DFG Projekt Dr. Scholle: Entwicklung neuer Loesungsmethoden in der Fluidmechanik auf der Grundlage erster Integrale der Navier-Stokes-Gleichung

Development of new solution methods in fluid dynamics based on first integrals of Navier Stokes equations

Projektleiter: Dr. Markus Scholle

Projektzeitraum: 01.04.2012 bis 31.03.2015

Projektmittel: 227.350 €

Mittelgeber: DFG

Abstract

Computational fluid dynamics (CFD) has emerged as an essential investigative tool in nearly every field of technology. Despite a well -developed mathematical theory and available commercial software codes the computation of solutions of the governing equations of motion is still challenging, especially due to the nonlinearity involved. Recently, a first integral of the two-dimensional Navier-Stokes equations has been constructed leading to a set of equations the differential order of which is lower than that of the original Navier-Stokes equations.

It is the aim of this project

1. to extend the present theory to three-dimensional and unsteady flow.

2. to develop methods for solving the first integral of the Navier-Stokes equations instead of solving the original Navier-Stokes equations. These are expected to be much more effcient while capturing the essential detail.

The accuracy and effciency of the new methods compared to conventional ones will be demonstrated via examples.