arXiv subjects

Ali Mani

Publications and source records attributed to Ali Mani.

At least 19 recordsLinked to original sources

arXiv2026

Generalized Forcing Method: Generation of Diverse Data for Training Linear Transport PDE Closure Models

Data-driven closure modeling for transport partial differential equations requires training data that are accurate, affordable, diverse, and directly tailored to the target closure fields. We develop the Generalized Forcing Method (GFM), a data-generation framework for training linear transport closure models. GFM generates such data by running simulations with a zero initial condition and an extra body force that is constructed compatibly with the reduced dynamics. This framework leads to implicit GFM (iGFM), which prescribes resolved trajectories, and explicit GFM (eGFM), which constructs a basis of admissible forcings. We apply eGFM to three linear transport closure problems: homogeneous shear flows, spatially inhomogeneous flows, and homogeneous shear flows with random coefficients. The results show that eGFM can identify accurate and stable reduced models when the reduced variables and model form are consistent with the underlying closure relation.

physics.flu-dyn↗

arXiv2026

A variable-coefficient model for decay of isotropic turbulence capturing effects of finite cascade time and Reynolds number

We study isotropic turbulence decay in the context of the k-epsilon model, which solves the dissipation and kinetic energy equations. In modeling the dissipation equation, the coefficient C_epsilon2, suggested by Hanjalic and Launder [Journal of Fluid Mechanics, 1972] [1], is related to the temporal decay power-law by n = 1/(C_epsilon2 -1 )) and is assumed to be a constant value. In this work, we perform high-fidelity numerical simulations to examine the mathematical terms responsible for the decay of isotropic turbulence, considering both scenarios of forced and decaying turbulence. Our data suggest that the instantaneous C_epsilon2 not only depends on the instantaneous Reynolds number but is also sensitive to the history of energy injection in turbulence. We attribute these observations to the finite time required for the cascade from energetic to dissipative scales. Considering data from both decaying and growing forced turbulence, we develop an evolution equation for C_epsilon2 with Reynolds-dependent coefficients. We demonstrate that this model accurately captures the time evolution of dissipation and kinetic energy over a wide range of Reynolds numbers under a wide range of forced and decay scenarios.

physics.flu-dyn↗

arXiv2026

An LES model with finite-rate phase change and subgrid spray based on a thermodynamically consistent four-equation multiphase model

In this work, an LES model with finite-rate phase change and subgrid spray based on a high-resolution numerical scheme for multiphase multi-component simulations which satisfies interface equilibrium and phase immiscibility conditions is proposed. The multiphase model is based on a robust implementation of the four-equation multiphase model which assumes a strict subgrid equilibrium of pressure, temperature, and velocity. Critically, the equilibrium assumptions of the four-equation model provide large computational savings compared to modeling the full non-equilibrium multiphase system. To obtain predictive capabilities with these restrictive equilibrium assumptions, a new phase-confined form of the Eulerian $\Sigma$ spray model is proposed to predict subgrid interfacial surface area while avoiding unphysical leakage across interfaces. Additionally, an improved finite rate phase change model which is thermodynamically bounded by the equilibration of the Gibbs-free energy is coupled with the $\Sigma$ equation to model complex phase change regimes. The full modeling framework is validated using the Engine Combustion Network (ECN) Spray A case in non-evaporating and evaporating conditions and shows excellent agreement with experimental measurements.

physics.flu-dyn↗

arXiv2025

Atwood effects on nonlocality of the scalar transport closure in three-dimensional Rayleigh-Taylor mixing

The importance of nonlocality is assessed in modeling mean scalar transport for turbulent Rayleigh-Taylor (RT) mixing at different Atwood numbers. Building on the two-dimensional incompressible work of Lavacot et al. (2024, JFM), the present work extends the Macroscopic Forcing Method (MFM) to variable density problems in three-dimensional space to measure moments of the generalized eddy diffusivity kernel in RT mixing for increasing Atwood numbers (A=0.05, 0.3, 0.5, 0.8). It is found that as A increases: 1) the eddy diffusivity moments become asymmetric, and 2) the higher-order eddy diffusivity moments become larger relative to the leading-order diffusivity, indicating that nonlocality becomes more important at higher A. There is a particularly strong temporal nonlocality at higher $A$, suggesting stronger history effects. The implications of these findings for closure modeling for finite-Atwood RT are discussed.

physics.flu-dyn↗

arXiv2025

A thermodynamically consistent and robust four-equation model for multi-phase multi-component compressible flows using ENO-type schemes including interface regularization

