Abstract
To reconstruct smooth velocity fields from measured incompressible flows, we introduce a statistical regression method that takes into account the mass continuity equation. It is based on a multivariate Gaussian process and formulated within the Bayesian framework, which is a natural framework for fusing experimental data with prior physical knowledge. The robustness of the method and its implementation to large data sets are addressed and compared to a method that does not include the incompressibility constraint. A two-dimensional synthetic test case is used to investigate the accuracy of the method and a real three-dimensional experiment of a circular jet in water is used to investigate the method’s ability to fill up a gap containing a vortex ring.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G.S. Ammar, W.B. Gragg, Superfast solution of real positive definite Toeplitz systems. SIAM J. Matrix Anal. Appl. 9, 61–76 (1988)
J.H.S. de Baar, M. Percin, R.P. Dwight, B.W. van Oudheusden, H. Bijl, Kriging regression of PIV data using a local error estimate. Exp. Fluids 55(1), 1–13 (2014)
R.H.F. Chan, X.Q. Jin, An Introduction to Iterative Toeplitz Solvers (SIAM, Philadelphia, 2007)
G.J. Davis, M.D. Morris, Six factors which affect the condition number of matrices associated with Kriging. Math. Geol. 29, 669–683 (1997)
S.L. Lee, A. Huntbatch, G.Z. Yang, Contractile analysis with kriging based on MR myocardial velocity imaging. Med. Image Comput. Comput. Assist. Interv. 11, 892–899 (2008)
F.J. Narcowich, J.D. Ward, Generalized Hermite interpolation via matrix-valued conditionally positive definite functions. Math. Comput. 63, 661–687 (1994)
M.K. Ng, J. Pan, Approximate inverse circulant-plus-diagonal preconditioners for toeplitz-plus-diagonal matrices. SIAM J. Sci. Comput. 32, 1442–1464 (2010)
C. Rasmussen, C. Williams, Gaussian Processes for Machine Learning (MIT, Cambridge, 2006)
D. Venturi, G. Karniadakis, Gappy data and reconstruction procedures for flow past a cylinder. J. Fluid Mech. 519, 315–336 (2004)
D. Violato, F. Scarano, Three-dimensional evolution of flow structures in transitional circular and chevron jets. Phys. Fluids 23, 1–25 (2011)
H. Wendland, Scattered Data Approximation. Cambridge Monographs on Applied and Computational Mathematics, vol. 17 (Cambridge University Press, Cambridge, 2005)
C.K. Wikle, L.M. Berliner, A Bayesian tutorial for data assimilation. Phys. D 230, 1–16 (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Azijli, I., Dwight, R., Bijl, H. (2015). A Bayesian Approach to Physics-Based Reconstruction of Incompressible Flows. In: Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (eds) Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-319-10705-9_52
Download citation
DOI: https://doi.org/10.1007/978-3-319-10705-9_52
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10704-2
Online ISBN: 978-3-319-10705-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)