Numerical simulation of thermally convective viscoplastic fluids by semismooth second order type methods

We study the numerical solution of thermally convective viscoplastic fluids with yield stress. Following [12], a Bousinessq approximation of the convection effect is considered. The resulting coupled model is then regularized by means of a local regularization technique. After discretization in space, a second order BDF method is used for the time discretization of the regularized problem, leading, in each time iteration, to a nonsmooth system of equations, which is amenable to be solved by generalized Newton methods. A semismooth Newton algorithm with a modified Jacobian is constructed for the solution of the discrete systems. The paper ends with a detailed computational experiment that exhibits the main properties of the numerical approach.

► We propose a local regularization approach of the convective viscoplastic flow problem based on primal and dual information. ► We developed a combined BDF-semismooth Newton algorithm for the numerical solution of the problem. ► Superlinear convergence of the proposed method is numerically verified.