A mixed corrected symmetric SPH (MC-SSPH) method for computational dynamic problems

Abstract

In this work, a mixed corrected symmetric smoothed particle hydrodynamics (MC-SSPH) method is proposed for solving the non-linear dynamic problems, and is extended to simulate the fluid dynamic problems. The proposed method is achieved by improving the conventional SPH, in which the constructed process is based on decomposing the high-order partial differential equation into multi-first-order partial differential equations (PDEs), correcting the particle approximations of the kernel and first-order kernel gradient of SPH under the concept of Taylor series, and finally making the obtained local matrix symmetric. For the purpose of verifying the validity and capacity of the proposed method, the Burgersʼ and modified KdV–Burgersʼ equations are solved using MC-SSPH and compared with other mesh-free methods. Meanwhile, the proposed MC-SSPH is further extended and applied to simulate free surface flows for better illustrating the special merit of particle method. All the numerical results agree well with available data, and demonstrate that the MC-SSPH method possesses the higher accuracy and better stability than the conventional SPH method, and the better flexibility and extended application than the other mesh-free methods.