[Paper Review] An Efficient Sliding Mesh Interface Method for High-Order Discontinuous Galerkin Schemes

Jakob Dürrwächter, Marius Kurz+4 more|arXiv (Cornell University)|Aug 10, 2020

Computational Fluid Dynamics and Aerodynamics75 references18 citations

TL;DR

This paper presents a high-order, conservative sliding mesh interface method for discontinuous Galerkin (DG) schemes, using a mortar method to enable accurate and efficient simulation of moving boundaries in 3D compressible flows. The approach ensures free-stream preservation and conservativity on planar interfaces, with minimal communication overhead via a priori MPI partner identification and data sorting, enabling scalable large-eddy simulations of industrial-scale turbine flows with only ~15% performance loss compared to baseline schemes.

ABSTRACT

Sliding meshes are a powerful method to treat deformed domains in computational fluid dynamics, where different parts of the domain are in relative motion. In this paper, we present an efficient implementation of a sliding mesh method into a discontinuous Galerkin compressible Navier-Stokes solver and its application to a large eddy simulation of a 1-1/2 stage turbine. The method is based on the mortar method and is high-order accurate. It can handle three-dimensional sliding mesh interfaces with various interface shapes. For plane interfaces, which are the most common case, conservativity and free-stream preservation are ensured. We put an emphasis on efficient parallel implementation. Our implementation generates little computational and storage overhead. Inter-node communication via MPI in a dynamically changing mesh topology is reduced to a bare minimum by ensuring a priori information about communication partners and data sorting. We provide performance and scaling results showing the capability of the implementation strategy. Apart from analytical validation computations and convergence results, we present a wall-resolved implicit LES of the 1-1/2 stage Aachen turbine test case as a large scale practical application example.

Motivation & Objective

• To develop a high-order, conservative sliding mesh interface method compatible with discontinuous Galerkin (DG) schemes for moving domains.
• To ensure conservativity and free-stream preservation in three-dimensional simulations with planar sliding interfaces.
• To minimize computational and communication overhead in parallel implementations for dynamic mesh topologies.
• To enable large-scale, wall-resolved large eddy simulations (LES) of industrial turbine flows using high-order DG methods.
• To provide an open-source, production-ready implementation for high-performance computing (HPC) environments.

Proposed method

• Uses the mortar method to couple non-conforming sliding mesh interfaces, ensuring high-order accuracy and conservation.
• Applies an arbitrary Lagrangian-Eulerian (ALE) formulation to account for mesh motion in the compressible Navier-Stokes equations.
• Employs a priori knowledge of MPI communication partners and data sorting to reduce inter-node communication to a minimum.
• Introduces a hierarchical sorting strategy using arrays ˜r, A, and m to map local mortar indices to globally consistent, contiguous data blocks.
• Implements a dual-storage approach (primary and replica arrays) for solution and flux data on mortars, enabling efficient, ordered communication.
• Uses a discontinuous Galerkin spectral element method (DGSEM) with polynomial mappings and weak formulation in reference elements.

Experimental results

Research questions

• RQ1 How can a high-order, conservative sliding mesh interface be implemented within a discontinuous Galerkin framework for 3D moving domains?
• RQ2 What is the impact of the sliding mesh interface on computational efficiency and parallel scalability in high-order DG simulations?
• RQ3 Can the proposed method maintain free-stream preservation and conservativity on planar interfaces in complex 3D geometries?
• RQ4 How does the communication overhead of the sliding mesh method compare to standard DG implementations in dynamic mesh scenarios?
• RQ5 To what extent can the method enable large-scale, wall-resolved large eddy simulations of industrial turbine flows?

Key findings

• The method achieves high-order accuracy and conservativity on planar sliding interfaces, with analytical validation confirming optimal convergence rates.
• The implementation incurs only a ~15% performance loss compared to the baseline non-sliding DG scheme, demonstrating high efficiency.
• The communication overhead is minimized through a priori MPI partner identification and data sorting, enabling efficient dynamic mesh topology handling.
• The method successfully enables a wall-resolved, implicit large eddy simulation (LES) of the 1-1/2 stage Aachen turbine test case, a large-scale industrial application.
• The framework is open-source and publicly available on GitHub, supporting reproducibility and further development.
• The mortar-based data structuring via arrays ˜r, A, and m ensures globally consistent data ordering, enabling correct and efficient MPI communication.