Nonlinear Fluid Research Articles

Fully nonlinear wave interaction with 2D floating body including nonlinear sloshing tank

Two-dimensional fully-nonlinear numerical sloshing tank (FN-NST) simulation program is developed based on boundary element method (BEM), potential theory with artificial free-surface damping, and space-fixed (global) coordinate system. The free surface in sloshing tank is updated by the mixed Eulerian-Lagrangian (MEL) method with material node approach (Full Lagrangian approach). The developed potential-based nonlinear model was validated through comparisons with available experimental and CFD (computational fluid dynamics) results and they show good agreements. The nonlinear sloshing model is then further implemented in the fully nonlinear wave and floating-body simulation program to observe the effects of liquid sloshing motion. In the fully nonlinear program, the entire nonlinear fluid pressure is integrated over the instantaneous wetted body surface and position, which is subsequently compared with the corresponding linear theory and results. The second-order effects are also identified from the fully-nonlinear simulation. The floater Response Amplitude Operators (RAOs) for frozen- and liquid-cargo cases are also compared for various wave frequencies and amplitudes to better identify the role of liquid cargo in the stability of rotational motions. The effects of the vertical location of liquid tank and artificial free-surface damping are also investigated.

Static Spherically Symmetric Perfect Fluid Solutions in Teleparallel F(T) Gravity

In this paper, we investigate static spherically symmetric teleparallel F(T) gravity containing a perfect isotropic fluid. We first write the field equations and proceed to find new teleparallel F(T) solutions for perfect isotropic and linear fluids. By using a power-law ansatz for the coframe components, we find several classes of new non-trivial teleparallel F(T) solutions. We also find a new class of teleparallel F(T) solutions for a matter dust fluid. After, we solve the field equations for a non-linear perfect fluid. Once again, there are several new exact teleparallel F(T) solutions and also some approximated teleparallel F(T) solutions. All these classes of new solutions may be relevant for future cosmological and astrophysical applications.

Analytical insights into the behavior of finite amplitude waves in plasma fluid dynamics

This study introduces innovative analytical solutions for the [Formula: see text]-dimensional nonlinear Jaulent–Miodek ([Formula: see text]) equation, a governing model elucidating the propagation characteristics of nonlinear shallow water waves with finite amplitude. Employing analytical methodologies such as the Khater II and unified methods, alongside the Adomian decomposition method as a semi-analytical approach, series solutions are derived with the primary aim of elucidating the fundamental physics dictating the evolution of [Formula: see text] waves. Within the realm of nonlinear fluid dynamics, the [Formula: see text] equation encapsulates the behavior of irrotational, inviscid, and incompressible fluid flow, wherein nonlinear effects and dispersion intricately balance to yield stable propagating waves. This equation encompasses terms representing nonlinear convection, dispersion, and nonlinearity effects. The analytical methodologies employed in this investigation yield solutions for various instances of the [Formula: see text] equation, demonstrating convergence, accuracy, and computational efficiency. The outcomes reveal that the Adomian decomposition method yields solutions congruent with those obtained through analytical techniques, thereby affirming the precision of the derived solutions. Furthermore, this study advances the comprehension of the physical implications inherent in the [Formula: see text] equation, serving as a benchmark for evaluating alternative methodologies. The analytical approaches elucidated in this research furnish accessible tools for addressing a diverse array of nonlinear wave equations in mathematical physics and engineering domains. In summary, the introduction of novel exact and approximate solutions significantly contributes to the advancement of knowledge pertaining to the [Formula: see text]-dimensional [Formula: see text] equation. The ramifications of this research extend to the modeling of shallow water waves, offering invaluable insights for researchers and practitioners engaged in the field.

Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate

Abstract Casson fluids containing carbon nanotubes of various lengths and radii on a moving permeable plate reduce friction and improve equipment efficiency. They improve plate flow dynamics to improve heat transfer, particularly in electronic cooling and heat exchangers. The core objective of this study is to investigate the heat transmission mechanism and identify the prerequisites for achieving high cooling speeds within a two-dimensional, stable, axisymmetric boundary layer. This study considers a sodium alginate-based nanofluid containing single/multi-wall carbon nanotubes (SWCNTs/MWCNTs) and Casson nanofluid flow on a permeable moving plate with varying length, radius, and nonlinear thermal radiation effects. The plate has the capacity to move either parallel to or perpendicular to the free stream. The governing partial differential equations for the boundary layer, which are interconnected, are transformed into standard differential equations. These equations are then numerically solved using the Runge–Kutta fourth-order scheme incorporated in the shooting method. This research analyses and graphically displays the effects of factors including mass suction, nanoparticle volume fraction, Casson parameter, thermal radiation, and temperature ratio. Additionally, a comparison is made between the present result and the previous finding, which presented in a tabular format. The coefficient of skin friction decreases in correlation with an increase in Casson fluid parameters and Prandtl number. Heat transfer rate decreases with a variation in viscosity parameter, while it is increasing with an increase in Prandtl number. In addition, this study demonstrates that heat transfer rate for MWCNT is significantly higher than that of SWCNT nanoparticles. Thermal radiation and temperature ratio reduce the heat transfer rate, whereas nanoparticle volume fraction and Casson parameter enhance it over a shrinking surface.

Short-period flow oscillation during eruptions of Onikobe geyser, NE Japan: Insights from thermal infrared observation and acoustic measurements

Geysers are episodic features with variable eruption intervals that range from minutes to years. Although many previous studies on geysers have focused on subsurface properties and processes such as plumbing geometry and recharge process, it is known that erupting fluid column exhibits short-term behaviors such as individual water jets from the vent. In the present study, we conducted observations at Onikobe geyser, NE Japan, a relatively small geyser (geysering well) erupting water up to ∼6–8 m every ∼10 min and observed the erupting fluid column using a thermal infrared camera and an acoustic sensor. We succeed in tracking the water jets by analyzing spatio-temporal temperature map obtained from the thermal infrared observation, which clearly shows the eruptions at Onikobe geyser are not completely stationary but rather a series of intermittent jets with a short period interval of <1 s. We estimate the exit velocity by fitting a ballistic model under the air drag condition of inertial resistance to the jet trajectory. The exit velocity and the averaged gas volume fraction of the erupting fluid are estimated to be ∼4–79 m/s and ∼0.93–0.96, respectively. The exit velocity is ∼30 m/s during the first bursts, then it rapidly increases to ∼50–80 m/s for ∼15 s, and then decreases to ∼20–30 m/s until ∼10 s before the eruption ends. Time series analyses of the thermal infrared and acoustic signals during an eruption indicate harmonic spectra with integer multiple peaks. The fundamental frequency showing ∼4 Hz at the beginning gradually decreases to ∼2 Hz for ∼15 s, keeps almost constant in the following 30 s, and then slightly increases near the end of the eruption. These harmonic spectra may be caused by a resonance mechanism, non-linear fluid motion, and/or subsurface two-phase flow. We discuss the case of a closed organ-pipe resonance in a subsurface crack and attribute the frequency decrease to a decrease in the water level in the crack (an increase in the length of the resonating liquid-vapor column) and/or a decrease in the gas volume fraction of the liquid-vapor mixture in the crack. Since such harmonic characteristics are observed at other geysers, further simultaneous observation of the short-period oscillations on the erupting column proposed in this study with seismic observations of harmonic tremor may provide an improved understanding of geyser subsurface phenomena.

