Incompressible Navier-Stokes Equations Research Articles

A Delaunay refinement algorithm for the particle finite element method applied to free surface flows

AbstractThis article proposes two contributions to the calculation of free‐surface flows using the particle finite element method (PFEM). The PFEM is based upon a Lagrangian approach: a set of particles defines the fluid and each particle is associated with a velocity vector. Then, unlike a pure Lagrangian method, all the particles are connected by a triangular mesh. The difficulty lies in locating the free surface from this mesh. It is a matter of deciding which of the elements in the mesh are part of the fluid domain, and to define a boundary—the free surface. Then, the incompressible Navier–Stokes equations are solved on the fluid domain and the particle position is updated using the velocity vector from the finite element solver. Our first contribution is to propose an approach to adapt the mesh with theoretical guarantees of quality: the mesh generation community has acquired a lot of experience and understanding about mesh adaptation approaches with guarantees of quality on the final mesh. The approach we use here is based on a Delaunay refinement strategy, allowing to insert and remove nodes while gradually improving mesh quality. We show that what is proposed allows to create stable and smooth free surface geometries. One characteristic of the PFEM is that only one fluid domain is modeled, even if its shape and topology change. It is nevertheless necessary to apply conditions on the domain boundaries. When a boundary is a free surface, the flow on the other side is not modeled, it is represented by an external pressure. On the external free surface boundary, atmospheric pressure can be imposed. Nevertheless, there may be internal free surfaces: the fluid can fully encapsulate cavities to form bubbles. The pressure required to maintain the volume of those bubbles is a priori unknown. For example, the atmospheric pressure would not be sufficient to prevent the bubbles from deflating and eventually disappearing. Our second contribution is to propose a multi‐point constraint approach to enforce global incompressibility of those empty bubbles. We show that this approach allows to accurately model bubbly flows that involve two fluids with large density differences, for instance water and air, while only modeling the heavier fluid.

An improved physics-informed neural network with adaptive weighting and mixed differentiation for solving the incompressible Navier–Stokes equations

An improved physics-informed neural network with adaptive weighting and mixed differentiation for solving the incompressible Navier–Stokes equations

Extremization to fine tune physics informed neural networks for solving boundary value problems

We propose a novel method for fast and accurate training of physics-informed neural networks (PINNs) to find solutions to boundary value problems (BVPs) and initial boundary value problems (IBVPs). By combining the methods of training deep neural networks (DNNs) and Extreme Learning Machines (ELMs), we develop a model which has the expressivity of DNNs with the fine-tuning ability of ELMs. We showcase the superiority of our proposed method by solving several BVPs and IBVPs which include linear and non-linear ordinary differential equations (ODEs), partial differential equations (PDEs) and coupled PDEs. The examples we consider include a stiff coupled ODE system where traditional numerical methods fail, a 3+1D non-linear PDE, Kovasznay flow and Taylor–Green vortex solutions to incompressible Navier–Stokes equations and pure advection solution of 1+1 D compressible Euler equation.The Theory of Functional Connections (TFC) is used to exactly impose initial and boundary conditions (IBCs) of (I)BVPs on PINNs. We propose a modification to the TFC framework named Reduced TFC and show a significant improvement in the training and inference time of PINNs compared to IBCs imposed using TFC. Furthermore, Reduced TFC is shown to be able to generalize to more complex boundary geometries which is not possible with TFC. We also introduce a method of applying boundary conditions at infinity for BVPs and numerically solve the pure advection in 1+1 D Euler equations using these boundary conditions.

A high-order upwind compact difference scheme for solving the streamfunction-velocity formulation of the unsteady incompressible Navier–Stokes equations

In this paper, we propose an upwind compact difference method with fourth-order spatial accuracy and second-order temporal accuracy for solving the streamfunction-velocity formulation of the two-dimensional unsteady incompressible Navier–Stokes equations. The streamfunction and its first-order partial derivatives (velocities) are treated as unknown variables. Three types of compact difference schemes are employed to discretize the first-order partial derivatives of the streamfunction. Specifically, these schemes include the fourth-order symmetric scheme, the fifth-order upwind scheme, and the sixth-order symmetric scheme derived by combining the two parts of the fifth-order upwind scheme. As a result, the fourth-order spatial discretization schemes are established for the Laplacian term, the biharmonic term, and the nonlinear convective term, along with the Crank–Nicolson scheme for the temporal discretization. The unconditional stability characteristic of the scheme for the linear model is proved by discrete von Neumann analysis. Moreover, six numerical experiments involving three test problems with the analytic solutions, and three flow problems including doubly periodic double shear layer, lid-driven cavity flow, and dipole-wall interaction are carried out to demonstrate the accuracy, robustness, and efficiency of the present method. The results indicate that the present method not only has good numerical performance but also exhibits quite efficiency.

