Meso-combustion can be defined as the combustion regime where the involved lenghts scales are close but slightly larger than the quenching distance of the flame, tipically smaller than a cm. By taking advantage of the high energetic density of liquid hydrocarbons, it would become possible to build small-sized combustion-based long-lived lighter electrical power systems. However combsution phenomena at these meso-scales have their own shortcomings. Indeed, by decreasing the system size, the usual phenomenological balance betwenne chemical reactions, mixing, turbulence and heat transfer is changed. In the present work, we focus on the DNS calculation of a cubic meso-combsution chamber of 8 x 10 x 8 mm3. This works presents the implementation of the numerical strategy used, with a specific attention to the no-slip wall compressible boundary condition. We then present an analysis of this particular reactive flow. The results are useful for future modeling of such a combustor.