Opto-mechatronic dynamic characteristics in iron oxide-based nanofluid using spatial and frequency domain analysis

Iron oxide nanoparticles (IONPs) exhibit low toxicity and high chemical stability, attractive for developing of nanofluids (NFs) for advanced medical applications. This research focuses on the study of the optical, mechanical, and electrical dynamics of iron oxide–ethanol NFs. A novel sensitive methodology for analyzing the influence of nanoparticles (NPs) over the optical and electrical processes exhibited by IONFs is reported. The IONPs were synthesized by a microemulsion route and were characterized by transmission electron microscopy, scanning electron microscopy, and X-ray diffraction. The NPs exhibit a mean diameter of 30 nm and they were identified as Fe2O3. UV–Vis spectroscopy allows us determining the volume fraction of the fluid as a function of time. The assistance of a Michelson interferometer integrated with an image processing methodology was employed to explore the dynamics of the nanostructures. The percentage of NPs involved in linear and nonlinear dynamic fluid processes was estimated by taking a double-stage (spatial and frequency domains) Fast Fourier Transform in the interferometric pattern. A DC voltage source was used to study the electrical conductivity of the NF as it was being sedimented. The opto-mechatronic parameters were correlated, considering the volume fraction as the main variable to determine the optical and electrical characteristics. For the Fe2O3 NF, it is identified that the linear effects of sedimentation present a stronger impact on the optical properties, while the nonlinear interactions have more influence on the electrical conductivity. The main findings of this research have potential applications in rheological instrumentation to analyze complex effects using transient opto-mechatronic components.

A review of implicit algebraic constitutive relations for describing the response of nonlinear fluids

A review of implicit algebraic constitutive relations for describing the response of nonlinear fluids

Associations Between Volume of Early Intravenous Fluid and Hospital Outcomes in Septic Patients With and Without Heart Failure: A Retrospective Cohort Study.

To evaluate the relationship between early IV fluid volume and hospital outcomes, including death in-hospital or discharge to hospice, in septic patients with and without heart failure (HF). A retrospective cohort study using logistic regression with restricted cubic splines to assess for nonlinear relationships between fluid volume and outcomes, stratified by HF status and adjusted for propensity to receive a given fluid volume in the first 6 hours. An ICU subgroup analysis was performed. Secondary outcomes of vasopressor use, mechanical ventilation, and length of stay in survivors were assessed. An urban university-based hospital. A total of 9613 adult patients were admitted from the emergency department from 2012 to 2021 that met electronic health record-based Sepsis-3 criteria. Preexisting HF diagnosis was identified by the International Classification of Diseases codes. None. There were 1449 admissions from patients with HF. The relationship between fluid volume and death or discharge to hospice was nonlinear in patients without HF, and approximately linear in patients with HF. Receiving 0-15 mL/kg in the first 6 hours was associated with lower likelihood of death or discharge to hospice compared with 30-45 mL/kg (odds ratio = 0.61; 95% CI, 0.41-0.90; p = 0.01) in HF patients, but no significant difference for non-HF patients. A similar pattern was identified in ICU admissions and some secondary outcomes. Volumes larger than 15-30 mL/kg for non-HF patients and 30-45 mL/kg for ICU-admitted non-HF patients were not associated with improved outcomes. Early fluid resuscitation showed distinct patterns of potential harm and benefit between patients with and without HF who met Sepsis-3 criteria. Restricted cubic splines analysis highlighted the importance of considering nonlinear fluid outcomes relationships and identified potential points of diminishing returns (15-30 mL/kg across all patients without HF and 30-45 mL/kg when admitted to the ICU). Receiving less than 15 mL/kg was associated with better outcomes in HF patients, suggesting small volumes may be appropriate in select patients. Future studies may benefit from investigating nonlinear fluid-outcome associations and a focus on other conditions like HF.

Elasto-inertial instability in torsional flows of shear-thinning viscoelastic fluids

