Surface Irrigation Flow Simulation Using Parabolic Hydrodynamic Equations
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Solution Overview
Problem
Current simulation methods for surface water flow movement in surface irrigation suffer from high relative errors between simulated and measured data, leading to poor accuracy and complex numerical solution processes.
Innovation Solution
A simulation method using improved full hydrodynamic equations, expressed as ∂ζ∂t=∂∂x[Kw∂ζ∂x]+∂∂y[Kw∂ζ∂y]-1g{∂∂x[(ζ-b)CxKw]+∂∂y[(ζ-b)CyKw]}-ic, with numerical solutions performed via a finite volume method, to obtain simulated surface water depth and vertical integral average velocities, incorporating surface relative elevation, border surface roughness, and infiltration rate data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If classical full hydrodynamic equations are used for simulation, then the simulation process can be performed, but the numerical solution process becomes complicated and simulation accuracy decreases
Solution Approach 1:
The patent transforms the classical hyperbolic full hydrodynamic equations into a parabolic form by changing the mathematical parameters and structure of the equations. This parameter transformation simplifies the numerical solution process while maintaining simulation accuracy, directly resolving the contradiction between complexity and precision.
Solution Approach 2:
The patent replaces the complex numerical solution methodology with a simplified parabolic equation approach. By substituting the traditional hyperbolic equation system with a parabolic form, the computational complexity is reduced while preserving the essential physical relationships, thereby improving both ease of solution and accuracy.
2Measurement precision
If related simulation methods are used, then the simulation can be performed, but the relative error between simulated and measured data is large
Solution Approach 1:
The patent modifies the mathematical parameters and structure of the hydrodynamic equations from hyperbolic to parabolic form. This parameter change enables the simulation results to better match measured data, significantly reducing relative errors and improving both accuracy and reliability simultaneously.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly reduces relative errors and enhances simulation accuracy and efficiency, making it more suitable for surface irrigation systems by employing a parabolic mathematical property compared to classical hyperbolic equations.
Implementation Method 1
g represents a gravitational acceleration with the unit of m/s2
Implementation Method 2
n is the border surface roughness coefficient with the unit of /m1/3
Data Source
AI summary
A simulation method of a surface water movement process in surface irrigation, comprising: acquiring surface relative elevation data, border surface roughness coefficient data and surface water infiltration rate data of a target border check; substituting surface relative elevation data, border surface roughness coefficient data and surface water infiltration rate data into improved full hydrodynamic equations, and performing numerical solution on improved full hydrodynamic equations to obtain a simulated surface water depth value and simulated values of vertical integral average velocities of an irrigation water flow in x-coordinate and y-coordinate directions of a certain measurement site in the target border check at a certain time; and obtaining simulated values of unit width discharge of the irrigation water flow in x-coordinate and y-coordinate directions, respectively according to simulated surface water depth value and simulated values of the vertical integral average velocities of the irrigation water flow in x-coordinate and y-coordinate directions.