A BDF2-Semismooth Newton Algorithm for the Numerical Solution of the Bingham Flow with Temperature Dependent Parameters

by   Sergio Gonzalez-Andrade, et al.

This paper is devoted to the numerical solution of the non-isothermal instationary Bingham flow with temperature dependent parameters by semismooth Newton methods. We discuss the main theoretical aspects regarding this problem. Mainly, we focus on existence of solutions and a multiplier formulation which leads us to a coupled system of PDEs involving a Navier-Stokes type equation and a parabolic energy PDE. Further, we propose a Huber regularization for this coupled system of partial differential equations, and we briefly discuss the well posedness of these regularized problems. A detailed finite element discretization, based on the so called (cross-grid P_1) - Q_0 elements, is proposed for the space variable, involving weighted stiffness and mass matrices. After discretization in space, a second order BDF method is used as a time advancing technique, leading, in each time iteration, to a nonsmooth system of equations, which is suitable to be solved by a semismooth Newton algorithm. Therefore, we propose and discuss the main properties of a SSN algorithm, including the convergence properties. The paper finishes with two computational experiment that exhibit the main properties of the numerical approach.


page 15

page 18


Efficient computation of the sinc matrix function for the integration of second-order differential equations

This work deals with the numerical solution of systems of oscillatory se...

Finite Element Error Analysis of Surface Stokes Equations in Stream Function Formulation

We consider a surface Stokes problem in stream function formulation on a...

Fully coupled mortar-type embedding of one-dimensional fibers into three-dimensional fluid flow

The present article proposes a partitioned Dirichlet-Neumann algorithm, ...

A Dual-Mixed Approximation for a Huber Regularization of the Herschel-Bulkey Flow Problem

In this paper, we extend a dual-mixed formulation for a nonlinear genera...

Numerical simulation of multiscale fault systems with rate- and state-dependent friction

We consider the deformation of a geological structure with non-intersect...

Preferential stiffness and the crack-tip fields of an elastic porous solid based on the density-dependent moduli model

In this paper, we study the preferential stiffness and the crack-tip fie...

Coupled-Cluster Theory Revisited

We propose a comprehensive mathematical framework for Coupled-Cluster-ty...

Please sign up or login with your details

Forgot password? Click here to reset