A pressure‐correction procedure with high‐order schemes implemented on unstructured meshes

Abstract

PurposeThe purpose of this paper is to present a pressure‐correction procedure for incompressible flows using unstructured meshes. A method of implementing high‐order spatial schemes on unstructured grids was introduced.Design/methodology/approachThe procedure used a collocated cell‐centered unstructured grid arrangement. In order to improve the accuracy of calculation, the widely used high‐order schemes for convection, developed for structured grids and in the form of either the normalized variable and space formulation (NVSF) or the total variation diminishing (TVD) flux limiters (FL), were introduced and implemented onto the unstructured grids. This implementation was carried out by constructing a local coordinate and introducing a virtual upstream node.FindingsThe procedure was validated by calculating the lid‐driven cavity flows which had benchmark numerical solutions. For comparison, these flows were also computed by a commercial package, the FLUENT. The results obtained by the present procedure agreed well with the benchmark solution although very coarse grids were used. For the FLUENT, however, worse agreements with the benchmark solutions were obtained although the grids used for computation were the same. These demonstrated the robustness of the presented numerical procedure.Originality/valueWith the present method, high‐order schemes in either NVSF or TVD FL forms for structured grids can be easily implemented onto unstructured grids. This provides more choices of high‐order schemes for calculating complex flows.