Extending slide-slip mesh update method to finite volume method

Abstract

For simulations of flows around rotating bodies, usually sliding mesh method or overset grid method is used. But both of them have to perform inter-mesh interpolation which introduces much numerical error and usually violates conservation. Shear-slip mesh update method (SSMUM) is another method for such flows. In each time step of SSMUM, a mesh slipping step follows a mesh deforming step to undo the deformation and results in a new mesh of good quality. Each vertex on the slipping interface can only move from one node to the next node in the circumference, which makes the interface always conformal and no need for inter-mesh interpolation. However, SSMUM didn't get enough attention in the community of finite volume method. In this paper, SSMUM is extended to cell center finite volume method. To guarantee conservation and obtain high order accuracy on a slipping interface, a remapping procedure is needed to transfer flow field from an old mesh to a new mesh. This was achieved by solving a linear convective PDE with one or two explicit steps, thus only resulting in little extra computing cost. Oscillating NACA0012 airfoil was simulated with the improved SSMUM. The results showed excellent agreement with the data by rigid rotating mesh. And the flow field was always smooth. It suggests that this improved SSMUM has advantages in getting conservative, smooth and high accuracy solutions for rotating problems.