Loading...
4 results
Search Results
Now showing 1 - 4 of 4
- Generalized Kelvin-Voigt equations for nonhomogeneous andincompressible fluidsPublication . Antontsev, Stanislav N.; de Oliveira, H.B.; Khompysh, KhonatbekIn this work, we consider the Kelvin-Voigt equations for non-homogeneous and incompressible fluid flows with the diffusion and relaxation terms described by two distinct power-laws. Moreover, we assume that the momentum equation is perturbed by an extra term, which, depending on whether its signal is positive or negative, may account for the presence of a source or a sink within the system. For the associated initial-boundary value problem, we study the existence of weak solutions as well as the large-time behavior of the solutions. In the case the extra term is a sink, we prove the global existence of weak solutions and we establish the conditions for the polynomial time decay and for the exponential time decay of these solutions. If the extra term is a source, we show how the exponents of nonlinearity must interact to ensure the local existence of weak solutions.
- Kelvin-Voigt equations perturbed by anisotropic relaxation, diffusion and dampingPublication . Antontsev, S. N.; de Oliveira, H.B.; Khompysh, Kh.The purpose of this work is the analysis of the existence and uniqueness of weak solutions to a Kelvin-Voigt problem wherein the viscous and relaxation parts of the stress tensor are given by distinct power-laws. We assume that the viscous and relaxation terms may be fully anisotropic and that the momentum equation is perturbed by a damping term which may also be fully anisotropic. In the particular case of considering this problem with a linear and isotropic relaxation term, we prove the existence of global and local weak solutions. The uniqueness of weak solutions is established in this case as well. For the full anisotropic problem, we show how all the anisotropic exponents of nonlinearity and all anisotropic coefficients must interact in order to be established global and local in time a priori estimates. (C) 2019 Elsevier Inc. All rights reserved.
- Parabolic turbulence k-epsilon model with applications in fluid flows through permeable mediaPublication . de Oliveira, H.B.In this work, we study a one-equation turbulence k-epsilon model that governs fluid flows through permeable media. The model problem under consideration here is derived from the incompressible Navier-Stokes equations by the application of a time-averaging operator used in the k-epsilon modeling and a volume-averaging operator that is characteristic of modeling unsteady porous media flows. For the associated initial- and boundary-value problem, we prove the existence of suitable weak solutions (average velocity field and turbulent kinetic energy) in the space dimensions of physics interest.
- Existence for a one-equation turbulent model with strong nonlinearitiesPublication . de Oliveira, H.B.; Paiva, A.The purpose of this article is to improve the existence theory for the steady problem of an one-equation turbulent model. For this study, we consider a very general model that encompasses distinct situations of turbulent flows described by the k-epsilon model. Although the boundary-value problem we consider here is motivated by the modelling of turbulent flows through porous media, the importance of our results goes beyond this application. In particular, our results are suited for any turbulent flows described by the k-epsilon model whose mean flow equation incorporates a feedback term, as the Coriolis force, the Lorentz force or the Darcy-Forchheimer's drag force. The consideration of feedback forces in the mean flow equation will affect the equation for the turbulent kinetic energy (TKE) with a new term that is known as the production and represents the rate at which TKE is transferred from the mean flow to the turbulence. For the associated boundary-value problem, we prove the existence of weak solutions by assuming that the feedback force and the turbulent dissipation are strong nonlinearities, i.e. when no upper restrictions on the growth of these functions with respect to the mean velocity and to the turbulent kinetic energy, respectively, are required. This result improves, in particular, the existence theory for the classical turbulent k-epsilon model which corresponds to assume that both the feedback force and the production term are absent in our model.