Karol Cascavita: Thursday 23 March at 3 pm, A415 Inria Paris.
Bingham fluids model are a group of non-Newtonian fluids with a wide and diverse range of applications in industry and research. These materials are governed by a yield limit stress, which determines solid- or fluid-like features. This behavior is model by a viscoplastic term that introduces a non-linearity in the constitutive equations. Hence, the great difficulty to solve the problem, due to the non-regularity along with the a priori unknown solid-fluid boundaries. The yield stress model considered is the Bingham model, which despite being the simplest viscoplastic model is still considered a hot problem to solve theoretically and experimentally.
The approaches proposed to handle this difficulties are mainly regularization methods and augmented Lagrangian algorithms. The first technique adds a regularization parameter to smooth the problem avoiding the singularity in the rigid zones. This procedure permits an straightforward implementation at the expense of a deterioration on the accuracy. The remaining technique solves the variational problem by uncoupling nonlinearities and the gradients.
All the above methods are mainly approximating solutions in a finite-element or a finite volume framework. In this work, we focus on a different discretization technique named the Discontinuous Skeletal method, introduced recently by Di Pietro et al. The aim of this work is to perform an h-adaptation to enhance the prediction of the solid-liquid boundary, exploding the salient features of the DISK method. For instance: supports general meshes, face and cell-based unknowns formulation, high-order reconstruction operator, locally conservative.