It is well known that inertia-free shearing flows of a viscoelastic fluid with curved streamlines, such as the torsional flow between a rotating cone and plate or the flow in a Taylor–Couette geometry, can become unstable to a three-dimensional time-dependent instability at conditions exceeding a critical Weissenberg ( $Wi$ ) number. However, the combined effects of fluid elasticity, shear thinning and finite inertia (as quantified by the Reynolds number $Re$ ) on the onset of elasto-inertial instabilities are not fully understood. Using a set of cone–plate geometries, we experimentally explore the entire $Wi$ – $Re$ phase space for a series of nonlinear viscoelastic fluids (with the dependence on shear rate $\dot{\gamma}$ quantified using a shear-thinning parameter $\beta _P(\dot {\gamma })$ ). We tune $\beta _P(\dot {\gamma })$ by varying the dissolved polymer concentration in solution. This progressively reduces shear thinning but leads to finite inertial effects before the onset of elastic instability, and thus naturally results in elasto-inertial coupling. Time-resolved rheometric measurements and flow visualization experiments allow us to investigate the effects of flow geometry, and document the combined effects of varying $Wi, Re$ and $\beta _P(\dot {\gamma })$ on the emergence of secondary motions at the onset of instability. The resulting critical state diagram quantitatively depicts the competition between the stabilizing effects of shear thinning and the destabilizing effects of inertia. We extend the curved streamline instability criterion of Pakdel &amp; McKinley (Phys. Rev. Lett., vol. 77, no. 12, 1996, p. 2459) for the onset of purely elastic instability in curvilinear geometries by using scaling arguments to incorporate shear thinning and finite inertial effects. The augmented condition facilitates predictions of the onset of instability over a broader range of flow conditions, and thus bridges the gap between purely elastic and elasto-inertial curved streamline instabilities.

Transient gap resonance between two closely-spaced boxes triggered by nonlinear focused wave groups

A two-dimensional (2D) viscous numerical wave flume is developed based on OpenFOAM® to investigate the transient gap resonance problem triggered by nonlinear focused wave groups. The narrow gap is formed by two closely-spaced boxes, where the weather-side box is allowed to heave freely under wave actions, but the rear one is firmly fixed. The overset mesh method is introduced in the numerical model to capture the weather-side box's large-amplitude motion accurately. This work mainly focuses on the coupled effects of free-surface nonlinearity and heave-freedom of the weather-side box on the fluid oscillations in the gap and heave motions of the weather-side box. The heave-freedom of the weather-side box is demonstrated to play an important effect on the period in which the maximum value of non-dimensional amplitude of fluid oscillation in the gap occurs. It is revealed that the free-surface nonlinearity significantly affects the nonlinear fluid oscillations in the gap but has a limited effect on the heave motions of the weather-side box. The four-phase combination method is further employed to conduct the higher harmonic component analysis to clarify the effects of higher harmonic components on the nonlinear response of fluid and box.

Comprehensive effects of aerodynamic performance and dynamic strength of aircraft wings after bird strike in numerical simulation

ABSTRCT To enhance the bird strike resistance of fixed-wing aircraft wings, a combined computational approach integrating nonlinear solid mechanics and fluid dynamics was employed to analyze the bird strike characteristics of both traditional aluminum alloy skins and novel composite materials skins. Additionally, a standardized procedure was established to simulate aircraft structural damage more comprehensively, swiftly, and accurately during bird strikes, along with diagnostic analysis of flow field changes near the wing post-impact. This method not only quantifies wing strength damage but also establishes corresponding relationships between damage severity and aerodynamic performance degradation. The research findings indicate that the deformation of composite material skin wings is only a quarter of that of aluminum alloy skin wings. Composite material skins absorb less harmful energy compared to aluminum alloy skins, with consistently lower stiffness reduction rates at various bird strike velocities. Velocity distribution on deformed wings with composite material skins exhibits minimal deviation compared to normal wings, thereby preventing airflow separation. The research results provide more comprehensive guidance for the selection of materials for bird strike resistance of aircraft wings and the airworthiness evaluation after bird strikes. Highlights This paper establishes a standardized procedure that enables a more comprehensive, faster, and higher-precision simulation of structural damage to the aircraft during a bird strike on the wing and allows for the diagnostic analysis of the flow field changes near the wing after bird strike. By coupling nonlinear solid mechanics and fluid dynamics computational methods, the aerodynamic performance of the wings at different angles of attack post-deformation is investigated. This approach not only quantifies the strength damage to the wings but also establishes corresponding relationships between the degree of damage and the deterioration in aerodynamic performance. The research yields insights into the aerodynamic performance degradation patterns with varying angles of attack for both composite material skin and aluminum alloy skin deformed wings. These findings can serve as valuable references for pilots in emergency situations, aiding in their decision-making regarding aircraft control.

