Improving Regularization Techniques for Incompressible Fluid Flows via Defect Correction

References

[1] M. Aggul, J. M. Connors, D. Erkmen and A. E. Labovsky, A defect-deferred correction method for fluid-fluid interaction, SIAM J. Numer. Anal. 56 (2018), no. 4, 2484–2512. 10.1137/17M1148219Search in Google Scholar

[2] M. Aggul, S. Kaya and A. E. Labovsky, Two approaches to creating a turbulence model with increased temporal accuracy, Appl. Math. Comput. 358 (2019), 25–36. 10.1016/j.amc.2018.12.074Search in Google Scholar

[3] M. Aggul and A. Labovsky, A high accuracy minimally invasive regularization technique for Navier–Stokes equations at high Reynolds number, Numer. Methods Partial Differential Equations 33 (2017), no. 3, 814–839. 10.37099/mtu.dc.etdr/147Search in Google Scholar

[4] G. A. Baker, Galerkin approximations for the Navier–Stokes equations, Technical report, 1976. Search in Google Scholar

[5] Y. Batugedara, A. E. Labovsky and K. J. Schwiebert, Higher temporal accuracy for LES-C turbulence models, Comput. Methods Appl. Mech. Engrg. 377 (2021), Paper No. 113696. 10.1016/j.cma.2021.113696Search in Google Scholar

[6] A. Bourlioux, A. T. Layton and M. L. Minion, High-order multi-implicit spectral deferred correction methods for problems of reactive flow, J. Comput. Phys. 189 (2003), no. 2, 651–675. 10.1016/S0021-9991(03)00251-1Search in Google Scholar

[7] A. Dunca and Y. Epshteyn, On the Stolz–Adams deconvolution model for the large-eddy simulation of turbulent flows, SIAM J. Math. Anal. 37 (2006), no. 6, 1890–1902. 10.1137/S0036141003436302Search in Google Scholar

[8] A. A. Dunca, M. Neda and L. G. Rebholz, A mathematical and numerical study of a filtering-based multiscale fluid model with nonlinear eddy viscosity, Comput. Math. Appl. 66 (2013), no. 6, 917–933. 10.1016/j.camwa.2013.06.013Search in Google Scholar

[9] A. Dutt, L. Greengard and V. Rokhlin, Spectral deferred correction methods for ordinary differential equations, BIT 40 (2000), no. 2, 241–266. 10.21236/ADA337779Search in Google Scholar

[10] D. Erkmen and A. E. Labovsky, Defect-deferred correction method for the two-domain convection-dominated convection-diffusion problem, J. Math. Anal. Appl. 450 (2017), no. 1, 180–196. 10.37099/mtu.dc.etdr/160Search in Google Scholar

[11] D. Erkmen and A. Labovsky, Improving regularization techniques for incompressible fluid flows via defect correction: Detailed version, Technical report, ResearchGate, 2021. 10.1515/cmam-2021-0074Search in Google Scholar

[12] K. J. Galvin, L. G. Rebholz and C. Trenchea, Efficient, unconditionally stable, and optimally accurate FE algorithms for approximate deconvolution models, SIAM J. Numer. Anal. 52 (2014), no. 2, 678–707. 10.1137/120887412Search in Google Scholar

[13] V. Girault and P.-A. Raviart, Finite Element Approximation of the Navier–Stokes Equations, Lecture Notes in Math. 749, Springer, Berlin, 1979. 10.1007/BFb0063447Search in Google Scholar

[14] M. Gunzburger, Finite Element Methods for Viscous Incompressible Flows. A Guide to Theory, Practice, and Algorithms, Academic Press, Boston, MA, 1989. 10.1016/B978-0-12-307350-1.50009-0Search in Google Scholar

[15] M. Gunzburger and A. Labovsky, High accuracy method for turbulent flow problems, Math. Models Methods Appl. Sci. 22 (2012), no. 6, Article ID 1250005. 10.1142/S0218202512500054Search in Google Scholar

[16] J. G. Heywood and R. Rannacher, Finite-element approximation of the nonstationary Navier–Stokes problem. IV. Error analysis for second-order time discretization, SIAM J. Numer. Anal. 27 (1990), no. 2, 353–384. 10.1137/0727022Search in Google Scholar

