ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

A TVD scheme has been implemented on a non structured 3D finite volume formulation for solving the Euler equations. To simultaneously, achieve adequate accuracy in smooth flows, high resolution at flow discontinuities and to avoid spurious oscillations, different flux limiter functions are applied in a wave-to-wave basis. This technique implements compressive limiter functions in waves from the family two to four and diffusive limiter functions in waves one and five, thus, the robustness of the TVD scheme is preserved and a reduction of the numerical viscosity can be achieved. This sort of adaptive scheme has satisfactorily been applied to the slip interface between two parallel flows and to supersonic flows over an airfoil and a blunted bi-conic body. The code has also been used to compute the flow around re-entry bodies.

Finite rate chemical effects can be introduced accounting for source terms in the Euler equations. Such source terms representing the chemical kinetics and vibration relaxation are often large, making the algorithm too stiff to be advanced explicitly. To avoid this stiffness an implicit treatment of the sources terms is implemented. To describe the hydrogen-oxigen-nitrogen mechanism 13 chemical species and 33 one step chemical reactions are employed.