arXiv subjects

Rajeev Jaiman

Publications and source records attributed to Rajeev Jaiman.

12 recordsLinked to original sources

arXiv2026

A finite-difference summation-by-parts, conditionally stable partitioned algorithm for conjugate heat transfer problems

In this work, we design and analyze a novel, provably conditionally stable, weakly coupled partitioned scheme to solve the conjugate heat transfer (CHT) problem. We consider a model CHT problem consisting of linear advection-diffusion and heat equations, coupled at an interface through continuity of temperature and heat flux. We employ high-order summation-by-parts finite-difference operators in conjunction with simultaneous-approximation-terms (SATs) in curvilinear coordinates for spatial derivatives, combined with first- and second-order time discretizations and temporal extrapolation at the interface. Energy stability is maintained by carefully selecting SAT parameters at the interface. A range of coupling parameters are explored to identify those that yield a stable scheme, and a stepwise approach for choosing SAT parameters that ensure stability is given. The effectiveness of the method is demonstrated through numerical experiments in a two-dimensional model problem on a rectangular domain with curvilinear grids. The proposed approach enables the development of high-order, conditionally stable partitioned solvers suitable for general geometries.

math.NA↗

arXiv2024

Harnessing Loss Decomposition for Long-Horizon Wave Predictions via Deep Neural Networks

Accurate prediction over long time horizons is crucial for modeling complex physical processes such as wave propagation. Although deep neural networks show promise for real-time forecasting, they often struggle with accumulating phase and amplitude errors as predictions extend over a long period. To address this issue, we propose a novel loss decomposition strategy that breaks down the loss into separate phase and amplitude components. This technique improves the long-term prediction accuracy of neural networks in wave propagation tasks by explicitly accounting for numerical errors, improving stability, and reducing error accumulation over extended forecasts.

cs.LG↗

arXiv2024

Flow-Induced Vibration of Flexible Hydrofoil Within Cavitating Turbulent Flow

The flow-induced vibration and cavitation dynamics of three-dimensional flow past a cantilever flexible hydrofoil are investigated using a large eddy simulation (LES) model, a homogeneous mixture cavitation model and the structural modes superposition method. The present work aims to explore a potential mechanism responsible for a propeller singing behavior, and thus focuses on the synchronized hydroelastic coupling among the pressure pulsation inside the flow field, the cavitation generation and the structural vibration. To begin, we validate the tip vortex dynamics of a flexible hydrofoil against the available experimental. Our results demonstrate that the tip vortex shedding and the blade vibration are responsible for the intense peak in the low-frequency tonal components of the noise source, and the trailing-edge vortex shedding induces broadband components. Additionally, the generation of sheet cavitation induces considerable synchronized hydrofoil vibration (subjected to a flutter-like response), and affects the pressure fluctuations in the flow field, which further dominate the features of the underwater noise sources. It is suggested that the cavitation behavior and structural vibrations co-dominate the characteristics of singing noise from a propeller blade.

physics.flu-dyn↗

arXiv2024

Modeling of Hydroacoustic Noise from Marine Propellers with Tip Vortex Cavitation

The present work aims to study the cavitating turbulent flow of a full-scale marine propeller and explore the physical mechanism underpinning the underwater radiated noise. We employ the standard dynamic large eddy simulation for the turbulent wake flow and the Schnerr-Sauer cavitation model, while the Ffowcs-Williams-Hawkings acoustic analogy is considered for the hydroacoustic modeling. For the current investigation, we consider a well-known Potsdam Propeller Test Case to analyze the turbulent cavitating flow and the associated hydroacoustic emissions. To begin, the modeling framework is validated using the available experimental data, and distinctive double-helical tip vortex cavitation and its qualitative patterns along the vortex trajectory are captured. In comparison to the non-cavitating condition, the pressure distribution on the propeller surface is more disordered for the cavitating condition, which is further reflected by a relatively stronger power of both low-frequency tonal peaks and high-frequency broadband components in the spectrum of thrust generation. Specifically, the generation of cavitation leads to the enhancement of the monopole noise source and the breakdown of cavitation bubbles as well as vortex structures in the turbulent wake. Furthermore, the tonal noise with the frequency corresponding to the harmonics of blade passing frequency is also enhanced. Generally speaking, the generation of cavitation structures enhances the hydroacoustics energy of URN at all orientations, especially in the downstream direction with sound pressure level increasing up to 20 dB.

