A finite volume mesh-tying method for computing flows in rotor-stator configurations

Abstract

A finite volume mesh-tying method for the accurate, time-implicit calculation of flows in rotor-stator configurations is presented. We specifically reconsider the problem of coupling two moving domains with patched, but possibly non-conforming meshes at the common interface in a mass and momentum conserving manner. Here, the interfacial mass fluxes and tractions are considered as Lagrange multipliers that adjust instantaneously in such a way that the flow field remains continuous across the interface. For simplicity and computational efficiency, both the Lagrange multipliers and the corresponding continuity constraints for the velocity and pressure are collocated at a finite number of points along the mesh-tying interface. Concomitantly, an iterative augmentation scheme is invoked to eliminate the multipliers from the semi-discrete system of equations and shown to converge even for small values of the associated penalty parameter, thus preventing any deterioration in conditioning. If an iterative linear system solver is employed, then the augmentation is tantamount to the execution of additional solver iterations. Furthermore, our mesh-tying formulation maintains the sparsity of the system matrix and can be incorporated into existing block-structured flow solvers with a minimal implementational effort. For cylindrical grids with azimuthally equisized cells and matching axial grid lines, the mesh-tying approach is demonstrated to preserve the accuracy order of the spatial discretization scheme regardless of the degree of mesh disparity and to maintain long-term temporal accuracy. Finally, we employ the mesh-tying method to calculate unsteady flows in two- and three-dimensional baffled stirred tanks.