Development of new solution methods in fluid dynamics based on first integrals of Navier-Stokes equations

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Computational fluid dynamics (CFD) has emerged as an essential investigative tool in nearly every field of technology. Despite a well-developed mathematical theory and available commercial software codes the computation of solutions of the governing equations of motion is still challenging, especially due to the nonlinearity involved. In contrast to the first project which was mainly related to the development of the general theory and its testing by applying the solving procedure to flows of prototypic character, this second part of the project is more focused on selected applications of current scientific relevance, especially on such problems where the use of the first integral of the equations of motion instead of the original Navier-Stokes equations appears to be beneficial. These are in particular: (i) various 2D flow problems with free surface, since a complex formulation of the field equations and a Dirichlet/Neumann formulation of the dynamic boundary condition are available here and (ii) 3D coating flows over cones and half-spheres, using lubrication approximation for reduction of complexity of the problem.Apart from the above, (iii) the formulation of turbulent flows within the framework of the first integral is a general topic requiring a thorough investigation, motivated by the particular importance of turbulent flows in general.