The understanding of the subzonal pressure hourglass control method with numerical quadrature

Abstract

The purpose of this work is to gain a better insight into the subzonal pressure hourglass control method proposed by Caramana and Shashkov (1998). We illuminate the connection between the subzonal pressure method and the numerical discretization of the momentum equation. The meaning of the variation of subzonal pressure and the hourglass parameter is clarified. By subtle analyzing the one-point quadrature scheme and the four-point quadrature scheme, we present a unified approach to construct the perturbed corner force for the subzonal pressure method. Furthermore, one of the original subzonal pressure formulas can be derived from the four-point Gauss–Lobatto quadrature. A new formula of the perturbed corner force is proposed based on the four-point Gauss quadrature. Some benchmark problems are performed with the compatible Lagrangian algorithm to illustrate the efficiency of the proposed formula.