Simulation of the 3D viscoelastic free surface flow by a parallel corrected particle scheme

In this work, the behavior of the three-dimensional （3D） jet coiling based on the viscoelastic Oldroyd-B model is investigated by a corrected particle scheme, which is named the smoothed particle hydrodynamics with corrected symmetric kernel gradient and shifting particle technique （SPH_CS_SP） method. The accuracy and stability of SPH_CS_SP method is first tested by solving Poiseuille flow and Taylor-Green flow. Then the capacity for the SPH_CS_SP method to solve the viscoelastic fluid is verified by the polymer flow through a periodic array of cylinders. Moreover, the convergence of the SPH CS_SP method is also investigated. Finally, the proposed method is further applied to the 3D viscoelastic jet coiling problem, and the influences of macroscopic parameters on the jet coiling are discussed. The numerical results show that the SPH_CS_SP method has higher accuracy and better stability than the traditional SPH method and other corrected SPH method, and can improve the tensile instability.

A Coupled ISPH-TLSPH Method for Simulating Fluid-Elastic Structure Interaction Problems

A fully Lagrangian algorithm for numerical simulation of fluid-elastic structure interaction(FSI)problems is developed based on the Smoothed Particle Hydrodynamics(SPH)method.The developed method corresponds to incompressible fluid flows and elastic structures.Divergence-free(projection based)incompressible SPH(ISPH)is used for the fluid phase,while the equations of motion for structural dynamics are solved using Total Lagrangian SPH(TLSPH)method.The temporal pressure noise can occur at the free surface and fluid-solid interfaces due to errors associated with the truncated kernels.A FSI particle shifting scheme is implemented to produce sufficiently homogeneous particle distributions to enable stable,accurate,converged solutions without noise in the pressure field.The coupled algorithm,with the addition of proposed particle shifting scheme,is able to provide the possibility of simultaneous integration of governing equations for all particles,regardless of their material type.This remedy without need for tuning a new parameter,resolves the unphysical discontinuity beneath the interface of fluid-solid media.The coupled ISPH-TLSPH scheme is used to simulate several benchmark test cases of hydro-elastic problems.The method is validated by comparison of the presented results with experiments and numerical simulations from other researchers.