Analysis of chemical reactive nanofluid flow on stretching surface using numerical soft computing approach for thermal enhancement

ABSTRACT In this work, computational intelligence methodologies are used to investigate the trihybrid nanofluid, a new theoretical model with remarkable thermal transmission properties to enhance liquid thermal performance. The nanostructure Cu, Al2O3, and TiO2 were immersed in the base liquid (C2H6O2) to produce (Cu + Al2O3 + TiO2/C2H6O2) trihybrid nanofluid. In a Darcy-Forchheimer porous medium over a stretching Riga sheet, this study examines the electromagnetic ternary hybrid nanofluid flow under various slip situations. The study takes into account the complex interactions between a number of variables, including as viscous dissipation, radiation, heat sources, and chemical reactions. Similarity transformations are used to convert complex partial differential equations for flow, energy, and concentration into nonlinear ordinary differential equations. The highly nonlinear equations of the problem are solved numerically with the use of techniques from the bvp4c approach. The results of the bvp4c method produce the reference dataset required for the Levenberg-Marquardt backpropagation of neural networks (LMBNN). The neural network performance is validated using regression analysis, mean square errors, and error histogram data. The model problem’s consistency and precision are evaluated using the absolute error, which is given for each model instance at around 10−06–10−08, 10−05–10−10 and 10−06 05–10−09. In order to reduce mean square error, the nonlinear fluid dynamics system’s numerical solutions have been taken into consideration. Using the comparative configurations of MSE, error histograms, state transitions, correlation, and regression, the reliability and competence of the stochastic technique are verified.

Laser and Astrophysical Plasmas and Analogy between Similar Instabilities

Multipulse laser–matter interactions initiate nonlinear and nonequilibrium plasma fluid flow dynamics and their instability creating microscale vortex filaments, loop-soliton chains, and helically paired structures, similar to those at the astrophysical mega scale. We show that the equation with the Hasimoto structure describes both, the creation of loop solitons by torsion of vortex filaments and the creation of solitons by helical winding of magnetic field lines in the Crab Nebula. Our experiments demonstrate that the breakup of the loop solitons creates vortex rings with (i) quasistatic toroidal Kelvin waves and (ii) parametric oscillatory modes—i.e., with the hierarchical instability order. For the first time, we show that the same hierarchical instability at the micro- and the megascale establishes the conceptual frame for their unique classification based on the hierarchical order of Bessel functions. Present findings reveal that conditions created in the laser-target regions of a high filament density lead to their collective behavior and formation of helically paired and filament-braided “complexes”. We also show, for the first time, that morphological and topological characteristics of the filament-bundle “complexes” with the loop solitons indicate the analogy between similar laser-induced plasma instabilities and those of the Crab and Double-Helix Nebulas—thus enabling conceptualization of fundamental characteristics. These results reveal that the same rotating metric accommodates the complexity of the instabilities of helical filaments, vortex rings, and filament jets in the plasmatic micro- and megascale astrophysical objects.

Kinetic glass transition in granular gases and nonlinear molecular fluids.

In this paper, we investigate, both analytically and numerically, the emergence of a kinetic glass transition in two different model systems: a uniformly heated granular gas and a molecular fluid with nonlinear drag. Despite the profound differences between these two physical systems, their behavior in thermal cycles share strong similarities, which stem from the relaxation time diverging algebraically at low temperatures for both systems. When the driving intensity--for the granular gas-or the bath temperature-for the molecular fluid-is decreased to sufficiently low values, the kinetic temperature of both systems becomes "frozen" at a value that depends on the cooling rate through a power law with the same exponent. Interestingly, this frozen glassy state is universal in the following sense: for a suitable rescaling of the relevant variables, its velocity distribution function becomes independent of the cooling rate. Upon reheating, i.e., when either the driving intensity or the bath temperature is increased from this frozen state, hysteresis cycles arise and the apparent heat capacity displays a maximum. The numerical results obtained from the simulations are well described by a perturbative approach.