LES on wind turbines by comparison of Vortex Particle Method and Finite Volume Method codes

The aim of this paper is to compare two different computational methods that analyse the flow around wind turbine using Large-Eddy-Simulations (LES). The first method uses a three-dimensional unsteady Lagrangian Vortex Particle method (VP) associated to a lifting-line (LL) approach providing radial loads, integrated thrust and power coefficients, circulations and angle of attack across the turbine blades. The second method solves the incompressible Navier-Stokes equations with the classical Finite Volume (FV) method coupled to the Actuator Line (AL) method to model the rotor blades. Both methods are compared by means of a benchmark consisting in a single full-scale NREL5MW wind turbine and the results are thus compared to Martínez-Tossas et al (2018). The comparisons involve loads, angle of attack and velocity along the blade. Wakes downstream of the turbine are analysed via the evolution of flow fields as mean velocity and vorticity. Results are found to be in good agreement with the verification case. A comparison is also performed on the evaluation of the numerical cost, precision and efficiency of both computational methods.

Nonlinear Asymptotic Stability and Transition Threshold for 2D Taylor–Couette Flows in Sobolev Spaces

In this paper, we investigate the stability of the 2-dimensional (2D) Taylor–Couette (TC) flow for the incompressible Navier–Stokes equations. The explicit form of velocity for 2D TC flow is given by u=(Ar+Br)(-sinθ,cosθ)T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u=(Ar+\\frac{B}{r})(-\\sin \ heta , \\cos \ heta )^T$$\\end{document} with (r,θ)∈[1,R]×S1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(r, \ heta )\\in [1, R]\ imes \\mathbb {S}^1$$\\end{document} being an annulus and A, B being constants. Here, A, B encode the rotational effect and R is the ratio of the outer and inner radii of the annular region. Our focus is the long-term behavior of solutions around the steady 2D TC flow. While the laminar solution is known to be a global attractor for 2D channel flows and plane flows, it is unclear whether this is still true for rotating flows with curved geometries. In this article, we prove that the 2D Taylor–Couette flow is asymptotically stable, even at high Reynolds number (Re∼ν-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re\\sim \ u ^{-1}$$\\end{document}), with a sharp exponential decay rate of exp(-ν13|B|23R-2t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\exp (-\ u ^{\\frac{1}{3}}|B|^{\\frac{2}{3}}R^{-2}t)$$\\end{document} as long as the initial perturbation is less than or equal to ν12|B|12R-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u ^\\frac{1}{2} |B|^{\\frac{1}{2}}R^{-2}$$\\end{document} in Sobolev space. The powers of ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document} and B in this decay estimate are optimal. It is derived using the method of resolvent estimates and is commonly recognized as the enhanced dissipative effect. Compared to the Couette flow, the enhanced dissipation of the rotating Taylor–Couette flow not only depends on the Reynolds number but also reflects the rotational aspect via the rotational coefficient B. The larger the |B|, the faster the long-time dissipation takes effect. We also conduct space-time estimates describing inviscid-damping mechanism in our proof. To obtain these inviscid-damping estimates, we find and construct a new set of explicit orthonormal basis of the weighted eigenfunctions for the Laplace operators corresponding to the circular flows. These provide new insights into the mathematical understanding of the 2D Taylor–Couette flows.

