A Simple, Efficient, High-order Accurate Sliding-Mesh Interface Approach to the Spectral Difference Method on Coupled Rotating and Stationary Domains

TL;DR

This paper introduces a high-order accurate, efficient sliding-mesh interface method for the spectral difference approach, enabling precise coupling of rotating and stationary domains in fluid dynamics simulations.

Contribution

It extends the straight mortar method with curved mortars for high-order accuracy and efficiency in coupled rotating-stationary domain problems.

Findings

Preserves high-order accuracy in inviscid and viscous flows.

Demonstrates computational efficiency and suitability for parallel processing.

Applicable to various rotating machinery and wind power problems.

Abstract

This paper presents a simple, efficient, and high-order accurate sliding-mesh interface approach to the spectral difference (SD) method. We demonstrate the approach by solving the two-dimensional compressible Navier-Stokes equations on quadrilateral grids. This approach is an extension of the straight mortar method originally designed for stationary domains by Kopriva, it employs curved dynamic mortars on sliding-mesh interfaces to couple rotating and stationary domains. On the nonconforming sliding-mesh interfaces, the related variables are first projected from cell faces to mortars to compute common fluxes, and then the common fluxes are projected back from the mortars to the cell faces to ensure conservation. To verify the spatial order of accuracy of the sliding-mesh spectral difference (SSD) method, both inviscid and viscous flow cases are tested. It is shown that the SSD method preserves the high-order accuracy of the SD method. Meanwhile, the SSD method is found to be very efficient in terms of computational cost. This novel sliding-mesh interface method is very suitable for parallel processing with domain decomposition. It can be applied to a wide range of problems, such as the aerodynamics of rotorcraft, wind turbines, and oscillating wing wind power generators, etc.