A Discontinuous Galerkin and Semismooth Newton Approach for the Numerical Solution of Bingham Flow with Variable Density

This paper is devoted to the study of Bingham flow with variable density. We propose a local bi-viscosity regularization of the stress tensor based on a Huber smoothing step. Next, our computational approach is based on a second-order, divergence-conforming discretization of the Huber regularized Bi...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors González-Andrade, Sergio, Méndez Silva, Paul E
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 18.04.2023
Subjects
Constitutive equations
Constitutive relationships
Discretization
Divergence
Galerkin method
Mathematical analysis
Newton methods
Regularization
Stability analysis
Viscoplastic materials
Yield stress
Online AccessGet full text

Cover

More Information
Summary:This paper is devoted to the study of Bingham flow with variable density. We propose a local bi-viscosity regularization of the stress tensor based on a Huber smoothing step. Next, our computational approach is based on a second-order, divergence-conforming discretization of the Huber regularized Bingham constitutive equations, coupled with a discontinuous Galerkin scheme for the mass density. We take advantage of the properties of the divergence conforming and discontinuous Galerkin formulations to incorporate upwind discretizations to stabilize the formulation. The stability of the continuous problem and the full-discrete scheme are analyzed. Further, a semismooth Newton method is proposed for solving the obtained fully-discretized system of equations at each time step. Finally, several numerical examples that illustrate the main features of the problem and the properties of the numerical scheme are presented.
ISSN:2331-8422