An iterative near-boundary reconstruction strategy for unstructured finite volume method

Abstract

Near-boundary approximation of the second-order cell-centered unstructured finite volume method is investigated and improved to avoid accuracy loss. In this work, an iterative strategy is proposed, combining with a vertex-based weighted least squares gradient reconstruction method, which is more accurate and efficient than several conventional methods. In the present approach, the solutions at boundary surfaces and the gradients in boundary cells are iteratively updated, to minimize overall numerical errors. In the meantime, a vectorial limiter is implemented to guarantee the correctness of the iterative process, and physical properties of boundaries are taken into account to correctly attain physical results. A series of numerical test cases show that the present method significantly reduces the error of near-boundary approximations. Moreover, since the iterative scheme is only activated for near-boundary solutions, the minor extra computational effort does not damage the overall performance of the solver.