Spectral/hp element modelling and high-order mesh generation for 3D time-dependent flow
From 16/01/2017 to 19/01/2017 | Universidad Politécnica de Madrid, Madrid, Spain
- Presenters: Spencer Sherwin and Joaquim Peiro
- Assisted by: Mike Turner, Julian Marcon and David Moxey
- Special lecture by: David Kopriva.
In this short course we will provide an introduction to high-order spectral/hp element methods and their application to the time-dependent incompressible and compressible Navier Stokes equations. We will first motivate the need and benefits of these high-order compact schemes and provide details of how to formulate the building blocks for elliptic scalar problems. These building blocks can then be used to develop semi-implicit solvers for the incompressible Navier-Stokes equations. This formulation will also be adopted to demonstrate the application of flow stability analysis. We will then discuss how to construct explicit discretizations of the compressible flow equations and motivate the application of adaptive methods based on interpolation theory and the adjoint equations. Finally, we will provide an introduction to high-order mesh generation. The lectures will also be supplemented by a series of tutorials on each topic based upon the open-source package Nektar++ (www.nektar.info). To complement this course Professor David Kopriva has also agreed to provide an introduction to the summation by parts concept and present his perspective on implementing spectral element discretization of the compressible flow equations.