Recovery-Based Error Estimator for Natural Convection Equations Based on Defect-Correction Methods.

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Heat transfer

Background:

• Natural convection (NC) equations are crucial for modeling fluid flow driven by density differences.
• High Rayleigh numbers in NC simulations lead to convection dominance, posing significant computational challenges.
• Existing numerical methods struggle with accuracy and efficiency for these complex scenarios.

Purpose of the Study:

• To develop an adaptive defect-correction method (DCM) for solving natural convection equations.
• To address the convection dominance problem associated with high Rayleigh numbers.
• To enhance the accuracy and computational efficiency of numerical solutions for NC.

Main Methods:

• Proposed an adaptive defect-correction method (DCM) tailored for natural convection equations.
• Integrated a novel recovery-type posteriori error estimator, leveraging gradient recovery and superconvergent theory.
• Applied the method to overcome challenges of large computations and solution gradient discontinuities.

Main Results:

• Demonstrated that the recovery-based error estimator effectively bounds the true error.
• Validated the reliability and efficiency of the proposed adaptive DCM.
• Confirmed the stability, accuracy, and efficiency through various numerical investigations.

Conclusions:

• The adaptive defect-correction method provides a robust solution for natural convection problems.
• The integrated error estimator enhances the precision and reliability of numerical simulations.
• The method offers a significant improvement in computational efficiency for high Rayleigh number flows.