Narrow Results

Different permutations of the single and the two-fold dam-break flow have been investigated using the mesh-free smoothed-particle hydrodynamics and the experimental setup. The free-surface deformation in the case with the wet bed for five different downstream water heights has been investigated and respective numerical and experimental results were presented. The results demonstrate that the increase of the water height over the wet bed leads to the reduction of the flow front velocity. Effect of considering or omitting the dam gate during the numerical simulation has also been examined, which proves that the simulations including the dam gate show improved agreement with the experimental results. Influence of the three-dimensional cubic, triangular, circular and square cylindrical obstacles and their position on flow characteristics has been investigated. As the distance between the triangular obstacle and the gate increases, a bore is created at the position closer to the top of the triangle. In addition, it is found that larger force is exerted on the circular cylinder in comparison to the square cylinder.

A series of numerical simulations using SPH (Smoothed Particle Hydrodynamics) method were carried out to study the hypervelocity impact of aluminum spheres on multi-plate structures. Both the morphologic characteristics of debris clouds and the damage of intermediate plates were investigated. The possible damage effects of debris cloud threat on back wall were also described qualitatively. Results showed that, comparing with single plate or double-plate structures, the multi-plate structure has higher resistance capacity to the impact from hypervelocity particles. Hence the multi-plate shield structure has a better shielding performance with a reduction in weight of the structure. It provides a promising alternative to the traditional shield in the spacecraft shield design.

In this paper, the numerical convergence, accuracy, stability, efficiency, and reality of the SPH simulation of the impact problem are analyzed by using several different kernel functions. Three are traditional kernel functions of the quadratic function, the cubic bell function, and the quintic function. Others are their corresponding corrected zero-order consistency kernel functions with different denominators. Several unnoticed features in the formulations and the simulation results of the corrected kernel are pointed out. The availability of these kernel functions on the impact problem is discussed. To achieve reality, an unphysical adhesive phenomenon is avoided by introducing three separation conditions.

In this paper, based on the basic principle of the SPH method’s kernel approximation, a new kernel approximation was constructed to compute first-order derivative through Taylor series expansion. Derivative in Newton’s method was replaced to propose a new SPH iterative method for solving nonlinear equations. The advantage of this method is that it does not require any evaluation of derivatives, which overcame the shortcoming of Newton’s method. Quadratic convergence of new method was proved and a variety of numerical examples were given to illustrate that the method has the same computational efficiency as Newton’s method.

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.

Based on the smoothed kernel approximation of the Smoothed Particle Hydrodynamics (SPH) method and Taylor series expansion, a new revised scheme for SPH method is proposed which significantly improves its accuracy, especially near the boundaries where the particle points do not entirely cover the compact support domain of kernel function and particles are irregularly distributed. The revised scheme is derived up to the first-and second-order derivatives both in one-dimensional and multi-dimensional cases. In order to demonstrate the ability of the proposed revised scheme, the scheme is applied to the interpolation of functions and the numerical solution of the convection–diffusion equations both in one- and two-dimensional cases.

In this paper, the meshless smoothed particle hydrodynamic (SPH) method is applied for solving the Black–Scholes model for European and American options, which are governed by a generalized Black–Scholes partial differential equation. We use the $𝜃$-method and SPH for discretizing the governing equation in time variable and option pricing, respectively. To validate our SPH method, we compare it with the analytical solution and also the finite difference method. The numerical tests demonstrate the accuracy and robustness of our method.

In this paper, a pure meshless method for solving the time fractional Schrödinger equation (TFSE) based on KDF-SPH method is presented. The method is used for the first time to numerically solve the TFSE. The method utilizes the finite difference method (FDM) to approximate the time fractional-order derivative defined in the Caputo sense. The spatial derivatives are discretized by the KDF-SPH meshless method. Expressions for the kernel approximation and the particle approximation are provided. To ensure the validity and flexibility of the numerical calculations, we conducted numerical simulations of one- and two-dimensional linear/nonlinear time Schrödinger equations (1D/2D TFLSE/TF-NLSE) in both bounded and unbounded regions. We also examined nonlinear time fractional Schrödinger equations that lack analytical solutions and compared our method with other meshless methods. Numerical results show that the proposed method can approximate to the second-order precision in space, which verifies the effectiveness and accuracy of the proposed method.