Onsager's ‘ideal turbulence’ theory

In 1945–1949, Lars Onsager made an exact analysis of the high-Reynolds-number limit for individual turbulent flow realisations modelled by incompressible Navier–Stokes equations, motivated by experimental observations that dissipation of kinetic energy does not vanish. I review here developments spurred by his key idea that such flows are well described by distributional or ‘weak’ solutions of ideal Euler equations. 1/3 Hölder singularities of the velocity field were predicted by Onsager and since observed. His theory describes turbulent energy cascade without probabilistic assumptions and yields a local, deterministic version of the Kolmogorov $4/5$ th law. The approach is closely related to renormalisation group methods in physics and envisages ‘conservation-law anomalies’, as discovered later in quantum field theory. There are also deep connections with large-eddy simulation modelling. More recently, dissipative Euler solutions of the type conjectured by Onsager have been constructed and his $1/3$ Hölder singularity proved to be the sharp threshold for anomalous dissipation. This progress has been achieved by an unexpected connection with work of John Nash on isometric embeddings of low regularity or ‘convex integration’ techniques. The dissipative Euler solutions yielded by this method are wildly non-unique for fixed initial data, suggesting ‘spontaneously stochastic’ behaviour of high-Reynolds-number solutions. I focus in particular on applications to wall-bounded turbulence, leading to novel concepts of spatial cascades of momentum, energy and vorticity to or from the wall as deterministic, space–time local phenomena. This theory thus makes testable predictions and offers new perspectives on large-eddy simulation in the presence of solid walls.

Numerical solutions of boundary problems in partial differential equations: A deep learning framework with Green's function

This work introduces Green Networks (GreenNets), a novel class of neural network architectures designed to address a wide spectrum of boundary problems in partial differential equations (PDEs). Demonstrated versatility includes solving the Poisson equation, convection-diffusion equation, and unsteady incompressible Navier-Stokes equations. GreenNets comprises two specialized variants: Boundary Transformation Green Network (BT-GreenNet), focusing on transforming Dirichlet boundary conditions into source terms, and Boundary Integral Green Network (BI-GreenNet), considering boundary integral terms with shared weights between the boundary and source integrals. Comparisons with existing deep learning and traditional numerical methods underscore their accuracy and efficiency. BT-GreenNet excels in efficiency, and BI-GreenNet offers enhanced flexibility. The research pinnacle, Boundary Unified Green Network (BU-GreenNet), merges BT-GreenNet and BI-GreenNet to address coupled PDEs, specifically unsteady incompressible Navier-Stokes equations. BU-GreenNet stands out by surpassing traditional numerical approaches, offering remarkable computational efficiency while faithfully capturing the intricate evolution of fluid dynamics phenomena. This research redefines the means of solution to boundary problems in PDEs through innovative neural network architectures, emphasizing practical utility and computational efficiency.

DeHNSSo: The Delft Harmonic Navier-Stokes Solver for nonlinear stability problems with complex geometric features

