2D Simulation of a wedge impact problem into the Newtonian and Herschel Bulkley Dilatant non-Newtonian fluids, using WCSPH method

The impact problems associated with water entry have important applications in various aspects of naval architecture and ocean engineering. Also the calculation of impact force is favorable to many researchers. The purpose of this study is to simulate the impact problem of a wedge into the Newtonian and also Herschel Bulkley dilatant non-Newtonian fluids using the Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method. Some non-Newtonian fluids, such as dilatant or Herschel Bulkley dilatant fluids can resist against the wedge entry due to their shear thickening effect. In this research a prediction and correction algorithm is used to solve the governing equations. Density correction and also artificial viscosity (which is used only in Newtonian fluids) are used to prevent the numerical instability. To show the validation, ability and robustness of the generated code to capture the free surface in Newtonian and non-Newtonian fluids, the dam break problem with the image boundary condition is simulated. After validating the code and the used method, the impact problem of a wedge with Monaghan repulsive force boundary condition in Newtonian and Herschel Bulkley Dilatant non-Newtonian fluids are investigated and the results of force, pressure coefficient and velocity of the wedge are presented and compared with experiments and also with each other. To save time, the initial values of hydrostatic pressure are imposed as an initial condition of the fluid.