Numerična simulacija toka ob porušitvi pregrade z uporabo modificirane sheme Runge-Kutta z validacijo

This paper presents a numerical scheme based on the second-order Runge‒Kutta method, combined with finite-difference spatial discretisation, for simulating dam-break flows governed by the one-dimensional SaintVenant equations. The proposed method introduces a flow decomposition coupled with an artificial viscosity term inspired by previous work, in order to improve the numerical stability and accuracy of the results. A comparative analysis is carried out between the classical scheme and the modified Runge‒Kutta second-order scheme using an analytical solution as a reference. The results show that the modified scheme is significantly better matched to the analytical solution. The method is then applied to several dam failure scenarios including complex conditions such as triangular and trapezoidal obstacles, sloping bottoms and dry bed/wet bed transitions. The numerical results are compared with experimental data and simulation results published in the specialist literature. In all cases, the modified scheme performs better confirming its robustness and accuracy for modelling the propagation of dam burst waves under complex hydraulic conditions.