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Abstract

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