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.

Implicit Solar Coronal Magnetohydrodynamic (MHD) Modeling with a Low-dissipation Hybridized AUSM-HLL Riemann Solver

“…Based on former works (Groth et al 2000;Feng et al 2007Feng et al , 2019Feng et al , 2021, we implement the condition of no "backflow" at the inner boundary (solar surface) by numerical flux to achieve better convergence and accuracy (Mengaldo et al 2014;Chen et al 2020). The inner boundary conditions are divided into two cases according to the flow with radial speed of v r in the inner boundary cell.…”