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<p>In this paper, based on the zero-energy-contribution idea and the penalty-based ensemble approach, an unconditionally stable penalty-based ensemble method for the stationary incompressible Navier–Stokes equations is developed and analyzed. Compared with the usual penalty-based ensemble method proposed by Fang (Numer. Algo. <CitationRef CitationID="CR4">2005</CitationRef>) that exhibits conditional stability, we prove the unconditional stability of the proposed penalty-based ensemble method. The theoretical finding is illustrated by numerical experiment.</p>

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On unconditional stability of a penalty-based ensemble method

  • 期刊论文

  • 发表日期：

    2025年11月21日

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  • Qijun Chu,
  • Pengzhan Huang

摘要

In this paper, based on the zero-energy-contribution idea and the penalty-based ensemble approach, an unconditionally stable penalty-based ensemble method for the stationary incompressible Navier–Stokes equations is developed and analyzed. Compared with the usual penalty-based ensemble method proposed by Fang (Numer. Algo. 2005) that exhibits conditional stability, we prove the unconditional stability of the proposed penalty-based ensemble method. The theoretical finding is illustrated by numerical experiment.