[17] J. G. Heywood, R. Rannacher and S. Turek, Artificial boundaries and flux and pressure conditions for the incompressible Navier–Stokes equations, Internat. J. Numer. Methods Fluids 22 (1996), no. 5, 325–352. 10.1002/(SICI)1097-0363(19960315)22:5<325::AID-FLD307>3.0.CO;2-YSearch in Google Scholar

[18] V. John and A. Liakos, Time-dependent flow across a step: The slip with friction boundary condition, Internat. J. Numer. Methods Fluids 50 (2006), no. 6, 713–731. 10.1002/fld.1074Search in Google Scholar

[19] W. Kress and B. Gustafsson, Deferred correction methods for initial boundary value problems, J. Sci. Comput. 17 (2002), no. 1–4, 241–251. 10.1023/A:1015113017248Search in Google Scholar

[20] A. Labovsky, W. J. Layton, C. C. Manica, M. Neda and L. G. Rebholz, The stabilized extrapolated trapezoidal finite-element method for the Navier–Stokes equations, Comput. Methods Appl. Mech. Engrg. 198 (2009), no. 9–12, 958–974. 10.1016/j.cma.2008.11.004Search in Google Scholar

[21] A. Labovsky, Approximate deconvolution with correction: a member of a new class of models for high Reynolds number flows, SIAM J. Numer. Anal. 58 (2020), no. 5, 3068–3090. 10.1137/20M1311600Search in Google Scholar

[22] W. Layton and R. Lewandowski, A high accuracy Leray-deconvolution model of turbulence and its limiting behavior, Anal. Appl. (Singap.) 6 (2008), no. 1, 23–49. 10.1142/S0219530508001043Search in Google Scholar

[23] W. Layton, C. C. Manica, M. Neda and L. G. Rebholz, Numerical analysis and computational testing of a high accuracy Leray-deconvolution model of turbulence, Numer. Methods Partial Differential Equations 24 (2008), no. 2, 555–582. 10.1002/num.20281Search in Google Scholar

[24] W. Layton and M. Neda, Truncation of scales by time relaxation, J. Math. Anal. Appl. 325 (2007), no. 2, 788–807. 10.1016/j.jmaa.2006.02.014Search in Google Scholar

[25] W. J. Layton and L. G. Rebholz, Approximate Deconvolution Models of Turbulence: Analysis, Phenomenology and Numerical Analysis, Lecture Notes in Math. 2042, Springer, Heidelberg, 2012. 10.1007/978-3-642-24409-4Search in Google Scholar

[26] C. C. Manica and S. K. Merdan, Finite element error analysis of a zeroth order approximate deconvolution model based on a mixed formulation, J. Math. Anal. Appl. 331 (2007), no. 1, 669–685. 10.1016/j.jmaa.2006.08.083Search in Google Scholar

[27] J. Mathew, Large eddy simulation of a premixed flame with approximate deconvolution modeling, Proc. Combustion Inst. 29 (2002), no. 2, 1995–2000. 10.1016/S1540-7489(02)80243-7Search in Google Scholar

[28] M. L. Minion, Semi-implicit spectral deferred correction methods for ordinary differential equations, Commun. Math. Sci. 1 (2003), no. 3, 471–500. 10.4310/CMS.2003.v1.n3.a6Search in Google Scholar

[29] M. L. Minion, Semi-implicit projection methods for incompressible flow based on spectral deferred corrections, Appl. Numer. Math. 48 (2004), no. 3–4, 369–387. 10.1016/j.apnum.2003.11.005Search in Google Scholar

[30] S. Stolz and N. A. Adams, An approximate deconvolution procedure for large-eddy simulation, Phys. Fluids 11 (1999), no. 7, Article ID 1699. 10.1063/1.869867Search in Google Scholar

[31] N. Wilson, A. Labovsky and C. Trenchea, High accuracy method for magnetohydrodynamics system in Elsässer variables, Comput. Methods Appl. Math. 15 (2015), no. 1, 97–110. 10.1515/cmam-2014-0023Search in Google Scholar

[32] W.-J. Yan and Y.-C. Ma, Shape reconstruction for the time-dependent Navier–Stokes flow, Numer. Methods Partial Differential Equations 24 (2008), no. 4, 1148–1158. 10.1002/num.20310Search in Google Scholar