International Journal of Computational Methods

High velocity impact welding (HVIW) involves processes like the impact of metal structures and strong fluid-structure interactions with complex phenomena such as interfacial waves and jet generation. It is very difficult to model the HVIW process with typical physics well captured due to the large deformation and moving interfaces, while the associated mechanisms inherent in HVIW are also not well understood. In this paper, the HVIW process is simulated using a modified smoothed particle hydrodynamics (SPH) model, in which the kernel gradient correction is used to improve computational accuracy and an artificial stress term is used to ease stress instability during the welding process. The mechanisms in HVIW are investigated, and typical phenomena including the wavy interface, jet formation, interfacial temperature and pressure distribution are captured. It is demonstrated that with proper impact welding velocity and initial welding angle, the modified SPH method can well reproduce the morphology evolution of the welding interface from straight to wavy and further to wavy interface with vortex shedding. Based on comprehensive numerical data from SPH simulations, the weldability windows for the HVIW are obtained and are compared with experimental and theoretical results. Welding limits for HVIW are also discussed in detail.

In order to improve the computational efficiency and spatial resolution of smoothed particle hydrodynamics (SPH) method, a SPH method with space-based variable smoothing length has been developed. In addition, since linked-list search algorithm cannot handle the variable smoothing length problems, an improved linked-list search algorithm and a balanced alternating digital tree (B-ADT) search algorithm have been proposed. The performance of the two improved search algorithms has been evaluated in detail. These methods have been used to simulate two cases of water entry impact and two cases of gas–liquid two-phase flow. The results show that, by using space-based variable smoothing length algorithm, computational cost can be greatly reduced and the numerical accuracy is maintained.

To reduce the error on the boundary and improve computational accuracy, the normal derivative of radial basis function (RBF) is introduced into the reproducing kernel particle method (RKPM), and the Hermit-type reproducing kernel particle method (Hermit-type RKPM) is proposed. The Hermit-type RKPM approximation function is constructed and the governing equation of the elasticity problems is deduced. Then the Hermit-type RKPM is applied to the numerical simulation of the elasticity problems, and the results illustrate that the proposed method is more accurate than the RKPM.

Water entry problems are very common in engineering and sciences. When objects move with relatively high speed, bubble cavities will be generated, and the behavior of moving objects will also be affected conversely. In this paper, the water entry problems are studied using smoothed particle hydrodynamics (SPH) method, which has special advantages in modeling free surfaces, moving interfaces. First, an improved fluid–solid interface treatment algorithm is presented, whose effectiveness is validated by a water entry of a buoyant cylinder. Then the water entry with different velocities and directions are researched. It is found that the velocities and angles of the moving objects will affect the movement of the object greatly, and the SPH model can give optimal predication of these corresponding conditions.

The Rayleigh–Taylor instability (RTI) problem is one of the classic hydrodynamic instability cases in natural scenarios and industrial applications. For the numerical simulation of the RTI problem, this paper presents a multiphase method based on the moving particle semi-implicit (MPS) method. Herein, the incompressibility of the fluids is satisfied by solving a Poisson Pressure Equation (PPE) and the pressure fluctuation is suppressed. A single set of equations is utilized for fluids with different densities, making the method relatively simple. To deal with the mathematical discontinuity of density in the two-phase interface, a transitional region is introduced into this method. For particles in the transitional region, a density smoothing scheme is applied to improve the numerical stability. The simulation results show that the present MPS multiphase method is capable of capturing the evolutionary features of the RTI, even in the later stage when the two-phase interface is quite distorted. The unphysical penetration in the interface is limited, proving the stability and accuracy of the proposed method.

In mesh-free methods, discrete equations are built according to physics information of micro-bodies arbitrarily spread in vicinal space. As the requirements about topology of micro-bodies are reduced, simulations with Lagrangian approach may be easier even with large distortions. Owing to the insufficiency of topological information, there is a challenge for mesh-free method to reflect physics especially as discontinuities exist. Based on the physical laws and developing trend of numerical simulation, a new mesh-free systematic method PECM (physics evoked cloud method) with excellent applicability has been developed. High fidelity to physics of the method is demonstrated through five one-dimensional challenging problems in which strong discontinuities exist.

