DECOUPLING PDE COMPUTATION WITH INTRINSIC OR INERTIAL ROBIN INTERFACE CONDITION.

Area of Science:

• Numerical analysis
• Computational physics
• Scientific computing

Background:

• Decoupled numerical methods are essential for complex multi-domain, multi-physics problems.
• Traditional interface conditions can introduce inaccuracies in decoupled simulations.
• Existing methods often lack a robust theoretical foundation for multi-modeling.

Purpose of the Study:

• To derive a mathematically and physically justified interface condition for decoupled numerical methods.
• To introduce a new approximate intrinsic or inertial type Robin condition.
• To establish a general framework for effective decoupled numerical methods in multi-modeling.

Main Methods:

• Investigating numerical approximation and decoupling stages.
• Tracking information transmission across interfaces in a multi-modeling problem.
• Deriving and validating a novel intrinsic Robin condition for semi-discrete models.

Main Results:

• An approximate intrinsic or inertial type Robin condition was derived.
• This new condition is mathematically and physically justified, outperforming classical Robin conditions.
• An equivalent semi-discrete model based on the new condition was introduced.

Conclusions:

• The novel intrinsic Robin condition offers a superior approach for decoupling in multi-physics applications.
• The developed framework enables the design of more effective decoupled numerical methods.
• Numerical experiments validate the effectiveness of this new decoupling strategy.