A nonlinear Harmonic Navier-Stokes (HNS) framework is introduced for simulating instabilities in laminar spanwise-invariant shear layers, featuring sharp and smooth wall surface protuberances. While such cases play a critical role in the process of laminar-to-turbulent transition, classical stability theory analyses such as parabolized or local stability methods fail to provide (accurate) results, due to their underlying assumptions. The generalized incompressible Navier-Stokes (NS) equations are expanded in perturbed form, using a spanwise and temporal Fourier ansatz for flow perturbations. The resulting equations are discretized using spectral collocation in the wall-normal direction and finite-difference methods in the streamwise direction. The equations are then solved using a direct sparse-matrix solver. The nonlinear mode interaction terms are converged iteratively. The solution implementation makes use of a generalized domain transformation to account for geometrical smooth surface features, such as humps. No-slip conditions can be embedded in the interior domain to account for the presence of sharp surface features such as forward- or backward-facing steps. Common difficulties with Navier-Stokes solvers, such as the treatment of the outflow boundary and convergence of nonlinear terms, are considered in detail. The performance of the developed solver is evaluated against several cases of representative boundary layer instability growth, including linear and nonlinear growth of Tollmien-Schlichting waves in a Blasius boundary layer and stationary crossflow instabilities in a swept flat-plate boundary layer. The latter problem is also treated in the presence of a geometrical smooth hump and a sharp forward-facing step at the wall. HNS simulation results, such as perturbation amplitudes, growth rates, and shape functions, are compared to benchmark flow stability analysis methods such as Parabolized Stability Equations (PSE), Adaptive Harmonic Linearized Navier-Stokes (AHLNS), or Direct Numerical Simulations (DNS). Good agreement is observed in all cases. The HNS solver is subjected to a grid convergence study and a simple performance benchmark, namely memory usage and computational cost. The computational cost is found to be considerably lower than high-fidelity DNS at comparable grid resolutions. Program summaryProgram Title: DeHNSSoCPC Library link to program files:https://doi.org/10.17632/9bnms99kk2.1Developer's repository link:https://github.com/SvenWesterbeek/DeHNSSoLicensing provisions: GPLv3Programming language: MatlabSupplementary material: The supplementary material contains the code as well as a user manual.Nature of problem: Fluid flows are subject to laminar-to-turbulent transition following the growth of instabilities. To avoid computationally demanding Direct Numerical Simulations (DNS), perturbation theory is often applied to their analysis. However, classical stability methods based on the Orr-Sommerfeld equation or the Parabolized Stability Equations neglect the influence of streamwise gradients in varying degrees. The validity of these assumptions is difficult to estimate a priori.Solution method: The Delft Harmonic Navier-Stokes Solver (DeHNSSo) solves the harmonic Navier-Stokes equations nonlinearly on domains featuring sharp and smooth spanwise invariant surface features using a generalized grid approach in combination with an embedded boundary method. This allows the user to include the effects of streamwise gradients on flow at a fraction of the cost of DNS.Additional comments including restrictions and unusual features: In DeHNSSo, the equations are solved using direct matrix solvers. As such, memory is treated as a scarce resource. The problem is formulated in a mode-independent manner such that left-hand side matrices need only be computed and stored once despite incorporating nonlinear terms. Additionally, DeHNSSo offers the user the possibility to prescribe inhomogeneous boundary conditions to introduce and solve the receptivity problem or manipulate instabilities. Due to the double Fourier expansion, the solver is restricted to spanwise and temporally periodic problems.

A reduced order model formulation for left atrium flow: an atrial fibrillation case

A data-driven reduced order model (ROM) based on a proper orthogonal decomposition-radial basis function (POD-RBF) approach is adopted in this paper for the analysis of blood flow dynamics in a patient-specific case of atrial fibrillation (AF). The full order model (FOM) is represented by incompressible Navier–Stokes equations, discretized with a finite volume (FV) approach. Both the Newtonian and the Casson’s constitutive laws are employed. The aim is to build a computational tool able to efficiently and accurately reconstruct the patterns of relevant hemodynamics indices related to the stasis of the blood in a physical parametrization framework including the cardiac output in the Newtonian case and also the plasma viscosity and the hematocrit in the non-Newtonian one. Many FOM-ROM comparisons are shown to analyze the performance of our approach as regards errors and computational speed-up.

Well‐posedness and time decay of fractional Keller–Segel–Navier‐Stokes equations in homogeneous Besov spaces

AbstractIn this paper, we consider the parabolic–elliptic Keller–Segel system, which is coupled to the incompressible Navier–Stokes equations through transportation and friction. It is shown that when the system is diffused by Lévy motion, the well‐posedness of the mild solution to the corresponding Cauchy problem in homogeneous Besov spaces is established by means of the Banach fixed point theorem. Furthermore, we prove the Lorentz regularity in time direction and the maximal regularity of solutions. In addition, we obtain the additional regularity and explore the time decay property of global mild solutions.

Fragmentation of colliding liquid rims

We present direct numerical simulations of the splashing process between two cylindrical liquid rims. This belongs to a class of impact and collision problems with a wide range of applications in science and engineering, and motivated here by splashing of breaking ocean waves. Interfacial perturbations with a truncated white noise frequency profile are introduced to the rims before their collision, whose subsequent morphological development is simulated by solving the two-phase incompressible Navier–Stokes equation with the adaptive mesh refinement technique, within the Basilisk software environment. We first derive analytical solutions predicting the unsteady interfacial and velocity profiles of the expanding sheet forming between the two rims, and develop scaling laws for the evolution of the lamella rim under capillary deceleration. We then analyse the formation and growth of transverse ligaments ejected from the lamella rims, which we find to originate from the initial corrugated geometry of the perturbed rim surface. Novel scaling models are proposed for predicting the decay of the ligament number density due to the ongoing ligament merging phenomenon, and found to agree well with the numerical results presented here. The role of the mechanism in breaking waves is discussed further and necessary next steps in the problem are identified.