Data-driven optimisation of wind farm layout and wake steering with large-eddy simulations

Abstract. Maximising the power production of large wind farms is key to the transition towards net zero. The overarching goal of this paper is to propose a computational method to maximise the power production of wind farms with two practical design strategies. First, we propose a gradient-free method to optimise the wind farm power production with high-fidelity surrogate models based on large-eddy simulations and a Bayesian framework. Second, we apply the proposed method to maximise wind farm power production by both micro-siting (layout optimisation) and wake steering (yaw angle optimisation). Third, we compare the optimisation results with the optimisation achieved with low-fidelity wake models. Finally, we propose a simple multi-fidelity strategy by combining the inexpensive wake models with the high-fidelity framework. The proposed gradient-free method can effectively maximise wind farm power production. Performance improvements relative to wake-model optimisation strategies can be attained, particularly in scenarios of increased flow complexity, such as in the wake steering problem, in which some of the assumptions in the simplified flow models become less accurate. The optimisation with high-fidelity methods takes into account nonlinear and unsteady fluid mechanical phenomena, which are leveraged by the proposed framework to increase the farm output. This paper opens up opportunities for wind farm optimisation with high-fidelity methods and without adjoint solvers.

Overview of the Application of Physically Informed Neural Networks to the Problems of Nonlinear Fluid Flow in Porous Media

To describe unsteady multiphase flows in porous media, it is important to consider the non-Newtonian properties of fluids by including rheological laws in the hydrodynamic model. This leads to the formation of a nonlinear system of partial differential equations. To solve this direct problem, it is necessary to linearize the equation system. Algorithm construction for inverse problem solution is problematic since the numerical solution is unstable. The application of implicit methods is reduced to matrix equations with a high rank of the coefficient matrix, which requires significant computational resources. The authors of this paper investigated the possibility of parameterized function (physics-informed neural networks) application to solve direct and inverse problems of non-Newtonian fluid flows in porous media. The results of laboratory experiments to process core samples and field data from a real oil field were selected as examples of application of this method. Due to the lack of analytical solutions, the results obtained via the finite difference method and via real experiments were proposed for validation.

Parametric simulations of fractal-fractional non-linear viscoelastic fluid model with finite difference scheme

Fractal-fractional derivatives are more general than the fractional derivative and classical derivative in terms of order. Fractal-fractional derivative is used in those models where the classical continuum hypothesis theory fails. More precisely, these derivative operators are used where the surface or space is discontinuous, e.g., porous medium. Fractal-fractional derivative is considered advance tool to analyze the fluid dynamic model more than fractional and classical model. Given the extensive applicability of fractal-fractional derivatives, the current analysis focuses on investigating the behavior of a non-linear Walter’s-B fluid model under the influence of time-varying temperature and concentration During the simulation process, we have also taken into account the effects of first-order chemical reactions, Soret numbers, thermal radiation, Joule heating, and viscous dissipation of energy. A magnetic field with a strength of B0 was applied to the left plate in the transverse direction. The classical mathematical model was first developed using relative constitutive equations and later generalized with the fractal-fractional derivative operator. Numerical solutions to the generalized model have been obtained using the finite difference method. Various graphs are drawn from the obtained numerical solutions to study the influence of physical parameters on the rheology of Walter’s-B fluid. It has been observed that by varying the fractional and fractal order of the generalized model, one can easily derive fractal, fractional, and classical models.

