Solid Mechanics Segregated Solver Acceleration With Jacobian-Free Newton-Krylov

Abstract

The segregated algorithm is a common approach for finite volumes solvers in solid mechanics, providing a memory-efficient and straightforward implementation. Due to the inter-coupling of the components through the source terms, it suffers from a slow convergence behavior in specific scenarios, such as geometries with significantly uneven dimensions. Examples of attempts to improve the performance of the segregated algorithm in such cases are available in the literature, for instance, with machine learning or with multigrid acceleration. On the other hand, Newton solvers and Jacobian-Free Newton-Krylov method have been successfully applied as standalone solvers for fluid mechanics applications, or even for multi-physics coupling in nuclear codes. Complementing recent work on Newton-Krylov as a standalone solver for solid mechanics, this paper proposes a novel approach to tackle the slow convergence issue by coupling the segregated algorithm with a Jacobian-Free Newton-Krylov method. The targeted advantage being the performance improvements for pure mechanical simulations with almost no parametrization from the code user. In the article, the method is introduced and benchmarked against the original segregated algorithm and the Anderson acceleration. 2D and 3D steady-state cases are considered, including small and large deformations, from linear to nonlinear mechanical behaviors. The OpenFOAM Fuel Behavior Analysis Tool (OFFBEAT) is a multidimensional fuel performance code developed jointly by the Paul Scherrer Institute (PSI) and the École Polytechnique Fédérale de Lausanne (EPFL). Using the PETSc library, the innovative coupling with the segregated algorithm has been implemented into OFFBEAT to produce the benchmarks. Still relying on the OpenFOAM framework and the segregated algorithm, the proposed method benefits from the validation of the existing code base. The results, obtained for serial executions, exhibit a promising reduction in computational time and number of iterations to convergence, paving the way for further development in solid mechanics solvers and a possible extension to other physics.