In this paper, the moving particle simulation(MPS) method and the least squares moving particle semi-implicit(LSMPS) method are compared by numerical verification. The MPS method was developed in 1996 by Koshizuka and Oka in order to solve incompressible flow with free surface. Although the original MPS method was difficult to solve various industrial problems with accuracy and stability, the todayʼs MPS method becomes one of the most popular particle method in the engineering fields by various numerical stabilization techniques. However, since spatial discretization models of the MPS method do not have consistency, the MPS method can not solve mathematically precisely differential equations. In order to solve this problem, the LSMPS method was developed in 2014 by Tamai and Koshizuka. The LSMPS method have arbitrary high-order accurate meshfree spatial discretization schemes, consistent time integration schemes, and generalized treatment of boundary conditions. In this paper, after summaries of the MPS method and the LSMPS method are described, two kinds of numerical verifications are performed for both methods.

This study aim to investigate the mechanism of adhesive locomotion in gastropod. It has been reported by previous study that the significant factors of locomotion mechanism are “propagation of muscular waves” and “interfacial friction against the ground”. Interfacial friction has been considered to be controlled by lifting the pedal up, or dynamic viscoelasticity of mucus. To lift pedal up in appropriate timing, complex signals from the center would be necessary although the mechanism of lifting is simple in kinetics. This study focused on the hypothesis of dynamic viscoelasticity of mucus reported by Denny from the point of view of automatic frictional control similar to the mechanism of locomotion in earthworm. Based on the matter of previous study, a simple mathematical model which captures essential factors obtained by qualitative observations is proposed, and the physical parameters in the model are estimated by quantitative results from careful experiments. It has been verified by numerical calculations with the model that the mutual interaction between flexible muscular contraction waves and nonlinear dynamic viscoelasticity of the mucus can achieve an efficient locomotion. The important result in this study is that two locomotion styles, direct wave and retrograde wave, which has been understood by different mechanism, can be realized by the same mechanism.