Analysis and numerical simulation of viscoelastic flows
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This paper presents the development of spectral element methods to simulate unsteady flows of viscoelastic fluids using a closed-form differential constitutive equation. The generation and decay Poiseuille planar flows are considered as benchmark problems ...
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In this work we will introduce and analyze the Arbitrary Lagrangian Eulerian formulation for a model problem of a scalar advection-diffusion equation defined on a moving domain. Moving from the results illustrated in our previous work [J. Num. Math. 7 (199 ...
A numerical model is presented for the simulation of complex fluid flows with free surfaces in three space dimensions. The model described in Maronnier et al. (J. Comput. Phys. 1999; 155(2):439) is extended to three dimensional situations. The mathematical ...
There is a growing interest in developing numerical tools to investigate the onset of physical instabilities observed in experiments involving viscoelastic flows, which is a difficult and challenging task as the simulations are very sensitive to num ...
We investigate adaptive finite element methods for low Mach, steady, laminar combustion. The finite element discretization of the flame equations involves least squares control of streamline derivatives and pressure-velocity coupling as well as a new shock ...
In order to better understand the sources of numerical instabilities occurring in the simulation of time-dependent flows of viscoelastic fluids at high Weissenberg numbers, we have used various types of linear stability analyses. In complement to the limit ...
The purpose of the present article is to provide a theoretical analysis heterogeneous model coupling ordinary differential equations (ODEs) and partial differential equations (PDEs), providing a local-in-time existence result for the solution. The heteroge ...
This work is dedicated to the construction of numerical techniques for the models of viscoelastic fluids that result from polymer kinetic theory. Our main contributions are as follows: Inspired by the interpretation of the Oldroyd B model of dilute polymer ...