My research interests include the analysis, numerical analysis and large scale computing necessary for solving partial differential equations, the Navier-Stokes equations, turbulence, turbulence modeling, and Large Eddy Simulation.
I am currently working on:
-- algorithm development for efficient large scale computations for fluid flow problems
-- approximate deconvolution turbulence modeling: model development, analysis, discretization methods
-- achieving long-time accuracy in fluid flow simulations by more closely aligning discretizations with underlying physics
I am grateful to the National Science Foundation for supporting my research through the grant
NSF DMS0914478, "Enabling long-time accuracy in turbulent flow simulations," Principal Investigator, $256,583 ($256,583), 2009-2012.
William Layton, University of Pittsburgh
Carolina Manica, Universidade Federal do Rio Grande do Sul, Brazil
Monika Neda, University of Nevada Las Vegas
Alexandr Labovsky, Florida State University
William Miles, Stetson University
Maxim Olshanskii, Moscow State M. V. Lomonosov University, Russia
Mike Sussman, University of Pittsburgh
Dave Millman, University of North Carolina Chapel Hill
Alexander Linke, Weierstrass Institute for Applied Analysis and Stochastics, Germany
2) L. Rebholz, Conservation laws of turbulence models, Journal of Mathematical Analysis and Applications, Volume 326 Issue 1, 2007, pp. 33-45.
3) L. Rebholz, An Energy and Helicity conserving finite element scheme for the Navier-Stokes Equations, SIAM Journal on Numerical Analysis, Volume 45, Issue 4, pp. 1622-1638, 2007.
4) W. Layton, C. Manica, M. Neda and L. Rebholz, Numerical Analysis and Computational Testing of a high-order Leray-deconvolution turbulence model, Numerical Methods for Partial Differential Equations, Volume 24, Issue 2, pp. 555-582, 2008.
5) L. Rebholz, A family of new high order NS-alpha models arising from helicity correction in Leray turbulence models, Journal of Mathematical Analysis and Applications, Volume 342, Issue 1, pp. 246-254, 2008.
6) W. Layton, C. Manica, M. Neda and L. Rebholz, The joint helicity-energy cascade for homogeneous, isotropic turbulence generated by approximate deconvolution models, Advances and Applications in Fluid Mechanics, Volume 4, Number 1, pp. 1-46, 2008.
7) A. Labovschii, W. Layton, C. Manica, M. Neda, L. Rebholz, I. Stanculescu, C. Trenchea, Architecture of approximate deconvolution models of turbulence, In part I of Quality and Reliability of Large-Eddy Simulations, ERCOFTAC Series, Volume 12, editors J. Meyers, B. Guerts, P. Sagaut, 2008.
8) A. Labovsky, W. Layton, C. Manica, M. Neda and L. Rebholz, The stabilized, extrapolated trapezoidal finite element method for the Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, Volume 198, pp. 958-974, 2009.
9) W. Layton, C. Manica, M. Neda, M. Olshanskii and L. Rebholz, On the accuracy of the rotation form in simulations of the Navier-Stokes equations, Journal of Computational Physics, Volume 228, Issue 9, 3433-3447, 2009.
10) L. Rebholz, Enhanced physics-based numerical schemes for two classes of turbulence models, Advances in Numerical Analysis, Volume 2009, 370289, 1-13, 2009.
11) W. Layton, C. Manica, M. Neda and L. Rebholz, Numerical analysis and computational comparisons of the NS-alpha and NS-omega regularizations, Computer Methods in Applied Mechanics and Engineering, to appear.
12) W. Miles and L. Rebholz, An enhanced physics based scheme for the NS-alpha turbulence model, Numerical Methods for Partial Differential Equations, to appear.
13) L. Rebholz and M. Sussman, On the high accuracy NS-alpha-deconvolution model of turbulent fluid flow, Mathematical Models and Methods in Applied Sciences, to appear.
14) W. Layton, L. Rebholz, and M. Sussman, Energy and helicity dissipation rates of the NS-alpha and NS-alpha-deconvolution models, IMA Journal of Applied Mathematics, to appear.
15) M. Olshanskii and L. Rebholz, A note on helicity balance of the Galerkin method for the 3D Navier-Stokes equations, Computer Methods in Applied Mechanics and Engineering, to appear.
* C. Manica, M. Neda, M. Olshanskii and L. Rebholz, Enabling accuracy of Navier-Stokes-alpha through deconvolution and enhanced stability, submitted.
* M. Olshanskii and L. Rebholz, Velocity-Vorticity-Helicity formulation and a solver for the Navier-Stokes equations, submittted.
* W. Layton, C.D. Pruett, and L. Rebholz, Temporally regularized direct numerical simulation, submitted.
