New cell–vertex reconstruction for finite volume scheme: Application to the convection–diffusion–reaction equation

摘要: Abstract The design of efficient, simple, and easy to code, second-order finite volume methods is an important challenge solve practical problems in physics engineering where complex very accurate techniques are not required. We propose extension the original Frink’s approach based on a cell-to-vertex interpolation compute vertex values with neighbour cell values. also specific scheme which enables use whatever collocation point we want cells overcome mass centre restrictive choice. method proposed for two- three-dimensional geometries time-discretization given time-dependent equation. A large number numerical simulations carried out highlight performance new method.