We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

Learn more about Indigenous Education and Cultural Services

Search the:

Apply Donate Crisis Centre

November 18, 2015

Speaker: Dr. Driss Yakoubi, Postdoctoral Fellow, Université Laval

Title: A Model For Two Coupled Fluids: Numerical Approximation by Finite Element

Abstract: This talk focuses on numerical analysis and simulation of two models in fluid mechanics.

The first one deals with a coupled two-fluid Reynolds-averaged Navier-Stokes (RANS) turbulence model, which couples the steady Navier-Stokes Equations (NSE) with the equation for the turbulent kinetic energy (TKE). The link includes the eddy viscosities, the boundary condition on the interface and the source term in the energy equation, which is only in $L^1$ and then presents a high complexity. We change the initial system to a new variational system, whose eddy viscosities and source term are regularized by convolution. We perform a full finite element discretization of an iterative linearization procedure and prove its convergence to the continuous scheme for large enough eddy viscosities.

The second part concerns two immiscible Newtonian fluids where the surface tension at the fluid interface has to be accounted for. The surface tension is modeled as a Continuum Surface Force (CSF). The CSF model allows us to treat the dynamic boundary condition at the interface implicitly. The main difficulty in this problem is that, of course, each fluid flows through a time-dependent domain. I will investigate the existence of a solution in the non-realistic case where the velocity satisfies homogeneous boundary conditions. Next, I will propose a discretization of it by the characteristics method in time and standard conforming finite elements in space.