Niveau requis : PhD
Date de début : 1 juin 2020
Durée de la mission : 12 months
Fast linear solvers for non-symmetric systems in incompressible CFD-simulations
Linear solvers are often the most time consuming part of implicit computational fluid dynamics (CFD) solvers for incompressible flows, such as code_saturne . The overall aim of the post-doc position is to contribute fast and reliable linear solvers for the different types of linear systems that arise in the CDO (compatible discrete operators ) discretization of the steady and time-dependent Navier-Stokes equations. Given the positive experience in code_saturne with k-cycle algebraic multigrid methods for symmetric systems (diffusion, Stokes), efficient solvers for non-symmetric systems are of particular interest. Such systems arise in the discretization of the scalar-valued or vector-valued convection-diffusion-reaction equation or the Navier-Stokes system of equations.
Whereas the extension of the existing solver to the convection-diffusion-reaction equation is relatively straightforward, the efficient treatment of the coupled Navier-Stokes system is an open question, at least as far as CDO-discretizations are concerned.
In addition to fast convergence, the developed solutions will have to exhibit good strong and weak parallel scalability, as even in industrial settings, CFD meshes can go beyond 10^9 cells.
Essential competences: C/C++ programming, curiosity and tenacity
Useful competences: distributed parallel computing with MPI, iterative linear solvers
This topic is a collaboration between CERFACS and EDF. The position is located at the Parallel Algorithms team at CERFACS in Toulouse with shared supervision from all project partners. Travel to the EDF offices in the greater Paris region is a possibility.
Contract duration: 12 months
The position is available immediately and will remain open until filled.
 J. Bonelle and A. Ern. Analysis of Compatible Discrete Operator schemes for elliptic problems on polyhedral meshes. ESAIM : Mathematical Modelling and Numerical Analysis, 48(2) : 553—581, 2014.