Removing Splitting/Modeling Error in Projection/Penalty Methods for Navier-Stokes Simulations with Continuous Data Assimilation (Communications in Mathematical Research, 2023)
We study continuous data assimilation (CDA) applied to projectionand penalty methods for the Navier-Stokes (NS) equations. Penalty and projection methods are more efficient than consistent NS discretizations, howeverare less accurate due to modeling error (penalty) and splitting error (projection). We show analytically and numerically that with measurement data andproperly chosen parameters, CDA can effectively remove these splitting andmodeling errors and provide long time optimally accurate solutions.
Keywords: Navier-Stokes equations; projection method; penalty method; continuous data assimilation.