Long time existence of the non-isentropic slightly compressible Navier-Stokes equations with boundary conditions

We investigate the long time existence of smooth solutions to the initial boundary value problem for the non-isentropic slightly compressible Navier–Stokes equations with slip or non-slip boundary conditions on the velocity. We verify that the compressible Navier–Stokes equations with boundary conditions admit a unique smooth solution on the time interval where the smooth solution of the incompressible Navier–Stokes equations exists, when the Mach number is sufficiently small. Moreover, we obtain the uniform convergence of smooth solutions for the compressible system toward those for the corresponding incompressible system on that time interval.

A Quasi-Variational-Hemivariational Inequality for Incompressible Navier-Stokes System with Bingham Fluid

In this paper we examine a class of elliptic quasi-variational inequalities, which involve a constraint set and a set-valued map. First, we establish the existence of a solution and the compactness of the solution set. The approach is based on results for an elliptic variational inequality and the Kakutani-Ky Fan fixed point theorem. Next, we prove an existence and compactness result for a quasi-variational-hemivariational inequality. The latter involves a locally Lipschitz continuous functional and a convex potential. Finally, we present an application to the stationary incompressible Navier-Stokes equation with mixed boundary conditions which model a generalized Newtonian fluid of Bingham type.

Mixing of a cylindrical gravity current in a stratified ambient

Simulation results from direct numerical simulations (DNSs) of cylindrical gravity currents propagating into a linearly stratified ambient with stratification strengths ranging from 0 to 0.8, at a moderate Reynolds number of Re=3450 are presented. The simulations are based on the incompressible Navier–Stokes equations, assuming small density differences such that the Boussinesq approximation is valid. The density of the ambient fluid increases linearly from the top (ρ0) to the bottom (ρb) of the domain. A comparative analysis is conducted between the stratified cases and the unstratified case to investigate the impact of ambient stratification strength on the mixing behaviour of cylindrical gravity currents. The energy conversion processes are analysed using the mechanical framework proposed by Winters et al. (1995). The energy budget is formulated by considering gravitational available potential energy, and the evolution of potential energy due to reversible stirring and irreversible diapycnal mixing in the system. The findings reveal a decrease in available potential energy and kinetic energy with increasing stratification strength, indicating lower energy exchange for gravity currents propagating in the stratified environment. Instantaneous and cumulative mixing efficiency calculations during the slumping phase indicate that Kelvin–Helmholtz billow play an important role in stirring the heavy fluid and causing irreversible mixing with the ambient fluid.

A fully conservative and shift-invariant formulation for Galerkin discretizations of incompressible variable density flow

This paper introduces a formulation of the variable density incompressible Navier-Stokes equations by modifying the nonlinear terms in a consistent way. For Galerkin discretizations, the formulation leads to favorable discrete conservation properties without the divergence-free constraint being strongly enforced. In addition, the formulation is shown to make the density field invariant to global shifts. The effect of viscous regularizations on conservation properties is also investigated. Numerical tests validate the theory developed in this work. The new formulation shows superior performance compared to other formulations from the literature, both in terms of accuracy for smooth problems and in terms of robustness.

Aeroacoustic simulation of human phonation based on the flow-induced vocal fold vibrations including their contact

This paper deals with the numerical simulation of the flow induced sound as generated in the human phonation process including vocal folds (VF) contact. The hybrid approach is used allowing to separate the acoustic and the biomechanical description of the considered problem. The two-dimensional fluid–structure interaction (FSI) problem is modelled by a simplified linear elastic model coupled to the incompressible Navier–Stokes equations in the arbitrary Lagrangian–Eulerian form and special attention is paid to the treatment of the contact problem in the FSI context. Following approach of [Sváček and Horáček, 2021] the incompressible flow model is modified by an addition of fictitious porosity term and the penalization inlet boundary condition is used. Further, the Lighthill acoustic analogy is applied for calculation of sound sources and their propagation through a vocal tract model. All partial differential equations, describing the elastic body vibration, the fluid flow and the acoustics, are approximated by finite element method. Numerical results of one-sided vocal fold paralysis are presented.

