Wave propagation and run-up in U-shaped channel bays are studied here in the framework of the quasi-1D Saint-Venant equations. Our approach is numerical, using the momentum conserving staggered-grid (MCS) scheme, as a consistent approximation of the Saint-Venant equations. We carried out simulations regarding wave focusing and run-ups in U-shaped bays. We obtained good agreement with the existing analytical results on several aspects: the moving shoreline, wave shoaling, and run-up heights. Our findings also confirm that the run-up height is significantly higher in the parabolic bay than on a plane beach. This assessment shows the merit of the MCS scheme in describing wave focusing and run-up in U-shaped bays. Moreover, the MCS scheme is also efficient because it is based on the quasi-1D Saint-Venant equations.

Identification of post-mortem interval started from the time when the dead body was found. The main question is to identify the time of death. In reality, the task is complicated since many local factors are involved in the process of decomposition. In most cases, the decomposition process is done by certain local insects that consume the biomass completely. This study uses a mathematical model for the post-mortem interval involving diptera and rabbit corpses as the biomass, based on experimental data from references. We formulate a type of logistic model with decaying carrying capacity only with diptera. The post-mortem interval is shown as the end period of consumption when larvae have entirely consumed the biomass. It is shown from the simulation that the decomposition lasts for 235 hours. The diptera are shown to disappear completely, leaving the remaining corpse after 120 hours.

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