Study On Smoothed Particle Hydrodynamics Algorithm And A Modified Finite Particle Method With Second Order Kernel Approximation

As the first mesh-free numerical method, Smoothed Particle Hydrodynamics(SPH) was presented in1977. This method has been studied widely since it waspresented. More and more researchers have been focusing their interesting on thistopic. This method has significant advantages in simulating the fluid flows with largedeformation or complex boundary.Based on the detailed analysis of SPH and its modified method (K2_SPH), animproved method is introduced, namely a modified Finite Particle Method withSecond order Kernel approximation (SK2_FPM). The advantages and disadvantagesof SPH, K2_SPH and SK2_FPM are compared through the precision analysis ofdifferent kernel approximation methods and the numerical experiments. The mainconclusions of this study are summaried as follows:Firstly, the basic theory and the corresponding numerical techniques of SPHwere introduced and analyzed systematically, including integral kernel approximationand particle approximation, properties and selection of the smoothed kernel function,artificial viscosity, artificial compressibility and boundary handling method, et al. Inthe meanwhile, the accuracy of the kernel approximation of SPH is deduced andanalyzed in detail, and the behaviors of the kernel function and its derivatives wereobtained under the conditions of particles being distributed regulaly and iregularly.Secondly, based on a modified method of SPH, K2_SPH, an improved kernelapproximation method was presented, namely SK2_FPM. The accuracies of thekernel approximation function and its derivatives of SK2_FPM were analyzedtheoretically. The results show that the accuracy of SK2_FPM is the same as that ofK2_SPH in order, while its predicted results could be better to some extent due toavoiding from the error of the kernel approximation of the function. The numericaltests show that compared to SPH, the accuracy and stability of SK2_FPM areimproved, especially when the particles are distributed iregularly or close to theboundaries.Finally, three classical cases (Poiseuille flow, Couette flow and linear standingwave) were simulated using the SPH, K2_SPH and SK2_FPM methods, respectively. The numerical results comfirmed that compared to the SPH and K2_SPH, theaccuracy and stability of the SK2_FPM were improved. Compared against SPH, thecomputational efficiency of SK2_FPM could be improved to some extent due to itssimpler of linear equation system.