Semi-Implicit VMS for Navier-Stokes with Exact Adjoint Linearization
Research Paper#Computational Fluid Dynamics (CFD)🔬 Research|Analyzed: Jan 4, 2026 00:07•
Published: Dec 25, 2025 19:46
•1 min read
•ArXivAnalysis
This paper presents a novel semi-implicit variational multiscale (VMS) formulation for the incompressible Navier-Stokes equations. The key innovation is the use of an exact adjoint linearization of the convection term, which simplifies the VMS closure and avoids complex integrations by parts. This leads to a more efficient and robust numerical method, particularly in low-order FEM settings. The paper demonstrates significant speedups compared to fully implicit nonlinear formulations while maintaining accuracy, and validates the method on a range of benchmark problems.
Key Takeaways
- •Develops a semi-implicit VMS formulation for the incompressible Navier-Stokes equations.
- •Employs exact adjoint linearization for the convection term.
- •Simplifies the VMS closure and avoids complex integrations.
- •Achieves significant speedups (2-4x) compared to fully implicit nonlinear formulations.
- •Maintains comparable accuracy across benchmark problems.
Reference / Citation
View Original"The method is linear by construction, each time step requires only one linear solve. Across the benchmark suite, this reduces wall-clock time by $2$--$4\times$ relative to fully implicit nonlinear formulations while maintaining comparable accuracy."