A Semismooth Newton Solution of the Steady-State Non-isothermal Bingham Flow with Temperature Dependent Nonlocal Parameters

Abstract:

In this paper, we discuss the numerical solution of the non-isothermal steady-state Bingham flow considering that the viscosity and the yield limit variate with temperature. In the present contribution, we focus on the asymptotic limit case of high thermal conductivity. In this case, the energy equation collapses into an implicit energy equation which involves the viscosity and the yield stress functions, while the temperature becomes a constant solution for this equation. Once we obtain the coupled limit system of this energy equation and the classical Bingham variational inequality of the second kind, we propose a mixed formulation for the resulting limit variational inequality and a finite element discretization for the resulting system of PDEs. Next, we develop a semismooth Newton algorithm for the coupled flow model. Finally, we carry on several numerical experiments for validating our method.

Año de publicación:

2021

Keywords:

Fuente:

scopus

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