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6 Two-dimensional axisymmetric Euler equations Although three-dimensional CFD calculations are state of the art, axisymmetric flow solvers are indispensable tools, for cases which allow their applicability. 11) where the vectors and are same as defined in eq. 9. 12) 38 Numerical method The numerical treatment of the geometrical source term source term . 17) The term describes the effect of the relaxation processes on the density and the pressure. 18) where denotes the total number of temperatures to be considered.

57) and are respectively the forward and backward reaction rate coefficients of reaction , where which generally depend on a reaction temperature. 58) The above equation is a general form of law of mass action, which ensures the preservation of total mass during a chemical reaction. The forward reaction rates are generally determined experimentally. 60) where is the activation energy and is a constant. 60 is known as the Arrhenius equation. The parameters , and the activation energy for different reactions are found from experimental data.

In particular, a truly nested sequence of locally adapted cells can be provided, which is required by the applied adaptation criteria, based on multiscale analysis. g. algebraic, elliptic or hyperbolic grid generation methods, by means of BSpline interpolation and approximation. Further details are given in references [8], [9], [10], [11], [12], [13], [14]. The computational domain is initially tessellated by a coarse multiblock structured grid. As basic element types, quadrilaterals and hexahedra are employed in two and three space dimensions, respectively.