On the finite‐element calculation of turbulent flow using the k‐ϵ model

Abstract Although the finite‐element (FE) method has been successful in analysing complex laminar flows, a number of difficulties can arise when two‐equation turbulence models (e.g. the k ‐ϵ model) are incorporated. This work describes a particular FE discretization of the k ‐ϵ model and reports its performance in recirculating flow. Severe problems encountered in attempts to obtain convergence of the numerical scheme are isolated and analysed, and methods by which the problems can be overcome are suggested. Insight gained in this work has enabled a practical turbulent flow FE code to be constructed which is robust and efficient. This code is the subject of a further paper.