Bingham-plastic model: The visco-plastic fluids have an “un-sheared” or “solid” zone under their yield stress point and their constitutive law represents a multi-valued function. In fact under their yield stress point they behave like a solid and above this point they behave like a Newtonian fluid with constant viscosity. The constitutive law for these fluids is given by:
In this paper, the solid zone is approximated via a highly viscous fluid whose viscosity is much (say, times) greater than the main fluid. This condition is used as long as stress is below the yield value, that is, . Above this limit, the following relations are used:
In fact, is calculated according to the gradient of velocity for each particle at each time-step and then it is used in the above criterion.
3.1.3 Herschel-Bulkley model. The constitutive law for the…show more content… A reasonably agreement is observed between the obtained result by the proposed ACISPH method, experimental [] and previous SPH results [21] which show the accuracy of the numerical method implemented.It is observed in Bingham model, that the flow tends to the fixed-point’ with increasing time. It is known that in Bingham dam-breaking model with increasing time, the shear stress is below the yield stress in the flow domain. It was also reported in other researches [24,10, rrt]. For a general greater velocity of the front, the slight discrepancy with the experimental results can be seen; primarily, this can be due to the differences in the experimental setup. Unfortunately the geometry is not perfectly clear in reference[].In the second , the treatment of the boundaries is not perfect, because no-slip boundary conditions in SPH represent a challenging problem yet. The final shape of the front and of the shear zone are finally well