Combustion of a single, resolved carbon particle is studied using a novel numerical approach that makes use of an overset grid. The model is implemented into the framework of a compressible Direct Numerical Simulation (DNS) code. A method to artificially reduce the speed of sound is presented. For Mach numbers lower than 0.1 this method may dramatically improve numerical efficiency without affecting any physical aspects except for the acoustics. The ability of the model to simulate solid fuel combustion is demonstrated and all parts of the model are validated against experimental and numerical data. A sensitivity of the carbon conversion rate to selected parameters (diffusion coefficients and homogeneous and heterogeneous kinetics) is investigated. A strong dependence on the oxygen diffusivity is observed and explained.