
On an Improved Global Linelet Preconditioner for Large-Scale Incompressible Flow Simulations
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Efficient solutions to large-scale fluid dynamics problems often require preconditioners that address the ill-conditioning arising from highly anisotropic meshes. This work introduces the Global Linelet Preconditioner (GLP), an algebraic and parallel method to enhance the performance of the Preconditioned Conjugate Gradient (PCG) solver when addressing linear systems dominated by mesh anisotropy[1]. Unlike traditional linelet preconditioners[2], GLP enables linelets to span multiple domain partitions and relies on algebraic rather than geometric construction, broadening its applicability to systems with similar matrix structures. Key contributions include a two-step assembly process where linelet slices are first built within individual subdomains and subsequently interconnected across partitions. This is complemented by a parallel-algebraic approach to solve the resulting tridiagonal systems efficiently. Incorporating a Schur Complement Method further ensures scalability and enables balanced load distribution, even with irregular domain decompositions. Numerical experiments demonstrate significant improvements in convergence rates and solver efficiency. To validate the method at higher Reynolds numbers, we conducted LES of flow past a 30P30N high-lift wing at Re=750000, using a hybrid unstructured mesh with 87 million elements (43% of them within the boundary layer). The CG converged up to 5.3 times faster when compared to diagonal preconditioning and other linelet methods. The algebraic GLP framework supports generalization beyond Poisson’s equations to other systems exhibiting linelet structure. Moreover, the method is effective for meshes with a high percentage of boundary layer elements, delivering substantial efficiency gains for flows at high Reynolds numbers. These findings, combined with its compatibility with alternative linelet construction methods, highlight the versatility and potential of GLP in addressing computational challenges in fluid dynamics and other domains. REFERENCES [1] R. de Olazábal, R. Borrell and O. Lehmkuhl, An algebraig global linelet preconditioner for incompressible flow solvers, Journal of Computational Physics, https://doi.org/10.1016/j.jcp.2024.113237 [2] O. Soto, R. Löhner, F. Camelli, A linelet preconditioner for incompressible flows, In t. J. Numer. Methods Heat Fluid Flow 13 (2003) 133-147 https://doi.org/ 10.1108/09615530310456796.