The present work is dedicated to the modeling of viscous flow past a NACA0012 foil fixed in a current below a free surface. To this end, the ${\delta }^{+}$-smoothed-particle hydrodynamics (SPH) model has been adopted. This SPH model prevents the inception of the numerical tensile instability in the flow region characterized by negative pressure since a tensile instability control (TIC) has been included. In the TIC, a pressure differencing formulation (PDF) has been adopted for the momentum equation in the flow region characterized by negative pressure. In order to completely remove the numerical noise in the vorticity field, in this work, the PDF is also applied for the region with positive pressure, but except for the free-surface region in order to ensure the free surface stability when wave breaking occurs. The mechanism of PDF being able to eliminate the numerical noise in the vorticity field is also briefly analyzed. In order to reduce the nonconservation of total momentum induced by the PDF, a particle-shifting technique (PST) is implemented in each time step for regularizing the particle position. In the numerical results, ${\delta }^{+}$-SPH results are validated by the experimental data and other verified numerical results. Improvements of the results of ${\delta }^{+}$-SPH with PDF with respect to the ones without using PDF are demonstrated. Parametrical studies based on the ${\delta }^{+}$-SPH model regarding the breaking and non-breaking waves generated by the flow past a submerged foil are also carried out.

Based on the fundamental theory of smoothed-particle hydrodynamics (SPH), a feasible algorithm for fluid–solid coupling on interface is applied to describe the dynamic behavior of fluid and solid by utilizing continuum mechanics governing equations. Numerical simulation is conducted based on the proposed SPH model and the fluid–solid interface coupling algorithm, and good agreement is observed with the experiment results. It is shown in the results that the present SPH model is able to effectively and accurately simulate the free-surface flow of fluid, deformation of the elastic solid and the fluid–solid impacting.

In the present study, the moving particle semi-implicit (MPS) method and finite element method (FEM) coupled method is developed for the 3D fluid–structure interaction (FSI) problems. Herein, the MPS method is employed for the simulation of fluid domain while the FEM approach is used for the analysis of structural domain. For the implementation of the coupled approach, we proposed a mapping algorithm to transfer quantity values between the particles of flow field and the elements of structural field. In this mapping algorithm, the nonmatching refinement levels of both domains are permitted, which implies that the much larger size of element can be used in the FSI simulation and the computational efficiency can be improved. With the benefit of the proposed MPS–FEM coupled method, the 3D FSI problem of dam-break flow impacting onto the flexible wall is numerically investigated. The evolutions of free surface and the impacting loads on the wall are compared against those regarding rigid tank. In addition, the deformation and the strength behaviors of the flexible wall are exhibited.

In this paper, a multiphase Godunov-type smoothed-particle hydrodynamics (MGSPH) method is presented for simulating multi-fluid Riemann problems with complex equations of state (EOSs). In this method, single-phase Riemann solvers are used between particles with same phase, and interfacial approximate Riemann solvers are introduced on the interfacial particle pairs. Various combinations of single-phase and interface approximate Riemann solvers are comparatively studied to find out the best combination for MGSPH. Five examples are presented to verify MGSPH method.

In the landslide-induced debris flow problem, the soil slope experiences three stages: slope instability, debris flow and deposition. This study develops a three-dimensional smoothed particle hydrodynamics model which adopts elastoplastic viscous constitutive relation to simulate this complex process. The Drucker–Prager model with nonassociated plastic flow rule is implemented for slope instability and deposition and constant viscosity is used for propagation stage. The model is validated with laboratory dry-granular dam-break experiments. Good agreements are found between the simulated results and the laboratory data on both the shape evolution and the velocity field. Then, we use the model to study the Yigong avalanche after detailed discussion of model parameters, the time of duration, deposited scope and estimated velocity essentially agree with site survey. Thus, the model is able to simulate instability and flow of dense granular materials at both experimental and field scale, and it could be a powerful tool for the landslide-induced debris flow study.