physics.flu-dyn↗

arXiv2024

A 3D phase-field based Eulerian variational framework for multiphase fluid-structure interaction with contact dynamics

Using a fixed Eulerian mesh, the phase-field method has been successfully utilized for a broad range of moving boundary problems involving multiphase fluids and single-phase fluid-structure interaction. Nevertheless, multiphase fluids interacting with multiple solids are rarely explored, especially for large-scale finite element simulations with contact dynamics. In this work, we introduce a novel parallelized three-dimensional fully Eulerian variational framework for simulating multiphase fluids interacting with multiple deformable solids subjected to contact dynamics. In the framework, each solid or fluid phase is identified by a standalone phase indicator. Moreover the phase indicators are initialized by the grid cell method, which restricts the calculation to several grid cells. A diffuse interface description is employed for a smooth interpolation of the physical properties across the phases, yielding unified mass and momentum conservation equations for the coupled dynamical interactions. For each solid object, temporal integration is carried out to track the strain evolution in an Eulerian frame of reference. The coupled differential equations are solved in a partitioned iterative manner. We first verify the framework against reference numerical data in a two-dimensional case of a rotational disk in a lid-driven cavity flow. The case is generalized to a rotational sphere in a lid-driven cavity flow to showcase large deformation and rotational motion of solids and examine the convergence in three dimensions. We then simulate the falling of an immersed solid sphere on an elastic block under gravitational force to demonstrate the translational motion and the solid-to-solid contact in a fluid environment. Finally, we demonstrate the framework for a ship-ice interaction problem involving multiphase fluids with an air-water interface and contact between a floating ship and ice floes.

physics.flu-dyn↗

arXiv2023

A numerical study on the oscillatory dynamics of tip vortex cavitation

In this paper, we numerically study the oscillatory dynamics associated with the tip vortex cavitation over an elliptical hydrofoil section using our 3D variational multiphase flow solver at a Reynolds number of $Re=8.95 \times 10^5$ via dynamic subgrid-scale modeling and homogeneous mixture theory. To begin, we examine the grid resolution requirements and introduce a length scale that considers both the tip vortex strength and the core radius, which is then employed to non-dimensionalize the spatial resolution in the tip vortex region and establish mesh requirements for large eddy simulation of tip vortex cavitation. We next perform simulations to analyze the dynamical modes of cavity oscillation at different cavitation numbers and compare them with the semi-analytical solution. The breathing mode of cavity surface oscillation is extracted from the results through the definition of an effective radius. The time-averaged effective radius demonstrates that the cavity experiences a growth region followed by decay as it progresses away from the tip. Further examination of the local breathing mode oscillations in these regions indicates the different behavior of cavity oscillations in the growth and decay regions, with the oscillations within the former being characterized by lower frequencies. For representative cavitation numbers $σ\in [1.2,2.6]$, we find that pressure fluctuations exhibit a shift of spectrum towards lower frequencies as the cavitation number decreases, similar to its influence on breathing mode oscillations. The results indicate the correlations between the breathing mode oscillations and the pressure fluctuations, with the low-frequency and relatively higher-frequency pressure fluctuations being correlated with the growth and decay regions, respectively.

physics.flu-dyn↗

arXiv2022

Combined space-time reduced-order model with 3D deep convolution for extrapolating fluid dynamics

There is a critical need for efficient and reliable active flow control strategies to reduce drag and noise in aerospace and marine engineering applications. While traditional full-order models based on the Navier-Stokes equations are not feasible, advanced model reduction techniques can be inefficient for active control tasks, especially with strong non-linearity and convection-dominated phenomena. Using convolutional recurrent autoencoder network architectures, deep learning-based reduced-order models have been recently shown to be effective while performing several orders of magnitude faster than full-order simulations. However, these models encounter significant challenges outside the training data, limiting their effectiveness for active control and optimization tasks. In this study, we aim to improve the extrapolation capability by modifying network architecture and integrating coupled space-time physics as an implicit bias. Reduced-order models via deep learning generally employ decoupling in spatial and temporal dimensions, which can introduce modeling and approximation errors. To alleviate these errors, we propose a novel technique for learning coupled spatial-temporal correlation using a 3D convolution network. We assess the proposed technique against a standard encoder-propagator-decoder model and demonstrate a superior extrapolation performance. To demonstrate the effectiveness of 3D convolution network, we consider a benchmark problem of the flow past a circular cylinder at laminar flow conditions and use the spatio-temporal snapshots from the full-order simulations. Our proposed 3D convolution architecture accurately captures the velocity and pressure fields for varying Reynolds numbers. Compared to the standard encoder-propagator-decoder network, the spatio-temporal-based 3D convolution network improves the prediction range of Reynolds numbers outside of the training data.

