Synchronization of Single-Side Locally Averaged Adaptive Coupling and Its Application to Shock Capturing

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Abstract
We propose a single-sided locally averaged adaptive coupling scheme for the synchronization of spatially extended systems. Coupling and synchronization are analyzed from the viewpoint of image filter construction and numerical dissipation. Single-sided locally averaged coupling is introduced based on the resolution argument of control process. Control sensors are adaptively selected and automatically adjusted according to the magnitude of local oscillations. We demonstrate that the present scheme can effectively suppress and control spatiotemporal oscillations and, thus, provide a powerful approach for shock capturing. Both the Navier-Stokes equation and Burgers' equation are used to illustrate the idea.