Numerical tools turn to be critical for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depend on the numerical tool quality and the design of efficient numerical schemes still receives important attention to provide robust and accurate solutions. In this study, we propose a comparative study between the efficiency of two volume finite numerical codes with second-order discretization implemented and different method to solve the non-conservative shallow water equations. The distinct methods are the MUSCL [Monotonic Upstream-Centered Scheme for Conservation Laws] and the MOOD [Multi-dimensional Optimal Order Detection], which optimise the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criterion where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. We benchmarked the numerical code against a 1D dam-break test to demonstrate the numerical code capacities to deal with irregular and discontinuous bathymetry in no dry zones, for both MUSCL and MOOD techniques. Using a simple one-dimensional analytical benchmark, ’Single wave on a sloping beach’, we show that the classical 1D shallow-water system can be accurately solved by the finite volume method, in particular, the numerical code equipped with the MOOD technique that provided better approximation with sharper shock and less numerical diffusion. For the code validation, we use the case study of Tohoku-Oki 2011 tsunami. Through a 2D simulation, DART and GPS buoys records were reproduced with MUSCL technique. A 1D simulation was performed to compare the MUSCL and the MOOD synthetic results, demonstrating that the quality of the solution may genuinely interfere with the scenario one can assess.