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The Smoothed Particle Hydrodynamics (SPH) method is among the numerical methods that have attracted the attention of many researchers in recent years. This method as a Lagrangian method based on the movement of particles is also one of the meshless methods. In this method, the initial location or distribution of particles can play an important role in reducing numerical errors and its computational efficiency. In this research, based on wave modeling, which is one of the most conventional hydraulic phenomena, and using previous modeling experiences, six optimal and common distributions of particles including square distribution (SC), Triangular distribution, distribution based on WVT algorithm, distribution based on Greedy algorithm, Hexagonal distribution and Fibonacci distribution based on Fibonacci al-gorithm have been investigated. Based on the results of the pressure, velocity and the free surface level of the fluid in the location of the reference gauges of the laboratory model, it was determined that the square, triangular, WVT, Greedy, Hexagonal and Fibonacci distributions have a modeling error equal to 13.85%, 13.75%, 12.63%, 13.24%, 9.07% and 9.37%, respectively, and the two primary hexagonal and Fibonacci distributions have a modeling error of less than 10%, and in other words, it has the best performance in using the SPH method in order to improve the efficiency of the computational model.

The Smoothed Particle Hydrodynamics (SPH) method is among the numerical methods that have attracted the attention of many researchers in recent years. This method as a Lagrangian method based on the movement of particles is also one of the meshless methods. In this method, the initial location or distribution of particles can play an important role in reducing numerical errors and its computational efficiency. In this research, based on wave modeling, which is one of the most conventional hydraulic phenomena, and using previous modeling experiences, six optimal and common distributions of particles including square distribution (SC), Triangular distribution, distribution based on WVT algorithm, distribution based on Greedy algorithm, Hexagonal distribution and Fibonacci distribution based on Fibonacci al-gorithm have been investigated. Based on the results of the pressure, velocity and the free surface level of the fluid in the location of the reference gauges of the laboratory model, it was determined that the square, triangular, WVT, Greedy, Hexagonal and Fibonacci distributions have a modeling error equal to 13.85%, 13.75%, 12.63%, 13.24%, 9.07% and 9.37%, respectively, and the two primary hexagonal and Fibonacci distributions have a modeling error of less than 10%, and in other words, it has the best performance in using the SPH method in order to improve the efficiency of the computational model. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that in many cases, science can predict the future. Based on the available information of the real system, the scientific method for future prediction is to develop a virtual model with similar response to the real system. The classical models are usually presented with a set of linear / nonlinear, ordinary / partial differential equations. The necessary and sufficient condition for future prediction is given by three axioms; A model with accurate description of the real system, perfect knowledge of the initial conditions, and perfect knowledge of present and future values of inputs to the system. In reality, none of these conditions are perfectly realizable and each axiom has some uncertainties. The failure in future prediction is exactly due to these uncertainties. The model description as the major axiom is always accompanied with uncertainty and although, there is no way to vanish it, there are different methods to reduce it. Soft computing is one of the recent approaches in the past few decades, not only used for modeling of systems in the field of engineering systems, but also used in the field of human sciences such as economy, management and social sciences.

Infiltration is considered as one of the most important soil parameters in the design and evaluation of furrow irrigation systems. Water is infiltrated through the wetted perimeter when it reaches a given point in the furrow until it recedes. The depth of infiltrated water at a given point, therefore, is a function of opportunity time, wetted perimeter, and soil intake characteristics (Oyonarte et al., 2002). Thus, in-depth knowledge of how the initial (e.g. initial water content) and boundary conditions (such as water head and wetted perimeter) of a furrow can act on the infiltration process is essential. Previous studies show that cumulative infiltration in furrow irrigation is highly affected by the water head and initial water content. In furrow irrigation, water infiltration into the soil is two-dimensional, both vertically and laterally (Bautista et al. 2014). Gravity forces are dominant in vertical infiltration, while suction forces dominate horizontal/lateral infiltration. Suction forces largely depend on soil matric potential, which is a function of the soil texture and structure, and play an important role in soil moisture retention, sorptivity, essential for plant growth, and lateral infiltration. Knowledge of lateral infiltration and edge effect is essential for designing furrow irrigation systems because many researchers have found that more than 60% of total infiltrated water is through the side walls of furrows. Several studies have been carried out to determine how initial and boundary conditions may affect the cumulative and lateral infiltration in furrow irrigation, but the combined effect of water head and initial water content on infiltration process is not investigated yet. Therefore, the main objective of this study is to investigate the combined effect of various initial (i.e., irrigation interval or initial water content) and boundary (i.e., water level or the wetted perimeter) conditions on the cumulative and lateral infiltration.

In this paper, it is shown that in many cases, science can predict the future. Based on the available information of the real system, the scientific method for future prediction is to develop a virtual model with similar response to the real system. The classical models are usually presented with a set of linear / nonlinear, ordinary / partial differential equations. The necessary and sufficient condition for future prediction is given by three axioms; A model with accurate description of the real system, perfect knowledge of the initial conditions, and perfect knowledge of present and future values of inputs to the system. In reality, none of these conditions are perfectly realizable and each axiom has some uncertainties. The failure in future prediction is exactly due to these uncertainties. The model description as the major axiom is always accompanied with uncertainty and although, there is no way to vanish it, there are different methods to reduce it. Soft computing is one of the recent approaches in the past few decades, not only used for modeling of systems in the field of engineering systems, but also used in the field of human sciences such as economy, management and social sciences. [ABSTRACT FROM AUTHOR]