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<p>This paper investigates an approximate block factorization technique for efficiently solving large saddle point systems derived from the discretization of the Navier–Stokes equations. The standard upper triangular approximation is revisited with the addition of a lower block, specifically designed to improve system conditioning and accelerate iterative solver convergence. Numerical experiments highlight the robustness and efficiency of the lower-upper triangular approximation as a preconditioning strategy, particularly in massively parallel environments. The method proves especially effective for simulating multiphase flows with high density and viscosity ratios, complex droplet dynamics, and significant interface deformations.</p>

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Efficient and scalable preconditioning for large saddle point systems in multiphase flow simulations

  • 期刊论文

  • 发表日期：

    2025年3月10日

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  • Simon El Ouafa,
  • Syphax Fereka,
  • Stéphane Vincent,
  • Vincent Le Chenadec,
  • Benoît Trouette

摘要

This paper investigates an approximate block factorization technique for efficiently solving large saddle point systems derived from the discretization of the Navier–Stokes equations. The standard upper triangular approximation is revisited with the addition of a lower block, specifically designed to improve system conditioning and accelerate iterative solver convergence. Numerical experiments highlight the robustness and efficiency of the lower-upper triangular approximation as a preconditioning strategy, particularly in massively parallel environments. The method proves especially effective for simulating multiphase flows with high density and viscosity ratios, complex droplet dynamics, and significant interface deformations.