Equations Of Boundary Conditions Research Articles

A reality-augmented adaptive physics informed machine learning method for efficient heat transfer prediction in laser melting

Physics informed neural network (PINN) method is proposed to alleviate problems in many science and engineering scenarios when data-collection is difficult, or traditional numerical calculations are lack of convenience because more time-consuming numerical calculations are required whenever one or more parameters of the process is changed. However, for advanced manufacturing processes like laser melting (LM), a basis of laser metal additive manufacturing, involve many complex physical phenomena (e.g. melting, convection, solidification, vaporization and interface evolution), the full equations of which are too complex to be solved by current PINN. This paper proposes a reality-augmented adaptive physics informed machine learning (RAA-PIML) method to meet the objectives of precise and fast predictive LM. It applies adaptive function, integrating heat transfer law and boundary condition equations to loss function, which has fast convergence and strong physics-based constraints. The reality-augmented data are acquired by few experiments and an accurate 3D heat transfer model covering turbulence. The conducted experimental results demonstrate that the developed solution exhibits higher efficiency than simulation, and superior performance than state-of-the-art methods, which shows outstanding potential in industry applications.

Trace Conservation Laws in T2/Zm Orbifold Gauge Theories

Abstract Gauge theory compactified on an orbifold is defined by gauge symmetry, matter contents, and boundary conditions (BCs). There are equivalence classes (ECs), each of which consists of physically equivalent BCs. We propose the powerful necessary conditions, trace conservation laws (TCLs), which achieve a sufficient classification of ECs in U(N) and SU(N) gauge theories on T2/Zm orbifolds (m = 2, 3, 4, 6). The TCLs yield the equivalent relations between the diagonal BCs without relying on an explicit form of gauge transformations. The TCLs also show the existence of off-diagonal ECs, which consist only of off-diagonal matrices, on T2/Z4 and T2/Z6. After the sufficient classification, the exact numbers of ECs are obtained.

Free and forced vibrations of elastically restrained cantilever with lumped oscillator

The efficiency assessment of cantilever-based energy harvesters relies on vibrational analysis, which necessitates modifications aimed at enhancing efficiency. These modifications involve manipulating the fundamental frequency to lower values and encompassing a wider range of resonances within a specified bandwidth. Consequently, this paper introduces an original analytical-numerical exploration into the vibratory response of a cantilever with a novel boundary condition involving an elastically restrained oscillator-spring arrangement. At the microbeam's tip, an oscillator is elastically confined by a linear spring, resulting in a novel set of coupled governing equations and a distinct shearing boundary condition. Microbeam equations is derived from the modified couple stress theory to capture size dependency. During free vibration analysis, a previously unreported characteristic equation is derived. This nonlinear transcendental equation is numerically solved utilizing root-solver algorithms, such as those available in MATLAB. Significantly, it is discovered that the inclusion of a lumped oscillator with an elastic support induces a minimal (new) natural frequency. Applying the extended Hamilton's principle, the effect of the lumped oscillator emerges both on the governing equations of motion and boundary conditions of the microbeam. Novelty of the paper focuses on the both characteristic equation and transmissibility by adopting the Galerkin’s modal decomposition technique. This finding carries vital implications as the efficiency of cantilever-based energy harvesters is directly contingent upon the resonance frequency. Notably, the oscillator mass and spring constant are two parameters that directly influence the vibratory response of the microbeam. In the context of forced vibrations, harmonic base excitation is considered as the input excitation, and the mechanical frequency response function is provided. The proposed system offers two distinct advantages for energy harvester systems: the creation of minimal resonance at lower values and the potential to manipulate the system's resonance toward a desired frequency spectrum.Article HighlightsModifying the boundary conditions of a cantilever beam with lumped-parameter system, can significantly change the behavior of the vibratory response.The boundary condition directly impact the resonance frequencies; which influences the maximum amount of harvestable voltage in vibration-based energy harvesters.Spring constant and mass of the lumped oscillator, are the key factors to alter the vibratory behavior and bandwidth of frequencies. Optimizing such mentioned parameters can help reaching to the maximum harvesting of energy.