physics.flu-dyn↗

arXiv2022

Predicting waves in fluids with deep neural network

In this paper, we present a deep learning technique for data-driven predictions of wave propagation in a fluid medium. The technique relies on an attention-based convolutional recurrent autoencoder network (AB-CRAN). To construct a low-dimensional representation of wave propagation data, we employ a denoising-based convolutional autoencoder. The AB-CRAN architecture with attention-based long short-term memory cells forms our deep neural network model for the time marching of the low-dimensional features. We assess the proposed AB-CRAN framework against the standard recurrent neural network for the low-dimensional learning of wave propagation. To demonstrate the effectiveness of the AB-CRAN model, we consider three benchmark problems, namely, one-dimensional linear convection, the nonlinear viscous Burgers equation, and the two-dimensional Saint-Venant shallow water system. Using the spatial-temporal datasets from the benchmark problems, our novel AB-CRAN architecture accurately captures the wave amplitude and preserves the wave characteristics of the solution for long time horizons. The attention-based sequence-to-sequence network increases the time-horizon of prediction compared to the standard recurrent neural network with long short-term memory cells. The denoising autoencoder further reduces the mean squared error of prediction and improves the generalization capability in the parameter space.

physics.flu-dyn↗

arXiv2022

An interface and geometry preserving phase-field method for fully Eulerian fluid-structure interaction

We present an interface and geometry preserving (IGP) method for the modeling of fully Eulerian fluid-structure interaction via phase-field formulation. While the hyperbolic tangent interface profile is preserved by the time-dependent mobility model, the proposed method maintains the geometry of the solid-fluid interface by reducing the volume-conserved mean curvature flow. To achieve the reduction in the curvature flow, we construct a gradient-minimizing velocity field (GMV) for the convection of the order parameter. The constructed velocity field enables the preservation of the solid velocity in the solid domain while extending the velocity in the normal direction throughout the diffuse interface region. With this treatment, the GMV reduces the normal velocity difference of the level sets of the order parameter which alleviates the undesired thickening or thinning of the diffuse interface region due to the convection. During this process, the time-dependent mobility coefficient is substantially reduced and there is a lesser curvature flow. The GMV ensures that the diffuse interface region moves with the solid bulk such that the fluid-solid interface conforms to the geometry of the solid. Using the unified momentum equation and the phase-dependent interpolation, we integrate the IGP method into a fully Eulerian variational FSI solver based on the incompressible viscous fluid and the neo-Hookean solid. We first demonstrate the ability of the phase-field-based IGP method for the convection of circular and square interfaces with a prescribed velocity field. The variational FSI framework with the IGP method is then examined for the flow passing a fixed deformable block in a channel domain. Finally, the vibration of a plate attached behind a stationary cylinder subjected to incoming flow is employed to assess the fully Eulerian framework for a large aspect ratio and sharp corners.

physics.flu-dyn↗

arXiv2021

Three-dimensional deep learning-based reduced order model for unsteady flow dynamics with variable Reynolds number

