One of the crucial questions in the management and mitigation of the consequences of a severe accident in light water reactors (LWR) is how to cool and stabilize the molten corium. For several designs of LWR, a deep pool of water is foreseen in the lower drywell of the containment. In the case of the failure of the reactor pressure vessel, the core melt materials will be discharged into the pool. By contact with water, it will fragment, solidify and settle on the bottom forming a porous debris bed. A two-dimensional continuum model of the deposition and relocation of particles is described in this paper. The mathematical model is based on a hyperbolic system of partial differential equations determining the distribution of the flowing layer depth and the depth-averaged velocity component tangential to the sliding bed. Because of the hyperbolicity of the system, successful implementation of a solver is challenging, notably when large gradients of the physical variables appear, e.g., for a moving front in the flowing layer or possibly formed shock waves during the deposition. In this paper, several numerical methods are applied to solve the system and compared, including the first-order upstream difference scheme, as well as the Roe’s Riemann solver, and high-resolution NOC (Non-Oscillatory Central Differencing) schemes, in which several TVD (Total Variation Diminishing) limiters and reconstruction methods are applied. The implemented solver has provided promising results, which are verified with analytical solutions in the steady state. The spatial convergence is also reported and quantified with the use of the grid convergence index (GCI). The performed simulations with this modeling approach give some useful insights for the study of the most critical parameters influencing granular bed formation process. It will contribute to the enhancement of the capabilities of the system code COCOMO simulating real reactor applications and providing more realistic data.