Computational fluid dynamics (CFD) is the numerical simulation of flow fields through the approximate solution of the governing partial differential equations (PDEs) of
mass, momentum and energy conservation coupled with the appropriate relations for thermodynamic and transport properties. CFD is a wide field of interest in modern
mathematics and engineering with a consistently increasing importance in the design and/or optimisation of industrial processes, mainly in aerodynamics, but also in
chemical engineering, material sciences and even in medicine. A major model to describe fluid mechanical phenomena are the Navier-Stokes equations. Throughout the last
decades a lot of effort has been made to improve the quality of their approximate solution. This, not surprisingly, has led to a bunch of already available CFD programs.
So, is there really a need to develop yet another flow solver?
This talk will answer that question in the affirmative by outlining what are the deficiencies of most modern CFD software, or, more generally speaking, of most modern
software which applies Finite Element Methods (FEM) to discretise the problem`s underlying PDEs. These deficiencies include, but are not restricted to,
·      poor exploitation of Peak rates of modern (parallel) computer hardware
·      only qualitative reasonable, but quantitatively insufficient accuracy
·      missing information on the level of accuracy of the simulation`s result in terms of the unknown exact solution
·      far too long calculation times for `real world` problems.
Furthermore the ideas will be covered which have been developed at the Chair of Prof. Turek to overcome these shortcomings. The philosophy behind this FEAST FEM-package
is as following:
·      explicit usage of high performance capabilities of modern computer hardware
·      encapsulation of parallelisation and load-balancing within the FEAST library
·      avoidance of known weaknesses with parallel multigrid methods (w.r.t. complex geometries, grid distortions) by applying hierarchical
solvers, so-called generalised multigrid / domain decomposition schemes a.k.a. ScaRC (Scalable Recursive Clustering)
·      accurate discretisation using FEM
·      incorporation of adaptivity concepts / error control
These ideas are now to be employed, tested and extended to build high performance applications in CFD and CSM (see also talk of H. Wobker).
The aim of my project will be to combine and adopt these ideas with methods for the solution of the 2-D nonstationary incompressible Navier-Stokes equations. In a first
step, the equations will be discretised separately in space and time (Fractional-Step-Theta-scheme, conforming Q1/Q1 FEM-approach). A discrete projection method of
second oder will be applied to decouple the space-problem into scalar subproblems which on their parts will then be treated by the highly efficient solver routines
partially already available within FEAST. For stabilisation purposes of the convective term an upwinding method will be used.
In a next step, the numerical performance of this Q1/Q1 solvers has to be analysed. Further, an attempt will be made to answer the question whether encapsulating
parallelisation and load-balancing into FEAST - and not leaving it to the application - is really feasible. Moreover, interlocking with the concepts of error control
and adaptive grid refinement developed by M. Grajewski (see other talk) has to be achieved.
Further development will possibly include topics as implementing more complex finite elements (conforming, non-conforming), more sophisticated stabilisation techniques
like FCT/TVD and extensions like turbulence modelling, Boussinesq model, maybe even some multi-phase flow. Ultimately, the aim is to release FEASTFLOW, the successor of
FEATFLOW.