WEAK SOLUTIONS TO THE EULER AND NAVIER-STOKES EQUATIONS
Magnus Svärd, University of Bergen
June 18, 2015, 2:30 pm, NASA Langley, Bldg 1268, Rm 1069
Abstract:
In an ideal world, an engineer could set up a CFD numerical simulation that to within a predefined tolerance approximates the true solution of the underlying PDE system. At present, this is impossible, even if we only consider the basic flow equations without any further modelling. It is not merely the accuracy that is impossible to predict a priori. We cannot know if we have approximated any solution, let alone the true solution, on a sufficiently fine grid. We do not even know if there exists any solutions for a general flow case.
In this talk I will discuss weak solutions to the Euler and Navier-Stokes equations. Weak solutions are a first step towards a more complete well-posedness theory which in turn is a prerequisite for predictive CFD. Throughout the years, a plethora of schemes have been designed with various properties. I will focus on the non-linear stability properties entropy, kinetic energy and positivity, and their relations to weak solutions.
Bio:
Magnus Svärd is a Professor of Applied and Computational Mathematics at the University of Bergen, Norway. His research is numerical analysis of the compressible Euler and Navier-Stokes equations with the aim to design robust and highly accurate schemes.
Current work at NASA Langley include non-linear stability analysis of far-field boundary conditions.