Discontinuous Galerkin simulation of sliding geometries using a point-to-point interpolation technique

The high-fidelity modelling of geometry which rotates or translates is a key requirement in fluid mechanics applications, enabling the simulation of parts such as rotors and pressure cascades. These prescribed motions can be imposed through the movement of the mesh representing the problem, where an interface is constructed across the nonconformal interface, bridging the static and moving regions of the mesh. The challenge is maintaining the solution accuracy across this interface, which will involve nonconformal elements on its sides due to the sliding meshes, while having a robust and efficient approach for complex interfaces. This work uses a point-to-point interpolation technique for such sliding interfaces, leveraging the high-order discontinuous Galerkin method for discretising governing equations and the Arbitrary Lagrangian-Eulerian (ALE) method in handling sliding meshes. With its straightforward and efficient approach, the point-to-point interpolation method has an advantage over other approaches in dealing with the complex interface while having excellent accuracy in preserving the discrete geometric conservation law (DGCL), as demonstrated in this study. Linear and non-linear hyperbolic systems, including the compressible Euler and Navier-Stokes equations, are considered with detailed analysis demonstrating the point-to-point method's accuracy using several examples and under various settings in the context of high-order methods for flow problems. • This work presents a high-order discontinuous Galerkin (DG) method for sliding interfaces based on the arbitrary Lagrangian Eulerian (ALE) approach. • We investigate the new approach of point-to-point interpolation for non-conformal elements at the sliding interface. • The solver is implemented within the open-source high-order spectral/ hp element framework Nektar++. • We demonstrate the accuracy of the method on linear and non-linear problems, highlighting good conservation of the discrete geometric conservation law (DGCL).