Synchronization of single-side locally averaged adaptive coupling and its application to shock capturing

Area of Science:

• Computational physics
• Numerical analysis
• Fluid dynamics

Background:

• Spatiotemporal oscillations in extended systems pose challenges for synchronization.
• Existing methods for controlling these oscillations can be complex or inefficient.

Purpose of the Study:

• To develop a single-sided locally averaged adaptive coupling scheme for system synchronization.
• To analyze coupling and synchronization using image filter construction and numerical dissipation concepts.
• To demonstrate the scheme's effectiveness in suppressing oscillations and capturing shocks.

Main Methods:

• Implementing a single-sided locally averaged adaptive coupling strategy.
• Utilizing control process resolution arguments for sensor selection.
• Adaptively adjusting control sensors based on local oscillation magnitudes.
• Applying the scheme to Navier-Stokes and Burgers' equations.

Main Results:

• The proposed scheme effectively suppresses and controls spatiotemporal oscillations.
• The method provides a powerful approach for shock capturing in simulations.
• Successful demonstration on both Navier-Stokes and Burgers' equations.

Conclusions:

• The single-sided locally averaged adaptive coupling scheme offers an efficient method for synchronizing spatially extended systems.
• This approach enhances numerical stability and accuracy, particularly for shock-related phenomena.
• The adaptive sensor selection mechanism contributes to robust oscillation control.