A reconstruction-based cell-centered high-order finite volume method for incompressible viscous flow simulation on unstructured meshes

•A new high-order (> 2nd) cell-centered finite volume method.•An efficient solution algorithm for incompressible flows on unstructured meshes.•Introduction of a new reconstruction stencil, so-called “wrapping stencil”, on unstructured meshes.•Effectiveness and robustness of the wrapping stencil for achieving high-order solution.•Various test cases for demonstrating the accuracy, efficiency, and robustness of the method. A new high-order (> 2nd order) cell-centered finite volume method is presented for incompressible flow simulation on unstructured meshes. Artificial compressibility is employed to couple the continuity and momentum equations in a manner that allows them to be solved simultaneously. A new numerical stencil, a so-called wrapping stencil, is utilized for linear and quadratic solution reconstruction in order to achieve more accurate and robust solution reconstruction not only for the interior cells, but also for the cells on the boundary, where fewer neighboring cells typically exist. The effectiveness of the current algorithm is demonstrated by various test cases, including an analytical solution reconstruction test, Kovasznay flow simulations with various Reynolds numbers, a driven cavity flow, and flow past a square cylinder. Based on the comparison with the standard low order scheme, the proposed second and third order schemes, based on linear and quadratic solution reconstruction, show superior accuracy, which sheds light on the method's applicability in solving more challenging incompressible flow problems.