Abstract

Mathematical Treatment of Exhaust Systems with Acoustic Properties Using Mathlie I. Algorithms

R.Schmid, J.Volkmann, G.Baumann (Department of Mathematical Physics, University of Ulm, Ulm, Germany)

e-mail: schmd@physik.uni-ulm.de

The first part of the two talks is concerned with algorithms applied to examples origin from an exhaust system. The origin of the example is an industrial application in the area of acoustic car design [Bernd Hagerodt, Berechnungen zur akustischen Auslegung von Abgasanlagen in der Fahrzeugentwicklung, ATZ Automobiltechnische Zeitschrift 102 (2000) 1, 50 - 57]. The model equations are determined by conservation of mass, momentum and energy. In addition there exists an equation of state for the ideal gas system. The aim of the examination of this system is to find analytic solutions for the density, velocity and temperature determining the physical properties of the system. Applying computer algebra to these model equations, we demonstrate that solutions can be derived. The tools used to construct the solutions are the Levi-Malzev decomposition and optimal systems of subalgebras. In addition to the acoustic example we examine gas dynamic equations. Both examples serve to demonstrate the practical application of theoretical work. The second part of the talks discusses the solution of the acoustic model.

Section : 12