In this work, a concise and robust computational framework is proposed to simulate compressible multi-phase multi-component flows. To handle both shocks and material interfaces, a positivity-preserving ENO-type scheme is coupled with multi-phase interface regularization terms. The positivity-preserving limiter is conservative and is applied locally for minimal degradation of the baseline ENO-type scheme. The interface regularization terms are extended from the conservative diffuse interface (CDI) model to accommodate multi-phase, multi-component flows. The ENO-type scheme is designed to be consistent with the thermodynamic equilibrium assumptions of the four-equation multi-phase model, naturally enforcing the interface equilibrium condition - preventing oscillations in pressure, velocity, and temperature around isothermal material interfaces - without requiring additional equations for volume fraction or mixture equation of state parameters, as is commonly done for the five-equation model. Additionally, non-dilute species diffusion models are extended to the multi-phase, multi-component setting. We show that this consistent framework is equally applicable for regimes ranging from single-phase to multi-phase multi-component flows. The proposed models and numerical schemes are implemented in the highly parallel Hypersonic Task based Research (HTR) Solver, and high-resolution simulations are performed using both CPUs and GPUs.

physics.flu-dyn↗

arXiv2025

Techniques for improved statistical convergence in quantification of eddy diffusivity moments

While recent approaches, such as the macroscopic forcing method (MFM) or Green's function-based approaches, can be used to compute Reynolds-averaged Navier--Stokes closure operators using forced direct numerical simulations, MFM can also be used to directly compute moments of the effective nonlocal and anisotropic eddy diffusivities. The low-order spatial and temporal moments contain limited information about the eddy diffusivity but are often sufficient for quantification and modeling of nonlocal and anisotropic effects. However, when using MFM to compute eddy diffusivity moments, the statistical convergence can be slow for higher-order moments. In this work, we demonstrate that using the same direct numerical simulation (DNS) for all forced MFM simulations improves statistical convergence of the eddy diffusivity moments. We present its implementation in conjunction with a decomposition method that handles the MFM forcing semi-analytically and allows for consistent boundary condition treatment, which we develop for both scalar and momentum transport. We demonstrate that for a two-dimensional Rayleigh--Taylor instability case study, using the same DNS for all forced MFM simulations results in convergence with O(100) simulations rather than O(1000) simulations. We then demonstrate the impacts of improved convergence on the quantification of the eddy diffusivity.

physics.flu-dyn↗

arXiv2024

A mass-conserving contact line treatment for second-order conservative phase field methods based on the generalized Navier boundary condition

A mass-conserving contact line treatment for second-order conservative phase field methods is presented and applied to the conservative diffuse interface (CDI) model. The treatment centers on a no-flux boundary condition for the phase field along with a slip boundary condition for the velocity that is based on the generalized Navier boundary condition (GNBC). Since the CDI model is a second-order partial differential equation, it does not permit a second (contact angle) boundary condition, in contrast to the popular fourth-order Cahn-Hilliard model. As such, we use one-sided stencils and extrapolations from the interior of the domain to compute phase-field-related quantities on and near the wall. Additionally, we propose novel modifications to the GNBC on the continuous and discrete levels that reduce spurious slip velocity when the contact angle achieves its equilibrium value. The proposed treatment is validated with the equilibrium drop and two-phase Couette flow test cases.

physics.flu-dyn↗

arXiv2024

Diffuse interface treatment in generalized curvilinear coordinates with grid-adapting interface thickness

A general approach for transforming phase field equations into generalized curvilinear coordinates is proposed in this work. The proposed transformation can be applied to isotropic, non-isotropic, and curvilinear grids without adding any ambiguity in determining the phase field parameters. Moreover, it accurately adapts the interface thickness to the local grid-size for a general curvilinear grid without creating oscillations. Three canonical verification tests are presented on four grids with varying skewness levels. The classic advection and drop in shear tests are extended to curvilinear grids and show that the original phase field on Cartesian grids and the proposed curvilinear form have an identical order of convergence. Additionally, the proposed method is shown to provide grid-independent convergence on a two-way coupled compressible Rayleigh-Taylor instability. These simulations illustrate the robustness and accuracy of the proposed method for handling complex interfacial structures on generalized curvilinear grids.

physics.comp-ph↗

arXiv2024

Nonlocality of the slip length operator for scalar and momentum transport in turbulent flow over superhydrophobic surfaces

