Numerical analysis of a bdf2 modular grad-div Stabilization method for the Navier-Stokes equations
Y. Rong, J. A. Fiordilino
TL;DR
This paper introduces a second-order modular algorithm for the Navier-Stokes equations that improves stability and efficiency over traditional methods, supported by theoretical analysis and computational tests.
Contribution
It presents a novel modular BDF2-based algorithm with enhanced stability and efficiency for grad-div stabilization in Navier-Stokes simulations.
Findings
Resistant to solver breakdown
More computationally efficient with higher grad-div parameters
Theoretical stability and convergence proven
Abstract
A second-order accurate modular algorithm is presented for a standard BDF2 code for the Navier-Stokes equations (NSE). The algorithm exhibits resistance to solver breakdown and increased computational efficiency for increasing values of grad-div parameters. We provide a complete theoretical analysis of the algorithms stability and convergency. Computational tests are performed and illustrate the theory and advantages over monolithic grad-div stabilizations.
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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Computational Fluid Dynamics and Aerodynamics · Power System Optimization and Stability