectivity. [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]