Nonlocal strain gradient-based dynamic stability of functionally graded piezoelectric nanoshells considering thermo-electro-mechanical coupling effects

In this paper, a nonclassical shell model is utilized to investigate the dynamic stability of functionally graded piezoelectric (FGP) nanoshells considering the thermo-electro-mechanical coupling effects. Also, the FGP nanoshells on elastic foundations are subjected to periodic axial loading. The theoretical formulations are derived by implementing the first-order shear deformation (FSD) shell theory into the nonlocal strain gradient theory (NSGT). Hamilton’s principle is utilized to obtain the equations of motion and related boundary conditions of the present nanoshell model. Moreover, the Mathieu-Hill equations determining the instability regions are presented and analyzed based on Bolotin’s method. Results demonstrate that the external electric voltage, the elastic foundations, the temperature rise, the static load factor, the power-law index and the small-scale parameters have significant influences on the dynamic stability responses of FGP nanoshells.

A ground fault location algorithm in double‐circuit transmission lines with T‐off connection to an industrial microgrid by using current and voltage phasors information of a single terminal

AbstractThe paper presents a ground fault location algorithm (GFLA) in double‐circuit transmission lines (DCTL) with a T‐off connection to an industrial microgrid (IMG) containing electric arc furnaces (EAF), renewable distributed generations (RDG), and static VAR compensator (SVC). The design presented utilizes the information on the current and voltage phasors of one side of the transmission lines (TL) during the fault period, and there is no need for the availability of information on the type of faulty phase(s) and even the faulty section. To find the exact location of the fault in this design, the voltage phasor equations governing the fault point in positive, negative, and zero‐sequence (PNZS) domains, the zero‐sequence current (ZSC) equation of the fault point, and the boundary condition equation of the fault point have been used. The simulation system is implemented in Simulink/MATLAB using accurate modelling of all network components. The algorithm has been tested and evaluated in different fault conditions, including various locations, phase types, phase‐to‐ground connection resistance, occurrence time, and microgrid (MG) operation modes. The successful results of various tests of the proposed design as well as the analysis of various sensitivities confirm the satisfying performance of the suggested algorithm.

Calculation of noise field in main transformer room of indoor substation based on thermal-acoustic coupling

In order to calculate the noise field distribution in the main transformer room of an indoor substation accurately, a thermal-acoustic coupling idea was introduced, and a noise field solving the algorithm based on thermal-acoustic coupling was proposed in view of the noise quality loss caused by the effect of ambient temperature changes. Firstly, the fluid-structure coupling model of the main transformer room is established, and the computational fluid dynamics method is used to calculate the flow field distribution and temperature boundary conditions under the action of the heat source; Then, extracting the rheological equation of the environmental boundary conditions in the flow field calculation, and use the difference function to couple the rheological equation to the sound grid to obtain the sound field coupling model under the condition of variable temperature; Finally, the modified parameter acoustic integral equation under the sound field coupling model is calculated based on the conventional Gauss numerical integration method, and the sound field of the main transformer room considering the effect of variable temperature is obtained. The algorithm has been successfully applied in the analysis of the noise field of Xi'an 110 kV Zhenxing Substation, and the error with the measured value is 2.083%.

Mass/heat transfer analogy method in the research of convective fluid flow through channels with a specific geometry

The present work contains the results of the comparative analysis of the literature data and the own investigations on mass and heat transfer coefficients occurring under conditions of the convective fluid flow through channels characterised by a specific geometry. The authors focused on the available experimental investigations on mass transfer. The considered experiments were carried out using the electrochemical method named limiting current technique. Two channel geometries were discussed: the annular channel of the conventional size and the long minichannel with a square cross-section area. Taking into consideration dimensionless numbers: Schmidt and Nusselt – analogical for mass and heat transfer – the formulas describing the phenomena under consideration were included. In the case of the annular channel the laminar and turbulent range of Reynolds numbers was studied. For the square minichannel – the laminar flow is considered. The analogy between mass and heat transfer introduced by Chilton and Colburn was applied in the analysis. An equivalent boundary condition is included in considerations concerning the mass and heat transfer. It is the Dirichlet boundary condition characterised by constant temperature of the wall which corresponds to the situation of constant ion concentration at the cathode surface in the limiting current technique. The main purpose of the present work was to verify the method for the determination of heat transfer coefficients using the analogy between mass and heat transfer processes in the case of convective fluid flow through the annular and square channels. The problem discussed in the present work is important and actual due to the possibility of the elimination of temperature measurements in the investigations of heat transfer processes occurring in channels characterised by a specific geometry. It should be noted that sometimes temperature measurement may be difficult or even impossible. This situation also causes high uncertainty of the obtained results. Due to this problem, the presented analysis was performed also with the use of thermal results based on the analytical solution. The verification of the use of mass/heat transfer analogy method in specific cases gives the extended knowledge of correct application of the limiting current technique in heat transfer research. The main objective of the work was achieved by conducting a comparative analysis of the adequate mass and heat transfer results. The existing literature data do not provide an answer to the question about the correctness of using the limiting current technique in the case of discussed annular channels or long square minichannels. The received results make us be critical of applying the mass/heat transfer analogy method in some heat transfer cases.

