2025/12/11 by Yayu Guo, Y. Guo, Azaïez, Mejdi +9
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Compressibility #Computation #Convergence (economics) #Coupling (piping) #Decoupling (probability) #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Navier–Stokes equations #Order (exchange) #Projection (relational algebra) #Projection method #Stability (learning theory)
paper · pdf · doi:10.1016/j.jcp.2026.115166
published in Journal of Computational Physics 564, 115166 (Elsevier BV)
openalex publication_date 2026/06/01 · openalex created_date 2026/06/28 · openalex updated_date 2026/06/28
The numerical simulation of incompressible flows is challenging due to the tight coupling of velocity and pressure. Projection methods offer an effective solution by decoupling these variables, making them suitable for large-scale computations. This work focuses on reduced-order modeling using incremental projection schemes for the Stokes equations. We present both semi-discrete and fully discrete formulations, employing BDF2 in time and finite elements in space. A proper orthogonal decomposition (POD) approach is adopted to construct a reduced-order model for the Stokes problem. The method enables explicit computation of reduced velocity and pressure while preserving accuracy. We provide a detailed stability analysis and derive error estimates, showing second-order convergence in time. Numerical experiments are conducted to validate the theoretical results and demonstrate computational efficiency.