Study On Some Important Numerical Algorithms For Smoothed Particle Hydrodynamics

SPH(smoothed particle hydrodynamics) is a meshless numerical method, which breaks through the dependence of the traditional numerical method on the grid and has been widely used in the field of fluid. However, some disadvantages still exist in conventional SPH method. For example, conventional SPH method has been frustrated with limited choice of the kernel function, uniformly distributed particles in the process of numerical simulation, unreasonable far field boundary condition, and failing to model flows around a body. Based on such considerations, this paper proposes a kerner gradient free(KGF) SPH method and an iterative particle homogenization method, which improve the numerical accuracy and stability. Also, this paper proposes a mixed non-reflection characteristic boundary condtion which is used to calculate the far field boundary condition when simulating flows around a body.Firstly, based on comparison and analysis of the conventional SPH method and FPM(finite particle method), this paper proposes kernel gradient free(KGF) SPH, the precision and stability of which are tested by some one-dimensional problems. The equations of motion for incompressible flows are descreted using KGF-SPH. The density re-initialization function and projecting point method are described in detail. Couette flow is used to test KGF-SPH and correlative numerical methods. The results show that KGF-SPH mthod is more accurate than SPH method, and more stable than FPM method. And, the KGF-SPH method can accurately simulate Couette flow.Secondly, when the Lagrangian-form Navier–Stokes equations are solved, the movement of particles results in non-uniform particle distribution which severely reduces the stability and accuracy of the calculation results. To solve this problem, an iterative particle homogenization method is proposed and applied in KGF-SPH simulation. The lid-driven shear cavity flow is numerically simulated by KGF-SPH with iterative particle homogenization method. The results show that although iterative particle homogenization method increases computational cost, it can ensure the uniformity of particle distribution, and improve the numerical stability and accuracy effectively.Thirdly, there is no suitable method to calculate the far field boundary condition in SPH simulation at present. Based on the characteristic boundary conditions proposed by Giles and Thompson, this paper proposes a mixed characteristic boundary condition for the SPH numerical simulation. One- and two-dimensional incompressible flows with a perturbation at the initial moment are modeled by the mixed characteristic boundary condition, and the results demonstrate that the mixed characteristic boundary condition can effectively suppress the reflected wave on the far field boundary, and improve the convergence rate.Finally, these methods developed in this paper are used to simulate flows around a body. When flows around a body are simulated, the improved SPH pre-processing method is used to distribute initial particles. The results show that these methods developed by this paper can accurately simulate flows around a body and obtain reasonable numerical results. The iterative particle homogenization method can keep particle distribution more uniform and obtain more accurate results than particle shifting technology. The mixed characteristic boundary condition not only has feasible numerical stibitly but also effectively suppresses the reflection of waves on the far-field boundary.