#### Collapse of Viscoplastic Fluid under Gravity

Viscoplastic fluid is a particular kind of Non-Newtonian fluid. The typical model of this kind of fluid is the Herschel-Bulkley model.

where \tau,\gamma,K are the stress, strain rate, and consistency, respectively. n is a scalar. \tau_c is called the yield stress. If the stress is less than \tau_c, there is no local deformation, thus the fluid would behave like solid. Therefore, the collapse of viscoplastic fluid will form some special final shape. We simplify this problem in a 2D geometry, and conduct both theoretical analysis and numerical simulations to solve this problem. Below is an example of the comparison.

Liu, Y., Balmforth, N.J., Hormozi, S. and Hewitt, D.R., Two–dimensional viscoplastic dambreaks, Journal of Non-Newtonian Fluid Mechanics, 2016 238(65–79)