TY - JOUR
T1 - An efficient split-step framework for non-Newtonian incompressible flow problems with consistent pressure boundary conditions
AU - Pacheco, Douglas R.Q.
AU - Schussnig, Richard
AU - Fries, Thomas Peter
N1 - Funding Information:
The authors acknowledge Graz University of Technology, Austria for the financial support of the Lead-project: Mechanics, Modeling and Simulation of Aortic Dissection.
Publisher Copyright:
© 2021 The Author(s)
PY - 2021/8/15
Y1 - 2021/8/15
N2 - Incompressible flow problems with nonlinear viscosity, as they often appear in biomedical and industrial applications, impose several numerical challenges related to regularity requirements, boundary conditions, matrix preconditioning, among other aspects. In particular, standard split-step or projection schemes decoupling velocity and pressure are not as efficient for generalised Newtonian fluids, since the additional terms due to the non-zero viscosity gradient couple all velocity components again. Moreover, classical pressure correction methods are not consistent with the non-Newtonian setting, which can cause numerical artifacts such as spurious pressure boundary layers. Although consistent reformulations have been recently developed, the additional projection steps needed for the viscous stress tensor incur considerable computational overhead. In this work, we present a new time-splitting framework that handles such important issues, leading to an efficient and accurate numerical tool. Two key factors for achieving this are an appropriate explicit–implicit treatment of the viscous and convective nonlinearities, as well as the derivation of a pressure Poisson problem with fully consistent boundary conditions and finite-element-suitable regularity requirements. We present first- and higher-order stepping schemes tailored for this purpose, as well as various numerical examples showcasing the stability, accuracy and efficiency of the proposed framework.
AB - Incompressible flow problems with nonlinear viscosity, as they often appear in biomedical and industrial applications, impose several numerical challenges related to regularity requirements, boundary conditions, matrix preconditioning, among other aspects. In particular, standard split-step or projection schemes decoupling velocity and pressure are not as efficient for generalised Newtonian fluids, since the additional terms due to the non-zero viscosity gradient couple all velocity components again. Moreover, classical pressure correction methods are not consistent with the non-Newtonian setting, which can cause numerical artifacts such as spurious pressure boundary layers. Although consistent reformulations have been recently developed, the additional projection steps needed for the viscous stress tensor incur considerable computational overhead. In this work, we present a new time-splitting framework that handles such important issues, leading to an efficient and accurate numerical tool. Two key factors for achieving this are an appropriate explicit–implicit treatment of the viscous and convective nonlinearities, as well as the derivation of a pressure Poisson problem with fully consistent boundary conditions and finite-element-suitable regularity requirements. We present first- and higher-order stepping schemes tailored for this purpose, as well as various numerical examples showcasing the stability, accuracy and efficiency of the proposed framework.
KW - Finite element methods
KW - Incompressible flow
KW - non-Newtonian fluids
KW - Pressure boundary conditions
KW - Pressure Poisson equation
KW - Split-step schemes
UR - http://www.scopus.com/inward/record.url?scp=85105361763&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2021.113888
DO - 10.1016/j.cma.2021.113888
M3 - Article
AN - SCOPUS:85105361763
SN - 0045-7825
VL - 382
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 113888
ER -