Towards a Scalable Hierarchical High-order CFD Solver

TL;DR

This paper introduces a scalable high-order implicit Discontinuous Galerkin CFD solver that leverages advanced preconditioning and Krylov methods to achieve near-linear weak scaling on thousands of cores, enabling large-scale simulations.

Contribution

It presents a novel scalable high-order CFD solver with a preconditioning technique and communication-avoiding Krylov methods, demonstrating near-linear scaling on large parallel architectures.

Findings

Near-linear weak scaling up to 2,048 cores

No significant degradation in convergence rate

Effective use of algebraic sparsified nested dissection preconditioning

Abstract

Development of highly scalable and robust algorithms for large-scale CFD simulations has been identified as one of the key ingredients to achieve NASA's CFD Vision 2030 goals. In order to improve simulation capability and to effectively leverage new high-performance computing hardware, the most computationally intensive parts of CFD solution algorithms -- namely, linear solvers and preconditioners -- need to achieve asymptotic behavior on massively parallel and heterogeneous architectures and preserve convergence rates as the meshes are refined further. In this work, we present a scalable high-order implicit Discontinuous Galerkin solver from the SU2 framework using a promising preconditioning technique based on algebraic sparsified nested dissection algorithm with low-rank approximations, and communication-avoiding Krylov subspace methods to enable scalability with very large processor counts. The overall approach is tested on a canonical 2D NACA0012 test case of increasing size to demonstrate its scalability on multiple processing cores. Both the preconditioner and the linear solver are shown to exhibit near-linear weak scaling up to 2,048 cores with no significant degradation of the convergence rate.