A stabilized MFE reduced-order extrapolation model based on POD for the 2D unsteady conduction-convection problem

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Heat transfer

Background:

• Accurate modeling of unsteady conduction-convection problems is crucial in various engineering applications.
• Existing reduced-order models often struggle with maintaining stability and accuracy for complex flow dynamics.
• The need for computationally efficient yet reliable methods for solving these problems is significant.

Purpose of the Study:

• To develop a novel stabilized mixed finite element reduced-order extrapolation (SMFEROE) model.
• To reduce the number of unknowns in the model for enhanced computational efficiency.
• To rigorously analyze the mathematical properties and validate the numerical performance of the proposed SMFEROE model.

Main Methods:

• Proper orthogonal decomposition (POD) technique for dimensionality reduction.
• Stabilized mixed finite element (MFE) formulation for robust solution.
• Mathematical analysis of existence, uniqueness, stability, and convergence.
• Numerical simulations for validation.

Main Results:

• Establishment of a novel SMFEROE model with significantly fewer unknowns.
• Demonstration of the existence, uniqueness, stability, and convergence of the SMFEROE solutions.
• Validation of the model's correctness and dependability through numerical simulations.

Conclusions:

• The developed SMFEROE model provides an efficient and accurate approach for solving 2D unsteady conduction-convection problems.
• The model's mathematical properties are rigorously proven, ensuring reliable predictions.
• Numerical results confirm the model's effectiveness and potential for practical applications.