TY - JOUR
T1 - On the incorporation of obstacles in a fluid flow problem using a Navier–Stokes–Brinkman penalization approach[Formula presented]
AU - Fuchsberger, Jana
AU - Aigner, Philipp
AU - Niederer, Steven
AU - Plank, Gernot
AU - Schima, Heinrich
AU - Haase, Gundolf
AU - Karabelas, Elias
N1 - Funding Information:
His research has been supported by grants from the Austrian Science Fund, NIH, Wellcome Trust, European FP7 and H2020 awards and resulted in more than 120 journal publications. His research interests are focused on the development of computational models of total cardiac function and their application to gain mechanistic insights into cardiovascular function in health and disease. His work has a translational focus on using cardiac simulation in industrial and clinical applications. As a Co-founder of NumeriCor he is actively involved in the commercialization of cardiac modeling technologies.
Funding Information:
G. Plank and G. Haase acknowledge support from the Austrian Science Fund (FWF) (grant nos. F3210-N18 , and I2760-B30 ) and by BioTechMed-Graz (grant no. Flagship Project: ILearnHeart). S. Niederer acknowledges support from the UK Engineering and Physical Sciences Research Council (grant nos. EP/M012492/1 , NS/A000049/1 and EP/P01268X/1 ), the British Heart Foundation (grant nos. PG/15/91/31812 , PG/13/37/30280 , SP/18/6/33805 ), US National Institutes of Health (grant no. NIH R01-HL152256 ), European Research Council (grant no. ERC PREDICT-HF 864055 ), Wellcome Trust, United Kingdom (grant no. WT 203148/Z/16/Z ) and Kings Health Partners London National Institute for Health Research (NIHR) Biomedical Research Centre, United Kingdom . We further acknowledge support by NAWI Graz and by the PRACE project “71138: Image-based Learning in Predictive Personalized Models of Total Heart Function” for awarding us access to the Austrian HPC resources VSC3 and VSC4.
Publisher Copyright:
© 2021 The Authors
PY - 2022/1
Y1 - 2022/1
N2 - Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and, vice versa, which forces are exerted on the solids by the moving fluid. Such problems appear in various contexts, ranging from numerous technical applications such as e.g. turbines to medical problems such as the regulation of cardiovascular hemodynamics by valves. Typically, the numerical treatment of such problems is posed within a fluid structure interaction (FSI) framework. General FSI models are able to capture bidirectional interactions, but are challenging to solve and computationally expensive. Simplified methods offer a possible remedy by achieving better computational efficiency to broaden the scope to demanding application problems with focus on understanding the effect of solids on altering fluid dynamics. In this study we report on the development of a novel method for such applications. In our method rigid moving obstacles are incorporated in a fluid dynamics context using concepts from porous media theory. Based on the Navier–Stokes–Brinkman equations which augments the Navier–Stokes equation with a Darcy drag term our method represents solid obstacles as time-varying regions containing a porous medium of vanishing permeability. Numerical stabilization and turbulence modeling is dealt with by using a residual based variational multiscale (RBVMS) formulation. The additional Darcy drag term and its respective stabilization are easily accommodated in any existing finite-element based Navier–Stokes solver. The key advantages of our approach – computational efficiency and ease of implementation – are demonstrated by solving a standard benchmark problem of a rotating blood pump posed by the Food and Drug Administration Agency (FDA). Validity is demonstrated by conducting a mesh convergence study and by comparison against the extensive set of experimental data provided for this benchmark.
AB - Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and, vice versa, which forces are exerted on the solids by the moving fluid. Such problems appear in various contexts, ranging from numerous technical applications such as e.g. turbines to medical problems such as the regulation of cardiovascular hemodynamics by valves. Typically, the numerical treatment of such problems is posed within a fluid structure interaction (FSI) framework. General FSI models are able to capture bidirectional interactions, but are challenging to solve and computationally expensive. Simplified methods offer a possible remedy by achieving better computational efficiency to broaden the scope to demanding application problems with focus on understanding the effect of solids on altering fluid dynamics. In this study we report on the development of a novel method for such applications. In our method rigid moving obstacles are incorporated in a fluid dynamics context using concepts from porous media theory. Based on the Navier–Stokes–Brinkman equations which augments the Navier–Stokes equation with a Darcy drag term our method represents solid obstacles as time-varying regions containing a porous medium of vanishing permeability. Numerical stabilization and turbulence modeling is dealt with by using a residual based variational multiscale (RBVMS) formulation. The additional Darcy drag term and its respective stabilization are easily accommodated in any existing finite-element based Navier–Stokes solver. The key advantages of our approach – computational efficiency and ease of implementation – are demonstrated by solving a standard benchmark problem of a rotating blood pump posed by the Food and Drug Administration Agency (FDA). Validity is demonstrated by conducting a mesh convergence study and by comparison against the extensive set of experimental data provided for this benchmark.
KW - Computational fluid dynamics
KW - Hemodynamics
KW - Large eddy simulation
KW - Penalization methods
KW - Variational multiscale methods
UR - http://www.scopus.com/inward/record.url?scp=85120632223&partnerID=8YFLogxK
U2 - 10.1016/j.jocs.2021.101506
DO - 10.1016/j.jocs.2021.101506
M3 - Article
AN - SCOPUS:85120632223
SN - 1877-7503
VL - 57
JO - Journal of Computational Science
JF - Journal of Computational Science
M1 - 101506
ER -