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

Mohsen Lahooti; Edward Laughton; Junjie Ye; Chris D Cantwell; David Moxey

doi:10.1016/j.jcp.2025.113734

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

Mohsen Lahooti^*, Edward Laughton, Junjie Ye, Chris D Cantwell, David Moxey

^*Corresponding author for this work

Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	113734
Journal	JOURNAL OF COMPUTATIONAL PHYSICS
Volume	524
DOIs	https://doi.org/10.1016/j.jcp.2025.113734
Publication status	Published - 13 Jan 2025

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title = "Discontinuous Galerkin simulation of sliding geometries using a point-to-point interpolation technique",

abstract = "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.",

author = "Mohsen Lahooti and Edward Laughton and Junjie Ye and Cantwell, {Chris D} and David Moxey",

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AU - Moxey, David

PY - 2025/1/13

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AB - 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.

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

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