Computational fluid dynamics (CFD) is increasingly used to study blood flows in
patient-specific arteries for understanding certain cardiovascular diseases. The
techniques work quite well for relatively simple problems but need improvements
when the problems become harder when (a) the geometry becomes
complex (eg, a few branches to a full pulmonary artery), (b) the model becomes
more complex (eg, fluid-only to coupled fluid-structure interaction), (c) both
the fluid and wall models become highly nonlinear, and (d) the computer on
which we run the simulation is a supercomputer with tens of thousands of
processor cores. To push the limit of CFD in all four fronts, in this paper, we
develop and study a highly parallel algorithm for solving a monolithically coupled
fluid-structure system for the modeling of the interaction of the blood
flow and the arterial wall. As a case study, we consider a patient-specific, full
size pulmonary artery obtained from computed tomography (CT) images, with
an artificially added layer of wall with a fixed thickness. The fluid is modeled
with a system of incompressible Navier-Stokes equations, and the wall is modeled by a geometrically nonlinear elasticity equation. As far as we know, this is the first time the unsteady blood flow in a full pulmonary artery is simulated
without assuming a rigid wall. The proposed numerical algorithm and software
scale well beyond 10 000 processor cores on a supercomputer for solving the
fluid-structure interaction problem discretized with a stabilized finite element
method in space and an implicit scheme in time involving hundreds of millions
of unknowns.
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A Robust Bubble Growth Solution Scheme for Implementation in CFD Analysis of Multiphase Flows
Although the full form of the Rayleigh–Plesset (RP) equation more accurately depicts the bubble behavior in a cavitating flow than its reduced form, it finds much less application than the latter in the computational fluid dynamic (CFD) simulation due to its high stiffness. The traditional variable time-step scheme for the full form RP equation is difficult to be integrated with the CFD program since it requires a tiny time step at the singularity point for convergence and this step size may be incompatible with time marching of conservation equations. This paper presents two stable and efficient numerical solution schemes based on the finite difference method and Euler method so that the full-form RP equation can be better accepted by the CFD program. By employing a truncation bubble radius to approximate the minimum bubble size in the collapse stage, the proposed schemes solve for the bubble radius and wall velocity in an explicit way. The proposed solution schemes are more robust for a wide range of ambient pressure profiles than the traditional schemes and avoid excessive refinement on the time step at the singularity point. Since the proposed solution scheme can calculate the effects of the second-order term, liquid viscosity, and surface tension on the bubble evolution, it provides a more accurate estimation of the wall velocity for the vaporization or condensation rate, which is widely used in the cavitation model in the CFD simulation. The legitimacy of the solution schemes is manifested by the agreement between the results from these schemes and established ones from the literature. The proposed solution schemes are more robust in face of a wide range of ambient pressure profiles.
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- Award ID(s):
- 2043325
- NSF-PAR ID:
- 10404699
- Date Published:
- Journal Name:
- Computation
- Volume:
- 11
- Issue:
- 4
- ISSN:
- 2079-3197
- Page Range / eLocation ID:
- 72
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Computational fluid dynamics (CFD) is increasingly used to study blood flows in patient‐specific arteries for understanding certain cardiovascular diseases. The techniques work quite well for relatively simple problems but need improvements when the problems become harder when (a) the geometry becomes complex (eg, a few branches to a full pulmonary artery), (b) the model becomes more complex (eg, fluid‐only to coupled fluid‐structure interaction), (c) both the fluid and wall models become highly nonlinear, and (d) the computer on which we run the simulation is a supercomputer with tens of thousands of processor cores. To push the limit of CFD in all four fronts, in this paper, we develop and study a highly parallel algorithm for solving a monolithically coupled fluid‐structure system for the modeling of the interaction of the blood flow and the arterial wall. As a case study, we consider a patient‐specific, full size pulmonary artery obtained from computed tomography (CT) images, with an artificially added layer of wall with a fixed thickness. The fluid is modeled with a system of incompressible Navier‐Stokes equations, and the wall is modeled by a geometrically nonlinear elasticity equation. As far as we know, this is the first time the unsteady blood flow in a full pulmonary artery is simulated without assuming a rigid wall. The proposed numerical algorithm and software scale well beyond 10 000 processor cores on a supercomputer for solving the fluid‐structure interaction problem discretized with a stabilized finite element method in space and an implicit scheme in time involving hundreds of millions of unknowns.
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Finite Time Blowup of 2D Boussinesq and 3D Euler Equations with $C^{1,\alpha}$ Velocity and Boundarynull (Ed.)Inspired by the numerical evidence of a potential 3D Euler singularity by Luo- Hou [30,31] and the recent breakthrough by Elgindi [11] on the singularity formation of the 3D Euler equation without swirl with $C^{1,\alpha}$ initial data for the velocity, we prove the finite time singularity for the 2D Boussinesq and the 3D axisymmetric Euler equations in the presence of boundary with $C^{1,\alpha}$ initial data for the velocity (and density in the case of Boussinesq equations). Our finite time blowup solution for the 3D Euler equations and the singular solution considered in [30,31] share many essential features, including the symmetry properties of the solution, the flow structure, and the sign of the solution in each quadrant, except that we use $C^{1,\alpha}$ initial data for the velocity field. We use a dynamic rescaling formulation and follow the general framework of analysis developed by Elgindi in [11]. We also use some strategy proposed in our recent joint work with Huang in [7] and adopt several methods of analysis in [11] to establish the linear and nonlinear stability of an approximate self-similar profile. The nonlinear stability enables us to prove that the solution of the 3D Euler equations or the 2D Boussinesq equations with $C^{1,\alpha}$ initial data will develop a finite time singularity. Moreover, the velocity field has finite energy before the singularity time.more » « less
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Motivated by the need for accurate determination of wall shear stress from profile measurements in turbulent boundary layer flows, the total shear stress balance is analysed and reformulated using several well-established semi-empirical relations. The analysis highlights the significant effect that small pressure gradients can have on parameters deduced from data even in nominally zero pressure gradient boundary layers. Using the comprehensive shear stress balance together with the log-law equation, it is shown that friction velocity, roughness length and zero-plane displacement can be determined with only velocity and turbulent shear stress profile measurements at a single streamwise location for nominally zero pressure gradient turbulent boundary layers. Application of the proposed analysis to turbulent smooth- and rough-wall experimental data shows that the friction velocity is determined with accuracy comparable to force balances (approximately 1 %–4 %). Additionally, application to boundary layer data from previous studies provides clear evidence that the often cited discrepancy between directly measured friction velocities (e.g. using force balances) and those derived from traditional total shear stress methods is likely due to the small favourable pressure gradient imposed by a fixed cross-section facility. The proposed comprehensive shear stress analysis can account for these small pressure gradients and allows more accurate boundary layer wall shear stress or friction velocity determination using commonly available mean velocity and shear stress profile data from a single streamwise location.more » « less
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We construct new first- and second-order pressure correctionschemes using the scalar auxiliary variable approach for the Navier-Stokes equations. These schemes are linear, decoupled and only require solving a sequence of Poisson type equations at each time step. Furthermore, they are unconditionally energy stable. We also establish rigorous error estimates in the two dimensional case for the velocity and pressure approximation of the first-order scheme without any condition on the time step.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/computation11040072