Local forcing mechanisms challenge parameterizations of ocean thermal forcing for Greenland tidewater glaciers

Abstract. Frontal ablation has caused 32 %–66 % of Greenland Ice Sheet mass loss since 1972, and despite its importance in driving terminus change, ocean thermal forcing remains crudely incorporated into large-scale ice sheet models. In Greenland, local fjord-scale processes modify the magnitude of thermal forcing at the ice–ocean boundary but are too small scale to be resolved in current global climate models. For example, simulations used in the Ice Sheet Intercomparison Project for CMIP6 (ISMIP6) to predict future ice sheet change rely on the extrapolation of regional ocean water properties into fjords to drive terminus ablation. However, the accuracy of this approach has not previously been tested due to the scarcity of observations in Greenland fjords, as well as the inability of fjord-scale models to realistically incorporate icebergs. By employing the recently developed IceBerg package within the Massachusetts Institute of Technology general circulation model (MITgcm), we here evaluate the ability of ocean thermal forcing parameterizations to predict thermal forcing at tidewater glacier termini. This is accomplished through sensitivity experiments using a set of idealized Greenland fjords, each forced with equivalent ocean boundary conditions but with varying tidal amplitudes, subglacial discharge, iceberg coverage, and bathymetry. Our results indicate that the bathymetric obstruction of external water is the primary control on near-glacier thermal forcing, followed by iceberg submarine melting. Despite identical ocean boundary conditions, we find that the simulated fjord processes can modify grounding line thermal forcing by as much as 3 °C, the magnitude of which is largely controlled by the relative depth of bathymetric sills to the Polar Water–Atlantic Water thermocline. However, using a common adjustment for fjord bathymetry we can still predict grounding line thermal forcing within 0.2 °C in our simulations. Finally, we introduce new parameterizations that additionally account for iceberg-driven cooling that can accurately predict interior fjord thermal forcing profiles both in iceberg-laden simulations and in observations from Kangiata Sullua (Ilulissat Icefjord).

Quasi-dynamic modeling and simulation of district heating systems: A laplace transform-based approach

The technological development direction for China's green and low-carbon energy transformation is constructing a multi-energy collaborative smart integrated energy system. As an essential subsystem of energy systems in northern China, district heating system (DHS) plays a crucial role in ensuring people's livelihood. The energy system transformation and the development of the new generation of heating systems impose increasing demands on the simulation computations of regional heating systems. This paper establishes a quasi-dynamic model for heating systems based on the Laplace transform as the foundation. It transforms the continuous thermal dynamics in the time domain into the Laplace domain for quantitatively analyzing the heat transfer loss characteristics and transmission delay characteristics in the heat transport process. Furthermore, it converts the internal complex transmission processes of the system into equivalent source-load boundary conditions to obtain a thermal state analysis model with clear physical significance. This approach significantly reduces the computational complexity of network analysis while ensuring computational accuracy. The established quasi-dynamic model is applied to cases of different scales. The computational results are compared and validated against the commercial simulation software Apros and actual operational data. The urban DHS case study calculation results show a mass flow mean relative error of 3.02% and a supply/return water temperature mean relative error of 2.46%, supporting more refined dynamic scheduling.

New Classification Method for Equivalence Classes on S1/Z2 and T2/Z3 Orbifolds

Abstract In 5D and 6D U(N) and SU(N) gauge theories compactified on S1/Z2 and T2/Z3 orbifolds, we propose a new method to classify the equivalence classes (ECs) of boundary conditions (BCs) without depending on the structure of gauge transformations. Some of the BCs are connected through gauge transformations and constitute ECs, each of which contains physically equivalent BCs. Previous methods for classifying ECs have been used for specific gauge transformations. In this paper, we show that a geometric property of orbifolds significantly narrows down the possibilities of connecting BCs and completes the classification of ECs.

