Abdallah Bradji | Searcharxiv

arXiv2023

Homogeneous incompressible Bingham viscoplastic as a limit of bi-viscosity fluids

In this paper, the existence of a weak solution for homogeneous incompressible Bingham fluid is investigated. The rheology of such a fluid is defined by a yield stress $τ_y$ and a discontinuous stress-strain law. This non-Newtonian fluid behaves like a solid at low stresses and like a non-linear fluid above the yield stress. In this work we propose to build a weak solution for Navier stokes Bingham equations using a bi-viscosity fluid as an approximation, in particular, we proved that the bi-viscosity tensor converges weakly to the Bingham tensor.

math.AP↗

arXiv2004

Some Improvements of Convergence Order of Finite Volume Solutions

In this article, we improve the convergence order of some finite volume solutions approximating some second order elliptic problems. We prove that finite volume approximations of order $O(h^{k+1})$, with $k$ integer, can be obtained after $k$ corrections, starting with finite volume solution of order $O(h)$, by using the same matrix and changing only the second member of the original system. This is done for general smooth second order elliptic problems in one dimension and for second order elliptic problems of the form $-Δu+pu=f$, with Dirichlet conditions. Numerical tests justifying theoretical results and showing the efficiency of the method are presented. The idea used behind these results is the one of Fox's difference correction in the context of finite difference method.

math.NA↗