  This paper aims to simulate viscoplastic flow in a shallow-water regime. We
specifically use the Bingham model in which the material behaves as a solid if
the stress is below a certain threshold, otherwise, it moves as a fluid. The
main difficulty of this problem is the coupling of the shallow-water equations
with the viscoplastic constitutive laws and the high computational effort
needed in its solution. Although there have been many studies of this problem,
most of these works use explicit methods with simplified empirical models. In
our work, to accommodate non-uniform grids and complicated geometries, we use
the discontinuous Galerkin method to solve shallow viscoplastic flows. This
method is attractive due to its high parallelization, h- and p-adaptivity, and
ability to capture shocks. Additionally, we treat the discontinuities in the
interfaces between elements with numerical fluxes that ensure a stable solution
of the nonlinear hyperbolic equations. To couple the Bingham model with the
shallow-water equations, we regularize the problem with three alternatives.
Finally, in order to show the effectiveness of our approach, we perform
numerical examples for the usual benchmarks of the shallow-water equations.
