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Improving Performance of Simplified Computational Fluid Dynamics Models via Symmetric Successive Overrelaxation

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  • Vojtěch Turek

    (Sustainable Process Integration Laboratory–SPIL, NETME Centre, Faculty of Mechanical Engineering, Brno University of Technology–VUT Brno, Technická 2, 616 00 Brno, Czech Republic)

Abstract

The ability to model fluid flow and heat transfer in process equipment (e.g., shell-and-tube heat exchangers) is often critical. What is more, many different geometric variants may need to be evaluated during the design process. Although this can be done using detailed computational fluid dynamics (CFD) models, the time needed to evaluate a single variant can easily reach tens of hours on powerful computing hardware. Simplified CFD models providing solutions in much shorter time frames may, therefore, be employed instead. Still, even these models can prove to be too slow or not robust enough when used in optimization algorithms. Effort is thus devoted to further improving their performance by applying the symmetric successive overrelaxation (SSOR) preconditioning technique in which, in contrast to, e.g., incomplete lower–upper factorization (ILU), the respective preconditioning matrix can always be constructed. Because the efficacy of SSOR is influenced by the selection of forward and backward relaxation factors, whose direct calculation is prohibitively expensive, their combinations are experimentally investigated using several representative meshes. Performance is then compared in terms of the single-core computational time needed to reach a converged steady-state solution, and recommendations are made regarding relaxation factor combinations generally suitable for the discussed purpose. It is shown that SSOR can be used as a suitable fallback preconditioner for the fast-performing, but numerically sensitive, incomplete lower–upper factorization.

Suggested Citation

  • Vojtěch Turek, 2019. "Improving Performance of Simplified Computational Fluid Dynamics Models via Symmetric Successive Overrelaxation," Energies, MDPI, vol. 12(12), pages 1-16, June.
  • Handle: RePEc:gam:jeners:v:12:y:2019:i:12:p:2438-:d:242612
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    References listed on IDEAS

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    1. Shi-Liang Wu & Cui-Xia Li, 2012. "A Modified SSOR Preconditioning Strategy for Helmholtz Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-9, December.
    2. Wang, Hui-Di & Huang, Zheng-Da, 2018. "On convergence and semi-convergence of SSOR-like methods for augmented linear systems," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 87-104.
    3. Zhao-Nian Pu & Xue-Zhong Wang, 2013. "Block Preconditioned SSOR Methods for -Matrices Linear Systems," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, April.
    4. Noriyuki Kushida, 2015. "Condition Number Estimation of Preconditioned Matrices," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-16, March.
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