Nonlinear Vibration of Truncated Open Conical Nanoshells Under Harmonic Excitation

The nonlinear forced vibration behavior of truncated open conical nanoshells is investigated in this paper. Nonlocal elasticity theory has been employed to modify the size-dependent effect of micro/nanostructure. Von Karman nonlinear strains are used to consider the geometric nonlinearity of the nanoshells. Using Hamilton’s principle, the equations of motion and boundary conditions of truncated open conical nanoshells are derived. Galerkin method is used to solve the governing equations. Then, to determine the nonlinear forced vibration behavior of truncated open conical nanoshells, complex averaging and arc-length continuation methods are employed. Finally, the effect of nonlocal parameters, cone apex angle, the amplitude of harmonic excitation, structural damping coefficient, and geometrical parameters on the nonlinear frequency response of the truncated open conical nanoshells are discussed.

Turbulent transition in a channel with superhydrophobic walls: anisotropic slip and shear misalignment effects

Superhydrophobic surfaces dramatically reduce skin friction of overlying liquid flows. These surfaces are complex and numerical simulations usually rely on models to reduce this complexity. One of the simplest consists of finding an equivalent boundary condition through a homogenisation procedure, which in the case of channel flow over oriented riblets, leads to the presence of a small spanwise component in the homogenised base flow velocity. This work aims at investigating the influence of such a three-dimensionality of the base flow on stability and transition in a channel with walls covered by oriented riblets. Linear stability for this base flow is investigated: a new instability region, linked to cross-flow effects, is observed. Tollmien–Schlichting waves are also retrieved but the most unstable are three-dimensional. Transient growth is also affected as oblique streaks with non-zero streamwise wavenumber become the most amplified perturbations. When transition is induced by Tollmien–Schlichting waves, after an initial exponential growth regime, streaky structures with large spanwise wavenumber rapidly arise. Modal mechanisms appear to play a leading role in the development of these structures and a secondary stability analysis is performed to retrieve successfully some of their characteristics. The second scenario, initiated with cross-flow vortices, displays a strong influence of nonlinearities. The flow develops into large quasi-spanwise-invariant structures before breaking down to turbulence. Secondary stability on the saturated cross-flow vortices sheds light on this stage of transition. In both cases, cross-flow effects dominate the flow dynamics, suggesting the need to consider the anisotropicity of the wall condition when modelling superhydrophobic surfaces.

On multiple solutions of the Grad–Shafranov equation

The Grad–Shafranov equation (GSE) for axisymmetric MHD equilibria is a nonlinear, scalar PDE which in principle can have zero, one or more non-trivial solutions. The conditions for the existence of multiple solutions has been little explored in the literature so far. We develop a simple analytic model to calculate multiple solutions in the large aspect ratio limit. We compare the results to the recently developed deflated continuation method to find multiple solutions in a realistic geometry and right-hand side of the GSE using the finite element method. The analytic model is surprisingly accurate in calculating multiple solutions of the GSE for given boundary conditions and the two methods agree well in limiting cases. We examine the effect of plasma shaping and aspect ratio on the multiple solutions and show that shaping generally does not alter the number of solutions. We discuss implications for predictive modelling, equilibrium reconstruction, plasma stability and disruptions.

Three-dimensional Finite Element Model of Three-phase Contact Line Dynamics and Dynamic Contact Angle

An unconventional model of three-phase contact liny dynamics is suggested for the numerical solution of the boundary value problem of dipping and spreading. The numerical modeling is conducted with the use of the finite-element method in Lagrange variables. The mathematical model of the process is described by the equation of motion, continuity, and natural boundary conditions on the free surface. To exclude the ity of viscous stresses in the mathematical model on three-phase contact lines (TPCL) there was suggested a gridded model of gliding that takes into consideration peculiarities of dissipative processes in the neighborhood of TPCL at the microlevel. To reduce oscillations of pressure in the neighborhood of TPCL, a finite element is used. The suggested method allows for natural monitoring of free surface and TPCL with an unconventional model for dynamic contact micro-angle. A stable convergent algorithm is suggested that is not dependent on the grid step size and that is tested through the example of a three-dimensional semispherical drop and a drop in the form of a cube. The investigations obtained are compared to well-known experimental and analytical results demonstrating a high efficiency of the suggested model of TPCL dynamics at small values of capillary number.

