Andre Savitsky

The purpose of this study was to address critical limitations in existing finite-difference schemes for solving convective transfer equations in aero-hydrodynamic calculations, particularly the non-conservative behavior of the widely used Courant-Isaacson-Rees scheme under specific velocity distributions. The methodology involved a comprehensive analysis of finite-difference schemes using the mass conservation equation for transported substances in compressible media. Test calculations were performed on one-dimensional and two-dimensional problems with varying velocity fields, including cases with velocity sign changes and zero-velocity zones. The proposed scheme uses max and min functions to blend positive and negative velocity components. This approach maintains conservation. The findings demonstrate that the traditional Courant scheme loses conservation when velocity signs change, particularly at stagnation points, leading to mass loss or artificial mass generation. In contrast, the new conservative finite-difference scheme maintains exact mass conservation, stability, and symmetry. It performs well with all tested velocity distributions, even in challenging cases where traditional schemes struggle. In conclusion, the developed scheme eliminates non-conservative behavior that affected existing methods, ensuring accurate representation of physical processes in hydrodynamic calculations. The practical implications include the ability to use larger time steps in numerical calculations while maintaining accuracy and stability, making it particularly valuable for complex aero-hydrodynamic simulations involving flow separation, stagnation points, and variable velocity fields.

Water is vital and an essential entity directly and indirectly for all living creatures from their birth, whereas electrical energy has a dominant role in the growth of society in general and for human beings in particular. Optimal use of water and production of electrical energy at minimum cost are potential research challenges. Hydraulic energy is one of the cheapest and the most exploited renewable energy resource for power generation worldwide, and is in line with the seventh United Nations Sustainable Development Goal (SDG 7). The Indus basin is a trans-boundary basin, and its modeling has been a source of interest for scientists and policymakers. Indus Basin Model Revised (IBMR) has many variants, all focusing on optimal use of water for irrigation purposes. In this paper, the modified IBMR model is proposed addressing both agriculture and power generation aspects simultaneously. This model optimizes the Consumer Producer Surplus (CPS) by considering different water inflow probabilities. A parameter has been introduced in the modified objective function to manipulate the supply of water to agriculture and hydropower generation. The proposed model has been implemented in Generic Algebraic Modeling System (GAMS) and case studies have been investigated in presence and absence of power generation. The results obtained show that, with incorporation of hydropower, basin wide income is increased up to 11.83% using 50% exceedance probability, and results are in agreement with reference power generation estimated by National Transmission and Dispatch Company (NTDC). The SDG 7 targets ensure the reasonable, dependable, sustainable and contemporary energy access to all. The current research is focusing on how Pakistan would achieve the SDG 7 targets. By 2040, it is anticipated that Pakistan’s energy mix will have around 40% of hydropower and 16% of renewable energy.