A high-order entropically-damped artificial compressibility approach on moving and deforming domains

Abstract

A wide range of incompressible flow applications require accurate, efficient, and stable solutions on moving and deforming domains. The entropically damped artificial compressibility (EDAC) method offers a pressure-dampening alternative to conventional Poisson’s or artificial compressibility methods (ACM). EDAC uses an artificial compressibility parameter, similar to the ACM, but does not require pseudo-iterations to converge the pressure field. This paper explores the accuracy of the EDAC scheme on moving and deforming domains using a high-order flux reconstruction (FR) spatial discretization. The method of manufactured solutions is used to verify observed orders of accuracy for FR implementations of EDAC on moving and deforming domains, followed by confirmation of freestream preservation. Then, simulations of a double shear layer, flow over an oscillating cylinder, and dynamic stall of a 2D NACA 0012 airfoil undergoing heaving and pitching motions are used to assess the ability of the scheme to preserve physics and to determine the impacts of the artificial compressibility factor and solution polynomial degree. Results demonstrate that artificial compressibility factors on the order of 0.025–0.05, combined with high-order solution polynomials, recovered reference solutions. These results demonstrate the suitability of FR discretizations of EDAC for incompressible flows on moving and deforming domains.