Superhydrophobic surfaces (SHS) are textured hydrophobic surfaces which have the ability to trap air pockets when immersed in water. This can result in significant drag reduction, due to substantially lower viscosity of air resulting in substantial effective slip velocity at the interface. Past studies of both laminar and turbulent flows model this slip velocity in terms of a homogenized Navier slip boundary condition with a slip length relating the wall slip velocity to the wall-normal velocity gradient. In this work, we seek to understand the effects of superhydrophobic surfaces in the context of mean scalar and momentum mixing. We use the macroscopic forcing method (Mani and Park, 2021) to compute the generalized eddy viscosity and slip length operators of a turbulent channel over SHS, implemented as both a pattern-resolved boundary condition and homogenized slip length boundary condition, for several pattern sizes and geometries. We present key differences in the mixing behavior of both boundary conditions through quantification of their near-wall eddy viscosity. Analysis of transport in turbulent flow over pattern-resolved surfaces reveals substantial nonlocality in the measured homogenized slip length for both scalar and momentum mixing when the Reynolds and Peclet numbers based on pattern size are finite. We present several metrics to quantify this nonlocality and observe possible trends relating to Reynolds number, texture size, and pattern geometry. The importance of nonlocality in the slip length operator and in the eddy diffusivity operator is demonstrated by examining the impact on Reynolds-averaged solutions for the mean scalar and velocity fields.

physics.flu-dyn↗

arXiv2024

Reynolds stress decay modeling informed by anisotropically forced homogeneous turbulence

Models for solving the Reynolds-averaged Navier-Stokes equations are popular tools for predicting complex turbulent flows due to their computational affordability and ability to provide or estimate quantities of engineering interest. However, results depend on a proper treatment of unclosed terms, which require progress in the development and assessment of model forms. In this study, we consider the Reynolds stress transport equations as a framework for second-moment turbulence closure modeling. We specifically focus on the terms responsible for decay of the Reynolds stresses, which can be isolated and evaluated separately from other terms in a canonical setup of homogeneous turbulence. We show that by using anisotropic forcing of the momentum equation, we can access states of turbulence traditionally not probed in a triply-periodic domain. The resulting data span a wide range of anisotropic turbulent behavior in a more comprehensive manner than extant literature. We then consider a variety of model forms for which these data allow us to perform a robust selection of model coefficients and select an optimal model that extends to cubic terms when expressed in terms of the principal coordinate Reynolds stresses. Performance of the selected decay model is then examined relative to the simulation data and popular models from the literature, demonstrating the superior accuracy of the developed model and, in turn, the efficacy of this framework for model selection and tuning.

physics.flu-dyn↗

arXiv2023

A model for drift velocity mediated scalar eddy diffusivity in homogeneous turbulent flows

Low Stokes number particles at dilute concentrations in turbulent flows can reasonably be approximated as passive scalars. The added presence of a drift velocity due to buoyancy or gravity when considering the transport of such passive scalars can reduce the turbulent dispersion of the scalar via a diminution of the eddy diffusivity. In this work, we propose a model to describe this decay and use a recently developed technique to accurately and efficiently measure the eddy diffusivity using Eulerian fields and quantities. We then show a correspondence between this method and standard Lagrangian definitions of diffusivity and collect data across a range of drift velocities and Reynolds numbers. The proposed model agrees with data from these direct numerical simulations, offers some improvement to previous models in describing other computational and experimental data, and satisfies theoretical constraints that are independent of Reynolds number.

physics.flu-dyn↗

arXiv2023

Targeted computation of nonlocal closure operators via an adjoint-based macroscopic forcing method

Reynolds-averaged Navier--Stokes (RANS) closure must be sensitive to the flow physics, including nonlocality and anisotropy of the effective eddy viscosity. Recent approaches used forced direct numerical simulations to probe these effects, including the macroscopic forcing method (MFM) of Mani and Park ($\textit{Phys. Rev. Fluids}$ $\textbf{6}$, 054607 (2021)) and the Green's function approach of Hamba ($\textit{Phys. Fluids}$ $\textbf{17}$, 115102 (2005)). The resulting nonlocal and anisotropic eddy viscosities are exact and relate Reynolds stresses to mean velocity gradients at all locations. They can be used to inform RANS models of the sensitivity to the mean velocity gradient and the suitability of local and isotropic approximations. However, these brute-force approaches are expensive. They force the mean velocity gradient at each point in the averaged space and measure the Reynolds stress response, requiring a separate simulation for each mean velocity gradient location. Thus, computing the eddy viscosity requires as many simulations as degrees of freedom in the averaged space, which can be cost-prohibitive for problems with many degrees of freedom. In this work, we develop an adjoint-based MFM to obtain the eddy viscosity at a given Reynolds stress location using a single simulation. This approach recovers the Reynolds stress dependence at a location of interest, such as a separation point or near a wall, on the mean velocity gradient at all locations. We demonstrate using adjoint MFM to compute the eddy viscosity for a specified wall-normal location in an incompressible turbulent channel flow using one simulation. In contrast, a brute-force approach for the same problem requires $N=144$ simulations (the number of grid points in the non-averaged coordinate direction). We show that a local approximation for the eddy viscosity would have been inappropriate.

