A high accuracy minimally invasive regularization technique for navier–stokes equations at high reynolds number

• Published in: Numerical methods for partial differential equations 2017-05, Vol.33 (3), p.814-839
• Main Authors: Aggul, Mustafa, Labovsky, Alexander
• Format: Article
• Language: English
• Subjects: Accuracy; artificial viscosity; Computational fluid dynamics; defect‐correction; deferred‐correction; High Reynolds number; Mathematical analysis; Mathematical models; Navier-Stokes equations; Navier‐Stokes; Regularization; Reynolds number; time‐dependent; Turbulence; Turbulent flow
• ISSN: 0749-159X; 1098-2426
• DOI: 10.1002/num.22124

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