## Section: Scientific Foundations

### Goals: accuracy and efficiency

Accurate predictions of physical quantities are of great interest in fluid mechanics, for example in order to analyze instabilities in reacting flows, predict forces acting on a body, estimate the flow through an orifice, or predict thermal conductivity coefficients. Due to the complex and highly nonlinear equations to be solved, it is difficult to know in advance how fine the spatial or temporal resolution should be and how detailed a given physical model has to be represented. We propose to develop a systematic approach to these questions based on auto-adaptive methods.

We note that most of the physical problems under consideration have a three-dimensional character and involve the coupling of models and extremely varying scales. This makes the development of fast numerical methods and efficient implementation a question of feasibility.