On the temporal and spatial fourth-order finite volume velocity de-averaging for unsteady incompressible flows simulation

摘要

Purpose - This paper aims to focus on the temporal and spatial fourth-order finite volume discretization of the incompressible form of the Navier-Stokes equations on structured uniform grids. The main purpose of the paper is to assess the accuracy enhancement with the inclusion of a high-order reconstruction of the point-wise velocity field on a fourth-order accurate numerical scheme for the solution of the unsteady incompressible Navier-Stokes equations.rnDesign/methodology/approach - The present finite volume method uses a fractional time-step for decoupling velocity and pressure. A Runge-Kutta integration scheme is implemented for integrating the momentum equation along with a polynomial interpolation and Simpson formula for space-integration. The formulation is based on step-by-step de-averaging process applied to the velocity field.rnFindings - The reconstruction of the point-wise velocity field on a higher-order basis is essential to obtain solutions that effectively stand for a fourth-order approximation of the point-wise one. Results are provided for the Taylor vortex decay problem and for co- and counter-rotating vortices to assess the increase in accuracy promoted by the inclusion of the high-order de-averaging procedure. Research limitations/implications - High-order reconstruction of the point-wise velocity field should be considered in high-order finite volume methods for the solution of the unsteady incompressible form of the Navier-Stokes equations on structured grids.rnPractical implications - The inclusion of a high-order reconstruction of the point-wise velocity field is a simple and effective method of enhancing the accuracy of a finite volume code for the computational fluid dynamics analysis.rnOriginality/value - The paper develops an improved version of a fourth-order accurate finite volume projection method with the inclusion of a high-order reconstruction step.