Holomorphic embedding method for large-scale reverse osmosis desalination optimization.

Area of Science:

• Computational Mathematics
• Chemical Engineering
• Applied Mathematics

Background:

• Nonlinear differential equations are crucial for modeling complex systems in fields like chemical and energy engineering.
• Traditional numerical methods for these problems can be computationally intensive, limiting large-scale design applications.

Purpose of the Study:

• To introduce a fast and flexible holomorphic embedding-based method for solving nonlinear differential equations.
• To apply this novel method to the industrial problem of reverse osmosis desalination design.

Main Methods:

• The proposed method approximates solutions using an approximation function within segmented domains, avoiding discrete point iteration.
• It leverages holomorphic embedding for efficient computation of solutions.

Main Results:

• The method achieved a six-fold increase in computational efficiency compared to traditional solvers for reverse osmosis desalination.
• It maintained the same level of accuracy as conventional methods while significantly reducing computation time.
• Over 11 million nonlinear differential equations were solved for various design parameters.

Conclusions:

• The holomorphic embedding-based method offers a computationally efficient and accurate approach for large-scale optimal design problems.
• This technique shows substantial promise for accelerating engineering design processes, particularly in desalination.
• The method's flexibility and speed make it suitable for diverse industrial applications involving nonlinear differential equations.