Directional ghost node approach to elliptic PDEs with arbitrary immersed interfaces

  • Nitti, Alessandro (Polytechnic University of Bari)

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The numerical solution of elliptic PDEs on simple computational meshes in the presence of Immersed Boundaries (IBs) has been addressed by a broad variety of methods [1]. This work lies in the class of second-order accurate finite difference solvers on staggered Cartesian grids. It delivers a novel approach which is supposed to gather the desirable features of IB methods with moderate computational expense. The directional ghost node method allows to: (i) preserve the second-order accuracy of the underlying numerical scheme, (ii) enforce Robin-type interface conditions on both closed and open boundaries, (iii) handle the proximity and the intersection of multiple immersed interfaces, (iv) numerically uncoupled non-simply connected sub-domains. Consistent enforcement of the interface conditions is achieved through a segregated discretization of the boundary-condition derivatives along the interface-aligned and transverse directions at each grid-line intersection. The effectiveness of the proposed method is tested against case studies drawn from different engineering scenarios, including potential flow past a Joukowski airfoil, path planning in a circular maze, and computation of the added-mass coefficient of a submarine model. REFERENCES [1] Mittal, R., & Seo, J. H. (2023). Origin and evolution of immersed boundary methods in computational fluid dynamics. Physical review fluids, 8(10), 100501.