Self-Adaptive parameter selection for hybrid regularization of the incompressible Navier–Stokes equations
Numerical Algorithms, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s11075-026-02480-y
- Dergi Adı: Numerical Algorithms
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, INSPEC, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Adaptive algorithms, Artificial compression, Finite element method, Hybrid regularization, Navier–Stokes equations, Penalty method
- Gazi Üniversitesi Adresli: Evet
Özet
The Ramshaw–Mesina hybrid regularization combines pressure penalty and artificial compression for the incompressible Navier–Stokes equations but requires careful parameter tuning. We develop a self-adaptive strategy that automatically adjusts both parameters at each time step from computable solution indicators. A key mechanism is a lower bound on the hybridization ratio: when it exceeds the initial ratio, it acts as a cross-coupling amplifier, propagating divergence-driven increases in the penalty parameter to the compression parameter simultaneously, and it automatically restores the Ramshaw–Mesina calibration scaling α2=O(Δt-2), β=O(Δt-1) under which the method is first-order accurate in time. We prove unconditional stability and error estimates with complete proofs, showing that time-varying parameters perturb neither the spatial nor the temporal convergence rates. Numerical experiments demonstrate that the adaptive method reduces divergence error by up to nearly two orders of magnitude relative to untuned parameters — for example, from 8.1×10-3 to 1.1×10-4 starting from the severely untuned pair (α02,β0)=(10,1) — and achieves two to three orders of magnitude improvement over penalty-only or compression-only methods, confirming the landmark Ramshaw–Mesina result. The adaptation constants themselves require no tuning: a sweep over their values shows only mild sensitivity. Tests include convergence studies on structured and unstructured meshes, a Reynolds-number study up to Re=2000, and lid-driven cavity benchmarks in two and three dimensions.