Description and Convergence Order Analysis of the Finite Element‐Volume Spatial Discretization Method

ABSTRACT This article reviews the Finite Element‐Volume spatial discretization method on tetrahedral meshes implemented in the TrioCFD code. TrioCFD is a computational fluid dynamics software specifically designed for simulating turbulent flows and heat transfer, with a primary focus on nuclear engineering applications. Its versatility also extends to a wide range of engineering applications. This article presents the principles of Finite Element‐Volume discretization and conducts an analysis of its properties and convergence orders. The time scheme can be explicit or semi‐implicit, and the velocity and pressure are updated based on a projection‐correction scheme. The discretization ensures local mass conservation, second‐order convergence for velocity, and first‐order convergence for pressure. Moreover, a super‐convergence is achieved in two‐dimension when the source term is a gradient. The accuracy and convergence rate of the numerical method is rigorously assessed in a variety of two‐ and three‐dimensional test cases, including steady Stokes and Navier–Stokes problems with manufactured solutions. The classical lid‐driven cavity flow is also addressed, and the results of comparisons between the solutions from the present numerical method and the results of reference literature are provided.