Mathematical models are a suitable tool for surface irrigation design. The EDOSIM model, as a surface irrigation simulation-optimization model, utilizes simulation with the volume balance model and meta-heuristic optimization. In this study, with the aim of improving the simulation of the advanced phase in the EDOSIM model, the Full Hydrodynamic model was replaced by the Volume Balance model for furrow irrigation design, leading to the development of the EDOSIM-HD model. The Saint-Venant equations were discretized using the implicit Preissmann’s finite difference scheme and transformed into a set of nonlinear equations in the form of a system of equations. The resulting system of equations was linearized using the Newton-Raphson method and solved using the Sparse matrix method. The results were compared with the SIRMOD software to validate the simulation. Using the particleswarm solver of the MATLAB software optimization toolbox, the inflow rate as a decision variable was used to optimize the hydraulic objective function consisting of efficiency, adequacy, and uniformity. The results in the experimental field showed that in the initial simulation with an inflow rate of 1.4 lps, important irrigation times, infiltration volume, performance indicators, profiles, and hydrographs showed a deep percolation loss of about 50 percent of water. Also, the results of the EDOSIM-HD model were closer to the Hydrodynamic model of the SIRMOD software than the EDOSIM model. By optimizing and increasing the optimal flow rate (1.8 lps) compared to the initial inflow rate, the advance, cut-off, depletion, and recession times were reduced, and the required infiltration time remained unchanged. The reduction in infiltration volume was also achieved by applying higher inflow rates in less time. All performance indicators also moved closer to their optimal state. Except for Tail Water Ration (TWR), which showed a slight increase of 11 percent (due to higher inflow rate), was negligible compared to the sharp 22% reduction in Depth Percolation Ratio (DPR), and 10% increase in Application Efficiency (Ea). Totally, according to the performance indicators obtained in the validation with the SIRMOD, the simulation of the EDOSIM-HD model was better than in the EDOSIM model in the advanced phase of furrow irrigation design
