Efficient Approximation with Space Filling Quadtrees: Application to Phase Equilibria in Binary Mixtures

Area of Science:

• Computational Chemistry
• Chemical Engineering
• Numerical Analysis

Background:

• Thermophysical property calculations are crucial for chemical process design.
• Existing iterative methods can be slow and prone to convergence failures, especially for mixtures.
• Efficient function approximation is needed to overcome these limitations.

Purpose of the Study:

• To develop a non-iterative numerical approximation technique for thermophysical properties.
• To achieve high accuracy and computational efficiency in function representation.
• To demonstrate the method's applicability to vapor-liquid equilibria calculations.

Main Methods:

• Utilizing adaptive subdivision with quadtrees and bi-Chebyshev expansions.
• Constructing a numerical approximation within a rectangular domain.
• Employing bisection steps for rapid leaf identification in the approximation data structure.

Main Results:

• The approximation function is evaluated in less than a microsecond.
• Achieved accuracy is on the order of the noise in the original function.
• For COSMO-SAC, the approximation is over 2000x faster with negligible deviations (<10⁻⁸).

Conclusions:

• The proposed method offers a highly efficient and non-iterative approach for thermophysical property approximation.
• This technique significantly accelerates calculations for models like COSMO-SAC.
• The method provides a robust alternative to traditional iterative solvers, enhancing reliability and speed.