On optimization of technical devices based on a hierarchy of mathematical models

A fuel collector problem is considered as an inverse problem of hydrodynamics: it is necessary to determine the distribution channel geometry of a collector for a uniform fuel distribution. However, the collector profiling based on the 3D stationary Navier-Stokes equations for turbulent flow of an incompressible viscous medium in rough channels requires impractical computational efforts. A hierarchy of mathematical models (1D Navier-Stokes equations for the collector profiling and 3D Navier-Stokes equations for 1D model validation) is used in this paper. It is shown that the hierarchy of models can significantly reduce amount of computational work needed for computing the optimal collector design. The developed approach is of interest for optimizing technical devices for various purposes.