A novel integration of regret-based methodology and bankruptcy theory for waste load allocation.

Developing a suitable index for Waste Load Allocation (WLA) is essential for both industrial polluters and environmental organizations. Identifying the index that best describes the quality conditions of the river is the main concern of this study. To achieve this purpose, a novel framework incorporating a regret-based index and a bankruptcy-based approach to address the impacts of low water quality and pollutant locations within the WLA are introduced. The framework includes a simulation-optimization model to minimize river quality regret for environmental organizations and total treatment cost for industrial polluters, employing Nash bargaining theory for conflict resolution. Additionally, a new bankruptcy approach, the Namin's rule, is proposed for redistributing the River Quality Regret Index among industrial polluters. Applying this methodology to data from the KhoramAbad River, a sensitivity analysis reveals that while there is no significant difference between the methodology and fuzzy risk when polluters are close, the methodology provides more accurate results as the distance between polluters increases. When the distance between two pollutants was 20 km, the sum of WLA was evaluated to be 300 kg per day higher than that in the compared method, potentially enhancing environmental justice.

A three-dimensional non-hydrostatic coupled model for free surface - Subsurface variable - Density flows.

A three dimensional coupled numerical model has been developed for incompressible density-driven free surface and saturated porous media flows. For free surface, a time-averaged Navier-Stokes equation has been used whereas Darcy's law has been utilized in porous media flow. The algorithm has been based upon a staggered finite volume scheme on a Cartesian grid that solves the 3D non-hydrostatic density-dependent Darcy equation in one step and complete 3D Navier-Stokes equations in two major steps based on a projection method. The 3D system is decomposed into a series of 2D vertical plane sub-systems which have been solved individually by a direct matrix solver. An iteration procedure can be deployed to achieve the fully 3D implicitness of the solution where high density gradients or sharp variation of free surface elevation is present. An efficient, simple and stable algorithm has been proposed to track the free surface elevation in a Cartesian coordinate system within which the water surface position has not been restricted to a specific layer. The model has been validated using five test cases to simulate integrated transient free surface and porous media flows where fluid density effects as well as the water surface gradient have a considerable effect on the velocity field. Two of the examples involve modeling free surface flow (Wave Reflection test) and a phreatic line prediction (Cone of depression test). Two other test cases involve significant contrasts in fluid density including 3D density-driven flow in porous media and 3D lock exchange tests. The final test of a salinity interface involved a complicated scenario consisting of a density contrast in both saturated porous media and free surface flow, subjected to injection and pumping simulated simultaneously using an integrated domain. Close agreement between numerical results and experimental data demonstrates the capability of the model for the coupled simulation of 3D density-driven flow in both integrated free surface and saturated porous media including freshwater recharge, saltwater discharge, hydrodynamic dispersion and turbulence effects.