A complete and accurate analysis of the complex spatial structure of heterogeneous hydrocarbon reservoirs requires detailed geological models, i.e. fine resolution models. Due to the high computational cost of simulating such models, single resolution up-scaling techniques are commonly used to reduce the volume of the simulated models at the expense of losing the precision. Several multi-scale techniques have also been developed for simulating heterogeneous reservoirs including those in which a limited number of blocks down-scale, i.e. splitting coarse blocks into fine cells around the well-zones in the case of simulation of hydraulic fracturing. In these cases, locally computed basis functions are employed to construct a global solver at a coarse-scale such as wavelet- and kernel-based up-scaling techniques. In this paper, a novel/robust 2D block-ordering system is presented, which enables solving multi-resolution up-scaling fluid flow simulations. The results will be described for a simple model, and fluid flow equations will be developed in order to show the structure of transmissibility matrix. It is confirmed that with a developed block-ordering system not only the accuracy of history match increases but also the CPU time decreases.