A high accuracy minimally invasive regularization technique for navier–stokes equations at high reynolds number
Document Type
Article
Publication Date
5-2017
Department
Department of Mathematical Sciences
Abstract
A method is presented, that combines the defect and deferred correction approaches to approximate solutions of Navier–Stokes equations at high Reynolds number. The method is of high accuracy in both space and time, and it allows for the usage of legacy codes a frequent requirement in the simulation of turbulent flows in complex geometries. The two-step method is considered here; to obtain a regularization that is second order accurate in space and time, the method computes a low-order accurate, stable, and computationally inexpensive approximation (Backward Euler with artificial viscosity) twice. The results are readily extendable to the higher order accuracy cases by adding more correction steps. Both the theoretical results and the numerical tests provided demonstrate that the computed solution is stable and the accuracy in both space and time is improved after the correction step. We also perform a qualitative test to demonstrate that the method is capable of capturing qualitative features of a turbulent flow, even on a very coarse mesh. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 814–839, 2017.
Publication Title
Numerical Methods for Partial Differential Equations
Recommended Citation
Aggul, M.,
&
Labovsky, A. E.
(2017).
A high accuracy minimally invasive regularization technique for navier–stokes equations at high reynolds number.
Numerical Methods for Partial Differential Equations,
33(3), 814-839.
http://doi.org/10.1002/num.22124
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/3803
Publisher's Statement
© 2016 Wiley Periodicals, Inc. Publisher’s version of record: https://doi.org/10.1002/num.22124