Accelerating steady-state CFD simulations by leveraging non-converged linear solutions

  • Klöppner, Florian (DLR e.V.)
  • Malvestiti, Matteo (DLR e.V.)
  • Er-Raiy, Aimad (Airbus Operations SAS)
  • Wendler, Johannes (DLR e.V.)
  • Rempke, Arne (DLR e.V.)
  • Krzikalla, Olaf (DLR e.V.)
  • Kunhappan, Deepak (DLR e.V.)
  • Huismann, Immo (DLR e.V.)

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Aircraft design requires the entirety of the flight envelope and, in turn, many extensive steady-state RANS simulations. The resulting non-linear problems are typically solved via quasi-Newton methods where for each iteration step a linear system results. For these, no exact solution is required. Instead, improving upon the previous solution suffices to ensure stable convergence. This leads to a tradeoff of lowering the amount of runtime spent in the linear solver at the expense of more iterations in the non-linear solution process itself. In short: Weaker linear solvers and solutions can speed up the overall solution process, opening the question, which linear solver is best suited and how strong it needs to be. This contribution investigates the effect of the linear solver on the non-linear solution process and generates best practices for speeding up convergence processes for large-scale steady-state simulations. As test case, the NASA Common Research Model [1] was chosen. Its modelling of a simplified airplane in cruise flight offers an application-oriented testcase with multiple grid series available. This study employs the CFD solver ”CFD for ONERA, DLR and Airbus” (CODA), allowing to compare solvers from the numerical linear algebra libraries Spliss [2] and PETSc [3]. For the GMRES solvers, multiple types of reconditioners are compared, starting from element-local LU solvers over linelet solvers up to multigrid. Where available, additional performance relevant modifications, such as the application of mixed precision or hybrid parallelisation, are tested. With some algorithms being restricted to working on the thread-local matrix, their algorithmic strength can vary when increasing the degree of parallelization. Hence, scalability studies are included to investigate the behavior of the solvers for high degrees of parallelism. [1] Vassberg J., Dehaan M., Rivers M., Wahls R., Development of a Common Research Model for Applied CFD Validation Studies, 26th AIAA Applied Aerodynamics Conference, 2012 [2] Krzikalla O., Rempke A., Wagner M., Gerhold T., Spliss: A Sparse Linear System Solver for Transparent Integration of Emerging HPC Technologies into CFD Solvers and Applications, New Results in Numerical and Experimental Fluid Mechanics XIII, 2021 [3] Balay S., Abhyankar S. et. al, PETSc Web page, https://petsc.org/, 2025