First-order system least-squares (FOSLS) for modeling blood flow.
The modeling of blood flow through a compliant vessel requires solving a system of coupled nonlinear partial differential equations (PDEs). Traditional methods for solving the system of PDEs do not scale optimally, i.e., doubling the discrete problem size results in a computational time increase of more than a factor of 2. However, the development of multigrid algorithms and, more recently, the first-order system least-squares (FOSLS) finite-element formulation has enabled optimal computational scalability for an ever increasing set of problems. Previous work has demonstrated, and in some cases proved, optimal computational scalability in solving Stokes, Navier-Stokes, elasticity, and elliptic grid generation problems separately. Additionally, coupled fluid-elastic systems have been solved in an optimal manner in 2D for some geometries. This paper presents a FOSLS approach for solving a 3D model of blood flow in a compliant vessel. Blood is modeled as a Newtonian fluid, and the vessel wall is modeled as a linear elastic material of finite thickness. The approach is demonstrated on three different geometries, and optimal scalability is shown to occur over a range of problem sizes. The FOSLS formulation has other benefits, including that the functional is a sharp, a posteriori error measure.
Heys
J J
JJ
Chemical and Materials Engineering Department, Arizona State University, Tempe, AZ 85287-6006, USA. jheys@asu.edu
DeGroff
C G
CG
Manteuffel
T A
TA
McCormick
S F
SF
D000465:Algorithms; D001011:Aorta / Q000473:pathology; D001698:Biomedical Engineering / Q000379:methods*; D001783:Blood Flow Velocity; D003198:Computer Simulation; D004548:Elasticity; D020342:Finite Element Analysis; D018056:Hemorheology; D006801:Humans; D021621:Imaging, Three-Dimensional; D016018:Least-Squares Analysis; D008955:Models, Cardiovascular; D015233:Models, Statistical; D009991:Oscillometry; D015203:Reproducibility of Results; D013997:Time Factors