A MEEVC discretization for two-dimensional incompressible Navier-Stokes equations with general boundary conditions

In this work, we present a mass, energy, enstrophy and vorticity conserving (MEEVC) mixed finite element discretization for two-dimensional incompressible Navier-Stokes equations as an alternative to the original MEEVC scheme proposed in A. Palha and M. Gerritsma (2017) [5]. The present method can incorporate general boundary conditions. Conservation properties are proven. Supportive numerical experiments with both exact and inexact quadrature are provided.

Data-driven surrogate modelling of multistage Taylor cone–jet dynamics

The Taylor cone jet is an electrohydrodynamic flow typically induced by applying an external electric field to a liquid within a capillary, commonly utilized in colloidal thrusters. This flow generation involves a complex multiphase and multiphysics process, with stability contingent upon specific operational parameters. The operational window is intrinsically linked to flow rate and applied electric voltage magnitude. High voltages can induce atomization instabilities, resulting in the production of an electrospray. Our study presents initially a numerical investigation into the atomization process of a Taylor cone jet using computational fluid dynamics. Implemented within OpenFOAM, our numerical model utilizes a volume-of-fluid approach coupled with Maxwell's equations to incorporate electric body forces into the incompressible Navier–Stokes equations. We employ the leaky-dielectric model, subjecting the interface between phases to hydrodynamic surface tension and electric stress (Maxwell stress). With this model, we studied the droplet breakup of a heptane liquid jet, for a range of operation of 1.53–7.0 nL s−1 and 2.4–4.5 kV of extraction. First, the developed high-fidelity numerical solution is studied for the jet breakup and acceleration of the droplets. Second, we integrate a machine learning model capable of extending the parametric windows of operation. Additionally, we explore the influence of extractor and acceleration plates on colloidal propulsion systems. This work offers a numerical exploration of the Taylor cone–jet transition and droplet acceleration using novel, numerically accurate approaches. Subsequently, we integrate machine learning models, specifically an artificial neural network and a one-dimensional convolutional neural network, to predict the jet's performance under conditions not previously evaluated by computationally heavy numerical models. Notably, we demonstrate that the convolutional neural network outperforms the artificial neural network for this type of application data, achieving a 2% droplet size prediction accuracy.

Abstract 1145: A Computational Fluid Dynamics Analysis Of Hemodynamic Differences In Patients With High Grade Asymptomatic Carotid Artery Stenosis

Introduction: Current assessment/management of internal carotid artery (ICA) stenosis is based on estimation of percentage (%) stenosis which does not account for trans-lesional flow, pressure gradient (PG), wall shear stress (WSS), or oscillatory shear index (OSI). Computation fluid dynamics (CFD) can be used to characterize such indices. Hypothesis: We hypothesize that patients asymptomatic >70% ICA stenosis will have hemodynamic differences that are independent of % stenosis. Aims: Evaluate hemodynamic indices in patients with asymptomatic >70% ICA stenosis via CFD. Methods: Patients with asymptomatic >70% ICA stenosis were included. 3D time-of-flight (TOF) and phase-contrast (PC) magnetic resonance imaging (MRI) sequences were obtained. CRIMSON was used to generate CFD models containing the carotid artery (CCA), ICA, and external carotid artery (ECA). PC MRI-derived flow waveforms were prescribed to the CCA and ECA. The ICA outlet was coupled to a three-element Windkessel model. Blood was modeled as an incompressible Non-Newtonian fluid with a dynamic viscosity of 0.004 kg m –1 s –1 and a density of 1,060 kg m -3 . Incompressible Navier-Stokes equations were used to solve for velocity and pressures. Results: Eight patients (average age 73.8 years, 62.5% male) with asymptomatic high-grade ICA stenosis (62.5% left) were included. Hypertension (87.5%), tobacco use (87.5%), and hyperlipidemia (75%) were common. Most patients were medically optimized with anti-hypertensive (100%), statin (87.5%), and aspirin (87.5%). Three patients (37.5%) underwent ICA intervention.. Mean peak systolic velocity was 406 cm/s and mean end-diastolic velocity was 127 cm/s. There was large variability in trans-lesional ICA flow, PG, WSS, and OSI (Table 1). Conclusions: Asymptomatic patients with the same % stenosis have differences in trans-lesional ICA flow, PG, WSS, and OSI. Future work is needed to determine the prognostic value of such differences.