A deconvolution-based fourth-order finite volume method for incompressible flows on non-uniform grids

This paper is concerned with the development of a new high-order finite volume method for the numerical simulation of highly convective unsteady incompressible flows on non-uniform grids. Specifically, both a high-order fluxes integration and the implicit deconvolution of the volume-averaged field are considered. This way, the numerical solution effectively stands for a fourth-order approximation of the point-wise one. Moreover, the procedure is developed in the framework of a projection method for the pressure-velocity decoupling, while originally deriving proper high-order intermediate boundary conditions. The entire numerical procedure is discussed in detail, giving particular attention to the consistent discretization of the deconvolution operation. The present method is also cast in the framework of approximate deconvolution modelling for largeeddy simulation. The overall high accuracy of the method, both in time and space, is demonstrated. Finally, as a model of real flow computation, a two-dimensional time-evolving mixing layer is simulated, with and without sub-grid scales modelling.