In this study, we intend to develop a high-order numerical approach using the immersed-boundary method to solve problems with complex and moving boundaries such as biological locomotion (animal swimming and flying) and biomedical flow systems. The basic idea is to use the compact finite-difference scheme to resolve the flow field and a higher-order forcing scheme to treat the immersed boundaries. In this work, the one-dimensional formulation of the numerical approach is presented and is tested extensively for its convergence. Such tests are necessary before more complicated tests in 2D/3D. An overall third-order accuracy is achieved as desired. Extension to higher dimensions is ongoing.

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