A very high-order accurate finite volume scheme on polygonal meshes for 3D incompressible flows with general slip conditions on curved boundaries
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Slip conditions are one of the most challenging boundary conditions in computational fluid dynamics for modelling several physical phenomena, such as micro-fluid flows, super-hydrophobic surfaces, bubbles rising in multiphase flows, and polymer processing. On curved walls, the formulation of slip bound- ary conditions must consider the local boundary curvature for correctly imposing vanishing tangential stress, which increases their complexity. On the numerical side, the conventional treatment of curved walls relies on curved meshes to eliminate the geometrical mismatch between the physical and computa- tional boundaries and achieve high-orders of convergence. However, sophisticated meshing algorithms are necessary, in addition to cumbersome quadrature rules on curved elements and complex non-linear transformations often required for the employed discretisation method. In the present work, a recently developed technique [1, 2, 3], referred to as reconstruction for off-site data (ROD) method, is employed to impose general slip boundary conditions on curved walls within a finite volume scheme on polygonal meshes. A reformulation of the general slip boundary conditions is firstly carried out based on a local orthonormal basis to allow a straightforward application of the ROD method, similar to scalar boundary conditions. Several benchmark test cases of fluid flow problems in three-dimensional arbitrary curved domains are addressed and confirm that the proposed method effectively achieves up to the eighth-order of convergence.
