RESUME / ABSTRACT  


High Order Finite Volume Methods for the Advection-Reaction-Diffusion Equation


by


Janusz Pudykiewicz







The system of conservation laws governing reactive flow describes a complex system in which the fluid dynamics is coupled with local processes such as chemical reactions or phase changes. In mathematical terms the reactive flow equations consist of Navier-Stokes equations coupled with continuity equations for a number of interacting scalar fields characterizing the chemical composition of fluid. In order to solve this very complex set of equations in an efficient manner we first discretise the spatial derivatives using a finite volume techniques. The system of semi-discrete ordinary differential equations obtained following this procedure is then solved using the third and fourth order Runge-Kutta schemes. A discussion of constraints which are required in order to maintain the monotonicity of the the scheme will be also presented. The effect of chemical reactions is represented without the operator splitting.