Analysis of Boundary Layer Flow Second-Grade Hybrid Nanofluid Subject to Lorentz Force

The suspension of nanoparticles in a fluid has been a sure way of steadily improving fluid behaviour. A further improvement in the fluid behaviour is achieved by the suspension of two dissimilar nanoparticles in a base fluid. This study analyses the boundary layer flow of second-grade hybrid nanofluid subject to Lorentz force. By considering Titanium Oxide and Molybdenum disulfide nanoparticles, due to their great lubricating and efficient heat transfer properties, the governing non-linear equations are formulated and rendered dimensionless with the help of similarity variables. The resulting boundary condition equations are transformed to initial condition equations by use of shooting technique and numerically solved by 4th-order Runge Kutta method in MATLAB bvp4c. It is noted that the fluid’s velocity profile increases with the increase in volume fraction and fluctuates with increasing fluid parameters and magnetic strength. The temperature profile grows with the Prandtl number and magnetic field and decreases with the increase in volume fraction and the second-grade fluid parameter.

Nonlinear isogeometric analysis of axially functionally graded graphene platelet-reinforced composite curved beams

The linear and nonlinear isogeometric finite element models of an axially functionally graded graphene platelet-reinforced composite (AFG-GPLRC) curved beam are established within the framework of the third-order shear deformation beam theory (TSDT) and von-Kármán’s nonlinear geometric relation. The AFG-GPLRC curved beams can be seen as composite structures in which the graphene platelets (GPLs) are continuously distributed in the matrix along the length direction of the curved beam according to different patterns. The modified Halpin-Tsai parallel model and the rule of mixture are implemented to predict the effective Young’s modulus and mass density as well as Poisson’s ratio, respectively. Hamilton's principle, TSDT, and von-Kármán’s strain-displacement relation are combined to derive the governing partial differential equation of motion and corresponding boundary conditions. Furthermore, the Non-Uniform Rational B-splines (NURBS)-based isogeometric analysis (IGA) approach together with a direct iterative technique are utilized to solve the nonlinear governing equation. The accuracy and efficiency of the proposed IGA framework are confirmed by comparing corresponding numerical solutions with other available results. The parametric investigations, such as the curved beam’s geometric parameters, boundary conditions, and GPL’s distribution patterns, on the nonlinear bending and vibration responses of the AFG-GPLRC curved beams are carried out by some illustrative examples.

Natural frequency analysis of bidirectional functionally graded plates based on a refined shear theory using nonconforming finite elements

In this study, we investigate the free vibrations of functionally graded plates using the refined shear deformation theory. These plates have material properties that vary in two directions: the z-axis and the x-axis. The variation follows a bidirectional gradation described by a power law based on the Voigt rule of mixture. The displacement field is characterized by four variables, chosen in such a way that shear strain and stress vanish, and traction is free at the upper and lower surfaces of the plate. This eliminates the need for a shear correction factor, as required in the first-order shear deformation theory. We derive the equations of motion and related boundary conditions using Hamilton’s principle and a finite element approach. The proposed element ensures C1-continuity by including the first derivative of the transverse deflection in the kinematic field. For spatial discretization, we employ a rectangular element with four nodes and two interpolation schemes. Lagrangian shape functions are used for in-plane displacement, while a Hermitian scheme is employed for transverse deflection. This enables us to determine the natural frequencies of the 2D-FG plates. We demonstrate the validity, convergence, and accuracy of the proposed element through illustrative examples and compare it with previous literature. Furthermore, we conduct numerical analyses to examine the effects of transverse shear function, boundary conditions, plate aspect ratio, slenderness ratio, and gradation indices on the natural frequencies. The developed model provides insights into the significance of natural frequencies in the design of various structural elements, including 2D-FG plates.

On the vibrations of sandwich structure with magneto-electro-rheological core and composite face sheet via mesh-free method

Multidirectional functionally graded materials due to high-mechanical resistance with other extraordinary properties in each direction have received much attention in recent years. Thus, in the current research, a numerical solution is presented to study the fundamental frequency characteristics of an MD-FG sector annular plate in a supersonic airflow. For obtaining exact displacement fields, the refined zig-zag theory is employed to obtain the transverse shear strain through layers of the composite lamina. A quasi-3D new refined theory is presented to model the displacement fields of the current sandwich structure. The Legendre-radial point interpolation method shape function is used to estimate the displacements while the mesh-free strong form approach discretizes the equations of motion and boundary conditions. Finally, the results show that Mach number, free stream speed, air yaw angle, temperature, and aerodynamic pressure have important roles in the dynamic stability performance of the sandwich sector annular plate in supersonic airflow. The results of the current report can be used in various high-temperature multidirectional compositionally graded materials for future works.

