M2P 2023

Solving fluid flow problems over complex 3D geometries using the RBF-FD Meshless Method and Algebraic Multigrid

  • Chandrasekar Jeyanthi, Keerthana (ESTECO S.p.A)
  • Munerato, Mauro (ESTECO S.p.A)
  • Miotti, Davide (Università degli Studi di Trieste)
  • Zamolo, Riccardo (Università degli Studi di Trieste)
  • Nobile, Enrico (Università degli Studi di Trieste)

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The traditional mesh-based methods form the basis of engineering analysis in today’s industries. Over the years, mesh generation has seen several advancements while there has also been the development of other numerical methods which replace the mesh generation process with simple techniques like node generation. These meshless methods have been gaining attention since the last decade to cut the mesh generation bottleneck. Some meshless methods, like the Smoothed Particle Hydrodynamics (SPH), have already reached the industry, although many are still in the research phase. One such method is the Radial Basis Function – Finite Differences (RBF-FD) ​(Fornberg & Flyer, 2015)​ that is emerging to its accuracy and flexibility. The node generator and solver developed by Zamolo, Davide and Nobile ​(Zamolo et al., 2022)​ target taking the RBF-FD meshless method closer to the industry. Constructing a robust meshless solver goes by utilizing the advancements in various fields of scientific computing. Hence, integrating the RBF-FD method with advanced linear system solvers becomes essential to reduce computational effort. Multigrid methods form state-of-the-art scalable solvers for solving linear systems arising from the discretization of the partial differential equations (PDEs). We resort to applying the algebraic multigrid methods (AMG) (​Stüben, 2001)​ as discretization is mesh independent. In this work, we focus on reducing the computational time while solving a steady-state incompressible laminar fluid dynamics problem over a complex 3D domain using the meshless RBF-FD method incorporating an AMG solver or preconditioner. We investigate the different coarsening and interpolation strategies for our intended problem to achieve better convergence. Also, we compare our results with the Incomplete LU (ILU) preconditioner to the Biconjugate Gradient Stabilized solver (BiCGSTAB) and BoomerAMG ​(Henson & Yang, 2002)​ of the HYPRE package. HYPRE ​(Falgout D. & Yang, 2002)​ is a standard C library that supplies various solvers and preconditioners for linear systems. As we move towards the industrial aspect, we also compare the performance of our solver with commercially available solvers. Building a stable serial version of the solver becomes the first step, and later we will explore the parallelizing capabilities of Julia.