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Finite Element Iterative Methods for the Stationary Double-Diffusive Natural Convection Model
1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China.
Entropy (Basel, Switzerland)
|February 25, 2022
Summary
This study proves the existence and uniqueness of a double-diffusive natural convection model. Three finite element iterative methods are developed, each with varying stability and viscosity conditions for heat and mass transfer analysis.
Area of Science:
- Fluid dynamics
- Heat and mass transfer
- Numerical analysis
Background:
- Natural convection is crucial in many engineering applications.
- Double-diffusive convection involves simultaneous heat and mass transfer.
- Understanding the behavior of such systems is essential for accurate modeling.
Purpose of the Study:
- To establish the existence and uniqueness of solutions for the stationary double-diffusive natural convection model.
- To develop and analyze finite element iterative methods for solving this model.
- To investigate the stability and performance of these methods under different viscosity conditions.
Main Methods:
- Fixed point theorem for proving existence and uniqueness.
- Finite element method for spatial discretization.
- Three distinct iterative schemes (Methods I, II, and III) for solving the resulting algebraic systems.
Main Results:
- The existence and uniqueness of a weak solution are proven using the fixed point theorem.
- Iterative Method I is stable under the uniqueness condition.
- Methods II and III offer stability under progressively stronger conditions, with Method III handling higher viscosity.
Conclusions:
- The developed finite element methods provide effective tools for analyzing double-diffusive natural convection.
- The choice of iterative method depends on the viscosity of the fluid system.
- Numerical experiments validate the theoretical findings on stability and performance across different viscosity regimes.
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