arXiv subjects

D. Yakoubi

Publications and source records attributed to D. Yakoubi.

3 recordsLinked to original sources

arXiv2026

A new formulation of Discontinuous Galerkin method for interface capturing approaches

In computational fluid dynamics, the numerical simulation of free-surface flows using interface capturing approaches (level set, pseudo-concentration) requires accurate resolution of a transport equation. In the present work, this equation is solved using a new formulation of the Lesaint--Raviart discontinuous Galerkin method, which is particularly suitable for problems without inflow boundaries. The motion is described by the incompressible Navier--Stokes equations with surface tension, discretized using the standard $P2-P1$ Taylor--Hood finite element method in space. Surface tension effects are represented using the so-called Continuum Surface Force model. Finally, the proposed approach is implemented and tested on several benchmarks, including the single rising bubble and the Rayleigh--Taylor instability.

math.NA↗

arXiv2019

Analysis of a time-discrete scheme for the Navier-Stokes/Allen-Cahn model

This paper address the approximation of the dynamic of two fluids with non matching densities and viscosities modeled by the Allen-Cahn equation coupled with the time dependent Navier-Stokes equations. Existence, uniqueness and a maximum principle are obtained for a totally implicit semi-discrete in time formulation. These results are based on an original stabilized fixed point algorithm for which well posedness and convergence is analyzed. Numerical experiments are performed to show the influence of the iterative process.

math.AP↗

arXiv2019

Shear rate projection schemes for non-Newtonian fluids

The operator splitting approach applied to the Navier-Stokes equations, gave rise to various numerical methods for the simulations of the dynamics of fluids. The separate work of Chorin and Temam on this subject gave birth to the so-called projection methods. The basic projection schemes, either the incremental or non-incremental variant (see [1]) induces an artificial Neumann boundary condition on the pressure. By getting rid of this boundary condition on the pressure, the so-call rotational incremental pressure-correction scheme as proposed by Timmermans et al. [2] for Newtonian fluids with constant viscosity gives a consistent equation for the pressure. In this work we propose a family of projection methods for generalized Newtonian fluids based on an extension of the rotational projection scheme. Called shear rate projections, these methods produces consistent pressure when applied to generalized Newtonian fluids. Accuracy of the methods will be illustrated using a manufactured solution. Numerical experiments for the flow past a cylinder, with a Carreau rheological model, will also be presented.

math.NA↗