physics.flu-dyn↗

arXiv2023

Nonlocality of Mean Scalar Transport in Two-Dimensional Rayleigh-Taylor Instability Using the Macroscopic Forcing Method

The importance of nonlocality of mean scalar transport in 2D Rayleigh-Taylor Instability (RTI) is investigated. The Macroscopic Forcing Method (MFM) is utilized to measure spatio-temporal moments of the eddy diffusivity kernel representing passive scalar transport in the ensemble averaged fields. Presented in this work are several studies assessing the importance of the higher-order moments of the eddy diffusivity, which contain information about nonlocality, in models for RTI. First, it is demonstrated through a comparison of leading-order models that a purely local eddy diffusivity is insufficient in capturing the mean field evolution of the mass fraction in RTI. Therefore, higher-order moments of the eddy diffusivity operator are not negligible. Models are then constructed by utilizing the measured higher-order moments. It is demonstrated that an explicit operator based on the Kramers-Moyal expansion of the eddy diffusivity kernel is insufficient. An implicit operator construction that matches the measured moments is shown to offer improvements relative to the local model in a converging fashion.

physics.flu-dyn↗

arXiv2023

Fast Macroscopic Forcing Method

The macroscopic forcing method (MFM) of Mani and Park and similar methods for obtaining turbulence closure operators, such as the Green's function-based approach of Hamba, recover reduced solution operators from repeated direct numerical simulations (DNS). MFM has been used to quantify RANS-like operators for homogeneous isotropic turbulence and turbulent channel flows. Standard algorithms for MFM force each coarse-scale degree of freedom (i.e., degree of freedom in the RANS space) and conduct a corresponding fine-scale simulation (i.e., DNS), which is expensive. We combine this method with an approach recently proposed by Sch\"afer and Owhadi (2023) to recover elliptic integral operators from a polylogarithmic number of matrix-vector products. The resulting Fast MFM introduced in this work applies sparse reconstruction to expose local features in the closure operator and reconstructs this coarse-grained differential operator in only a few matrix-vector products and correspondingly, a few MFM simulations. For flows with significant nonlocality, the algorithm first "peels" long-range effects with dense matrix-vector products to expose a local operator. We demonstrate the algorithm's performance for scalar transport in a laminar channel flow and momentum transport in a turbulent one. For these, we recover eddy diffusivity operators at 1% of the cost of computing the exact operator via a brute-force approach for the laminar channel flow problem and 13% for the turbulent one. We observe that we can reconstruct these operators with an increase in accuracy by about a factor of 100 over randomized low-rank methods. We glean that for problems in which the RANS space is reducible to one dimension, eddy diffusivity and eddy viscosity operators can be reconstructed with reasonable accuracy using only a few simulations, regardless of simulation resolution or degrees of freedom.

physics.comp-ph↗

arXiv2023

Inverse asymptotic treatment: capturing discontinuities in fluid flows via equation modification

A major challenge in developing accurate and robust numerical solutions to multi-physics problems is to correctly model evolving discontinuities in field quantities, which manifest themselves as interfaces between different phases in multi-phase flows, or as shock and contact discontinuities in compressible flows. When a quick response is required to rapidly emerging challenges, the complexity of bespoke discretization schemes impedes a swift transition from problem formulation to computation, which is exacerbated by the need to compose multiple interacting physics. We introduce "inverse asymptotic treatment" (IAT) as a unified framework for capturing discontinuities in fluid flows that enables building directly computable models based on off-the-shelf numerics. By capturing discontinuities through modifications at the level of the governing equations, IAT can seamlessly handle additional physics and thus enable novice end users to quickly obtain numerical results for various multi-physics scenarios. We outline IAT in the context of phase-field modeling of two-phase incompressible flows, and then demonstrate its generality by showing how localized artificial diffusivity (LAD) methods for single-phase compressible flows can be viewed as instances of IAT. Through the real-world example of a laminar hypersonic compression corner, we illustrate IAT's ability to, within just a few months, generate a directly computable model whose wall metrics predictions for sufficiently small corner angles come close to that of NASA's VULKAN-CFD solver. Finally, we propose a novel LAD approach via "reverse-engineered" PDE modifications, inspired by total variation diminishing (TVD) flux limiters, to eliminate the problem-dependent parameter tuning that plagues traditional LAD. We demonstrate that, when combined with second-order central differencing, it can robustly and accurately model compressible flows.

