Convection and total variation flow

François Bouchut (1) , David Doyen (1) , Robert Eymard (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

The flow of a Bingham fluid with inertial terms is simplified into a nonlinear hyperbolic scalar conservation law, regularised by the total variation flow operator (or 1-Laplacian). We give an entropy weak formulation, for which we prove the existence and the uniqueness of the solution. The existence result is established using the convergence of a numerical approximation (a splitting scheme where the hyperbolic flow is treated with finite volumes and the total variation flow with finite elements). Some numerical simulations are also presented.

Mots clés: Bingham fluid; hyperbolic scalar conservation law; total variation flow; 1-Laplacian; entropy for-mulation; finite volumes; finite elements

Domaines: Analyse numérique [math.NA]

François Bouchut, David Doyen, Robert Eymard. Convection and total variation flow. IMA Journal of Numerical Analysis, 2014, 34 (3), pp.1037-1071. ⟨10.1093/imanum/drt039⟩. ⟨hal-00770644v5⟩