We present a deep learning-based reduced order model (DL-ROM) for predicting the fluid forces and unsteady vortex patterns. We consider flow past a sphere to examine the accuracy of our DL-ROM predictions. The proposed methodology relies on a three-dimensional convolutional recurrent autoencoder network (3D CRAN) to extract the low-dimensional flow features from full-order snapshots. The low-dimensional features are evolved in time using a long short-term memory-based recurrent neural network and reconstructed back to the full-order as flow voxels. These 3D voxels are introduced as static and uniform query probes in the point cloud domain to reduce the unstructured mesh complexity while providing convenience in 3D CRAN training. We analyze a novel procedure to recover the interface description and the force quantities from the 3D flow voxels. The 3D CRAN methodology is first applied to an external flow past a static sphere at a single Reynolds number of Re = 300. We provide an assessment of the computing requirements in terms of the memory usage, training costs, and testing times associated with the 3D CRAN framework. Subsequently, variable Re-based flow information is infused in one 3D CRAN to learn a complicated symmetry-breaking flow regime (280 < Re < 460) for the flow past a sphere. Effects of transfer learning are analyzed for training this complicated 3D flow regime on a relatively smaller time series dataset. The 3D CRAN framework learns the flow regime nearly 20 times faster than the parallel full-order model and predicts unsteady flows with an excellent to good accuracy. Based on the predicted flow fields, the network demonstrates an R2 accuracy of 98.58% for drag and 76.43% for lift over the sphere in the chosen flow regime. The proposed framework aligns with the development of a digital twin for 3D unsteady flow field with variable Re effects.

physics.flu-dyn↗

arXiv2020

A variational interface-preserving and conservative phase-field method for the surface tension effect in two-phase flows

We present a finite element based variational interface-preserving and conservative phase-field formulation for the modeling of incompressible two-phase flows with surface tension dynamics. The preservation of the hyperbolic tangent interface profile of the convective Allen-Cahn phase-field formulation relies on a novel time-dependent mobility model. The mobility coefficient is adjusted adaptively as a function of gradients of the velocity and the order parameter in the diffuse interface region in such a way that the free energy minimization properly opposes the convective distortion. The ratio of the convective distortion to the free energy minimization is termed as the convective distortion parameter, which characterizes the deviation from the hyperbolic tangent shape due to the convection effect. The mass conservation is achieved by enforcing a Lagrange multiplier with both temporal and spatial dependence on the phase-field function. We integrate the interface-preserving and conservative phase-field formulation with the incompressible Navier-Stokes equations and the continuum surface tension force model for the simulation of incompressible two-phase flows. A positivity preserving scheme designed for the boundedness and stability of the solution is employed for the variational discretization using unstructured finite elements. We examine the convergence and accuracy of the Allen-Cahn phase-field solver through a generic one-dimensional bistable diffusion-reaction system in a stretching flow. We quantify and systematically assess the relative interface thickness error and the relative surface tension force error with respect to the convective distortion parameter. Two- and three-dimensional rising bubble cases are further simulated to examine the effectiveness of the proposed model on the volume-preserving mean curvature flow and the interface-preserving capability.

physics.comp-ph↗

arXiv2020

Transverse flow-induced vibrations of a sphere in the proximity of a free surface: A numerical study

We present a numerical study on the transverse flow-induced vibration (FIV) of an elastically mounted sphere in the vicinity of a free surface at subcritical Reynolds numbers. To begin, We verify and analyze the mode transitions and the motion trajectories of a fully submerged sphere vibrating freely in all directions for the Reynolds number up to $30\,000$. Next, the response dynamics of a transversely vibrating sphere is studied for three values of normalized immersion ratio ($h^*=h/D$, where $h$ is the distance from the top of the sphere to undisturbed free-surface level and $D$ is the sphere diameter), at $h^*=1$ (fully submerged sphere with no free-surface effect), $h^*=0$ (where the top of the sphere touches the free surface) and $h^*=-0.25$ (where the sphere pierces the free surface). At the lock-in range, we observe that the amplitude response at $h^*=0$ is decreased significantly compared to the case at $h^*=1$. It is found that the vorticity flux is diffused due to the free-surface boundary and the free surface acts as a sink of energy that leads to a reduction in the transverse force and amplitude response. When the sphere pierces the free surface at $h^*=-0.25$, the amplitude response at the lock-in state is found to be greater than all the submerged cases studied with the maximum peak-to-peak amplitude of $\sim2D$. We find that the interaction of the piercing sphere with the air-water interface causes a relatively large surface deformation and has a significant impact on the synchronization of the vortex shedding and the vibration frequency. Increased streamwise vorticity gives rise to a relatively larger transverse force to the piercing sphere at $h^*=-0.25$, resulting in greater positive energy transfer per cycle to sustain the large-amplitude vibration. Lasty, we study the sensitivity of FIV response on the mass ratio, $m^*$, and Froude number, $Fr$, at the lock-in state.

physics.flu-dyn↗