physics.comp-ph↗

arXiv2023

Direct numerical simulation of electrokinetic transport phenomena in fluids: variational multi-scale stabilization and octree-based mesh refinement

Computational modeling of charged species transport has enabled the analysis, design, and optimization of a diverse array of electrochemical and electrokinetic devices. These systems are represented by the Poisson-Nernst-Planck (PNP) equations coupled with the Navier-Stokes (NS) equation. Direct numerical simulation (DNS) to accurately capture the spatio-temporal variation of ion concentration and current flux remains challenging due to the (a) small critical dimension of the diffuse charge layer (DCL), (b) stiff coupling due to fast charge relaxation times, large advective effects, and steep gradients close to boundaries, and (c) complex geometries exhibited by electrochemical devices. In the current study, we address these challenges by presenting a direct numerical simulation framework that incorporates (a) a variational multiscale (VMS) treatment, (b) a block-iterative strategy in conjunction with semi-implicit (for NS) and implicit (for PNP) time integrators, and (c) octree based adaptive mesh refinement. The VMS formulation provides numerical stabilization critical for capturing the electro-convective flows often observed in engineered devices. The block-iterative strategy decouples the difficulty of non-linear coupling between the NS and PNP equations and allows the use of tailored numerical schemes separately for NS and PNP equations. The carefully designed second-order, hybrid implicit methods circumvent the harsh timestep requirements of explicit time steppers, thus enabling simulations over longer time horizons. Finally, the octree-based meshing allows efficient and targeted spatial resolution of the DCL. These features are incorporated into a massively parallel computational framework, enabling the simulation of realistic engineering electrochemical devices. The numerical framework is illustrated using several challenging canonical examples.

math.NA↗

arXiv2022

Assessment of an energy-based surface tension model for simulation of two-phase flows using second-order phase field methods

Second-order phase field models have emerged as an attractive option for capturing the advection of interfaces in two-phase flows. Prior to these, state-of-the-art models based on the Cahn-Hilliard equation, which is a fourth-order equation, allowed for the derivation of surface tension models through thermodynamic arguments. In contrast, the second-order phase field models do not follow a known energy law, and deriving a surface tension term for these models using thermodynamic arguments is not straightforward. In this work, we justify that the energy-based surface tension model from the Cahn-Hilliard context can be adopted for second-order phase field models as well and assess its performance. We test the surface tension model on three different second-order phase field equations; the conservative diffuse interface model of Chiu and Lin [1], and two models based on the modified Allen-Cahn equation introduced by Sun and Beckermann [2]. Additionally, we draw the connection between the energy-based model with a localized variation of the continuum surface force (CSF) model. Using canonical tests, we illustrate the lower magnitude of spurious currents, better accuracy, and superior convergence properties of the energy-based surface tension model compared to the CSF model, which is a popular choice used in conjunction with second-order phase field methods, and the localized CSF model. Importantly, in terms of computational expense and parallel efficiency, the energy-based model incurs no penalty compared to the CSF models.

physics.flu-dyn↗

arXiv2022

Direct 3D observation and unraveling of electroconvection phenomena during concentration polarization at ion-exchange membranes

A decade ago, two-dimensional microscopic flow visualization proved the theoretically predicted existence of electroconvection roles as well as their decisive role in destabilizing the concentration polarization layer at ion-selective fluid/membrane interfaces. Electroconvection induces chaotic flow vortices injecting volume having bulk concentration into the ion-depleted diffusion layer at the interface. Experimental quantification of these important flow patterns have so far only been carried out in 2D. Numerical direct simulations suggest 3D features, yet experimental proof is lacking. 3D simulations are also limited in covering extended spacial and temporal scales. This study presents a new comprehensive experimental method for the time-resolved recording of the 3D electroconvective velocity field near a cation-exchange membrane. For the first time, the spatio-temporal velocity field can be visualized in 3D at multiples of the overlimiting current density. In contrast to today's simulations, these experiments cover length and time scales typical for actual electrodialytic membrane processes. We visualize coherent vortex structures and reveal the changes in the velocity field and its statistics during the transition from vortex rolls to vortex rings with increasing current density. The transition is characterized by changes in the rotational direction, mean square velocity, and temporal energy spectrum with only little influence on the spatial spectrum. These findings indicate a more significant impact of EC's structural change on the mean square velocities and temporal spectra than on the spatial spectra. This knowledge is a prerequisite for engineering ion-selective surfaces that will enable the operation of electrically driven processes beyond the diffusion-limited Nernst regime.

physics.flu-dyn↗