To What Extent Is Aeroelasticity Impacting Multi-Megawatt Wind Turbine Upscaling? A Critical Assessment

Aeroelasticity is recognized as the key enabler that allowed for the massive upscaling of wind turbines in the last decade, leading to long, slender, and flexible blades that equip rotors with lower specific power and unprecedented energy conversion capabilities. In this study, a selection of case studies with increasing size, specifically the NREL 5 MW, the DTU 10 MW, and the IEA 15 MW Reference Wind Turbines (RWTs) is considered to explore to what extent aeroelastic effects impact the functioning of these rotors. The rotors are not only different in size, with the 15 MW having blades nearly double the length of its 5 MW predecessor, but also in technological level as they belong to different phases of wind turbine development. To evaluate how these machines interact with complex inflow conditions, equivalent boundary conditions have been considered for all simulations, including a realistic atmospheric boundary layer, atmospheric turbulence, and wind shear. To carry out the comparative study, a new aero-servo-elastic module called CALMA is introduced herein, by coupling the engineering software OpenFAST with the CFD software CONVERGE, which solves the wind field and provides inflow conditions for the calculation of loads. Results show how not only aeroelasticity increasingly affects the power performance of the new-generation rotors, but is also a key driver of structural design, for example allowing for an alleviation of 1P load variations due to a sheared and turbulent inflow, thus proving that the inclusion of aeroelasticity in the design process is a key enabler to current and future upscaling trends.

Patient-specific computational flow simulation reveals significant differences in paravisceral aortic hemodynamics between fenestrated and branched endovascular aneurysm repair

BackgroundEndovascular aneurysm repair with four-vessel fenestrated endovascular aneurysm repair (fEVAR) or branched endovascular aneurysm repair (bEVAR) currently represent the forefront of minimally invasive complex aortic aneurysm repair. This study sought to use patient-specific computational flow simulation (CFS) to assess differences in postoperative hemodynamic effects associated with fEVAR vs bEVAR. MethodsPatients from two institutions who underwent four-vessel fEVAR with the Cook Zenith Fenestrated platform and bEVAR with the Jotec E-xtra Design platform were retrospectively selected. Patients in both cohorts were treated for paravisceral and extent II, II, and V thoracoabdominal aortic aneurysms. Three-dimensional finite element volume meshes were created from preoperative and postoperative computed tomography scans. Boundary conditions were adjusted for body surface area, heart rate, and blood pressure. Pulsatile flow simulations were performed with equivalent boundary conditions between preoperative and postoperative states. Postoperative changes in hemodynamic parameters were compared between the fEVAR and bEVAR groups. ResultsPatient-specific CFS was performed on 20 patients (10 bEVAR, 10 fEVAR) with a total of 80 target vessels (40 renal, 20 celiac, 20 superior mesenteric artery stents). bEVAR was associated with a decrease in renal artery peak flow rate (−5.2% vs +2.0%; P < .0001) and peak pressure (−3.4 vs +0.1%; P < .0001) compared with fEVAR. Almost all renal arteries treated with bEVAR had a reduction in renal artery perfusion (n = 19 [95%]), compared with 35% (n = 7) treated with fEVAR. There were no significant differences in celiac or superior mesenteric artery perfusion metrics (P = .10-.27) between groups. Time-averaged wall shear stress in the paravisceral aorta and branches also varied significantly depending on endograft configuration, with bEVAR associated with large postoperative increases in renal artery (+47.5 vs +13.5%; P = .002) and aortic time-averaged wall shear stress (+200.1% vs −31.3%; P = .001) compared with fEVAR. Streamline analysis revealed areas of hemodynamic abnormalities associated with branched renal grafts which adopt a U-shaped geometry, which may explain the observed differences in postoperative changes in renal perfusion between bEVAR and fEVAR. ConclusionsbEVAR may be associated with subtle decreases in renal perfusion and a large increase in aortic wall shear stress compared with fEVAR. CFS is a novel tool for quantifying and visualizing the unique patient-specific hemodynamic effect of different complex EVAR strategies. Clinical RelevanceThis study used patient-specific CFS to compare postoperative hemodynamic effects of four-vessel fenestrated endovascular aneurysm repair (fEVAR) and branched endovascular aneurysm repair (bEVAR) in patients with complex aortic aneurysms. The findings indicate that bEVAR may result in subtle reductions in renal artery perfusion and a significant increase in aortic wall shear stress compared with fEVAR. These differences are clinically relevant, providing insights for clinicians choosing between these approaches. Understanding the patient-specific hemodynamic effects of complex EVAR strategies, as revealed by CFS, can aid in future personalized treatment decisions, and potentially reduce postoperative complications in aortic aneurysm repair.