A Comparative Study of Dam-Break Problem over a Sandy Bottom by an Unstructured Finite Volume Method

The study described in this work focuses on the dam-break problem over a sandy bed. The goal is to analyze the effects and reactions of various parameters involved in the problem. The problem is mathematically modeled using a coupled model and a non-capacity model. To solve the mathematical model numerically, an unstructured finite volume method is employed. This method allows for the discretization of the problem domain into a mesh of cells, where the conservation equations are solved at the cell level. In order to achieve second-order accuracy in both space and time, the MUSCL method is used for spatial discretization, while the Runge–Kutta method is used for time integration. One particular aspect of the numerical implementation is the treatment of the source term, which is handled using an original approach. This treatment ensures the accurate representation of the physical phenomena involved in the dam-break problem. To enhance the accuracy of the results and reduce computational time, an adaptive mesh is employed. This means that the mesh is dynamically refined or coarsened in regions of interest based on certain criteria, allowing for a higher level of accuracy in those areas while saving computational resources in less critical regions. The study considers several cases, likely involving different initial conditions, boundary conditions, or parameter values. The results obtained from these simulations are presented and analyzed, highlighting the differences observed for different computational times.