Comparative simulation of nonlinear radiative nano casson and maxwell fluids with periodic magnetic force and sensitivity analysis

This study investigated cyclic magneto-hydrodynamic radiative effects in Casson and Maxwell fluids, including nonlinear radiation and Arrhenius activation energy. It promotes non-Newtonian fluid use in diverse fields like industry, manufacturing, sciences, medicine, and engineering. Using boundary layer approximations, non-dimensional equations are formulated. For numerical solutions, widely recognized explicit finite difference method (EFDM) has been utilized. To ensure the robustness of EFDM results, stability and convergence tests are performed. Exploration involve a detailed sensitivity analysis by using RSM, offering a thorough understanding of influential parameters. These analyses explore complex interactions among physical parameters, affecting Nusselt number, skin friction, and Sherwood number. Maxwell fluid's velocity is more affected by periodic magnetic force than Casson fluid, during the presence of nonlinear radiation. Additionally, nonlinear thermal radiation has a greater impact on temperature and concentration profiles compared to linear radiation for both fluids. Moreover, Casson fluid has a stronger influence on the average heat transfer rate compared to Maxwell fluid with nonlinear thermal radiation which is 8.6 % greater than the Maxwell fluid. On the other hand, at constant thermal radiation (Ra), due to decrease of Brownian motion (Nb), the rate of heat transfer is reduced by 1.2 % and 0.3 % respectively for Maxwell and Casson fluid. Also, for thermophoresis parameter (Nt), this rate is reduced by 2 % and 1.6 % respectively. The investigation also revealed that the Ra exhibits a positive sensitivity towards average Nusselt number, while Nb and Nt are displayed a negative sensitivity.

Simultaneous analysis and design optimization for seismic retrofitting of hysteretic structures with fluid viscous dampers

Fluid viscous dampers, if properly sized and placed, can significantly improve the performance and safety of existing structures during an earthquake. This has motivated the development of several approaches to optimize the design of fluid viscous dampers. The optimization approaches available typically have an iterative nature, and in every iteration, expensive time-history analyses are performed. This paper presents a novel optimization-based approach for retrofitting hysteretic structures with fluid viscous dampers that does not require the computation of time-history analyses. The sizing and placement of the dampers are defined using a simultaneous analysis and design optimization approach based on nonlinear programming. In this approach, the equations of motion are treated as equality constraints of the optimization problem. As a consequence, design sensitivity analysis methods are not needed to calculate the gradients of the objective and constraint functions. Two design scenarios are considered: structures with hysteretic behavior retrofitted with linear or nonlinear fluid viscous dampers. The optimization variables include the damping coefficients of the dampers and the structural response over time. The manufacturing cost of the dampers is minimized, with constraints on the inter-story drifts. A continuation scheme on the design-driving inter-story drift constraints is proposed to effectively solve the class of problems considered. The numerical results demonstrate that the proposed approach can solve complex design optimization problems using reasonable computational resources and time. It is also shown that, thanks to the proposed approach, additional constraints can be incorporated in the problem formulation with minimal modeling effort, and without the need to develop additional sensitivity analyses for computing the gradients of the added constraints. The Julia codes used in this study are freely available on GitHub: https://github.com/pollinico/SAND_opt_nonlinFVDs.

Learning Reduced Fluid Dynamics

Predicting the state evolution of ultra high-dimensional, time-reversible fluid dynamic systems is a crucial but computationally expensive task. Existing physics-informed neural networks either incur high inference cost or cannot preserve the time-reversible nature of the underlying dynamics system. We propose a model-based approach to identify low-dimensional, time reversible, nonlinear fluid dynamic systems. Our method utilizes the symplectic structure of reduced Eulerian fluid and use stochastic Riemann optimization to obtain a low-dimensional bases that minimize the expected trajectory-wise dimension-reduction error over a given distribution of initial conditions. We show that such minimization is well-defined since the reduced trajectories are differentiable with respect to the subspace bases over the entire Grassmannian manifold, under proper choices of timestep sizes and numerical integrators. Finally, we propose a loss function measuring the trajectory-wise discrepancy between the original and reduced models. By tensor precomputation, we show that gradient information of such loss function can be evaluated efficiently over a long trajectory without time-integrating the high-dimensional dynamic system. Through evaluations on a row of simulation benchmarks, we show that our method reduces the discrepancy by 50-90 percent over conventional reduced models and we outperform PINNs by exactly preserving the time reversibility.