The set of equations governing reactive flow in spherical geometry 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 on an icosahedral mesh defined in Cartesian coordinates. The system of ordinary differential equations obtained following this procedure is then solved using several different numerical methods including 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. In particular, it will be shown that the solver is both mass conserving and nonoscillatory which make it ideally suited for the solution of the complex reactive flow problems in spherical geometry. This property will be illustrated by the examples of application of the scheme for the simulation of tropospheric chemistry. In conclusion, the advantages of using geodesic grids for the simulation of reactive flows will be summarized.