Selçuk Journal of Applied Mathematics

 Selçuk Journal of
  Applied Mathematics


Summer-Autumn, 2001
  Volume  2
  Number 2

Research Center of 
  Applied Mathematics

 SJAM Summer-Autumn 2001, Volume 2 - Number 2

Problem solving for scientific computing: data modelling instead of algorithms?

Victor G. Ganzha1, Dmytro Chibisov1, Evgenii V. Vorozhtsov2

1 Institut für Informatik, Technische Universität München, D-80290 München, Germany;
   email: ;

2 Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk 630090, Russia;

Received: December 20, 2001

We present an approach to rapid solving of modelling problems for fluid dynamics. We show how the problem solving process in fluid dynamics can be expressed through the incremental successive data modelling on the basis of graphical description techniques like class diagrams in UML. As will be shown, in contrast to algorithmic approach the data modelling in terms of objects and relations among them enable one to describe the physical and mathematical properties and relations of the fluid flow. At the same time, it provides the necessary facilities to obtain the numerical code automatically from an abstract problem description. Moreover the tool prototype called GROOME to numerical code generation on the basis of graphical object oriented description techniques is presented. In order to demonstrate these facilities we consider a fluid dynamics problem involving shock waves in two-dimensional inviscid gas flow.


Key words
Euler equations, finite volume method, object-oriented modelling, problem solving environment

Mathematics Subject Classification (1991): 65M10, 68C20

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