arXiv subjects

Yantao Yang

Publications and source records attributed to Yantao Yang.

At least 19 recordsLinked to original sources

arXiv2026

A second-order diffusive-interface immersed boundary method for incompressible flow with phase change and moving interfaces

Accurately resolving interfacial gradients is critical for simulating two-phase flows, particularly those involving phase transitions or active matter. The traditional diffuse-interface immersed boundary methods (IBMs) are highly efficient for such problems, but they typically suffer from a reduction to first-order accuracy near the phase-changing boundaries. We clarify that the main reason is the local derivative discontinuities. Here, we propose a smooth extension strategy to restore formal second-order spatial accuracy. By extrapolating the scalar field across the interface, the method structurally ensures derivative continuity. To preserve the divergence-free condition in incompressible fluid solvers, this smooth extension is applied exclusively to the scalar transport equations. The velocity field retains the standard diffuse-interface treatment. The proposed framework is systematically validated against classical phase-change benchmarks, specifically one-dimensional evaporation and boiling problems. Additionally, the method is applied to the spontaneous autophoretic motion of isotropic particles. The numerical results confirm the capability of our method in resolving the complex multi-physics boundary couplings.

physics.flu-dyn↗

arXiv2025

A Unified Numerical Framework for Turbulent Convection and Phase-Change Dynamics in Coupled Fluid-Porous Systems

This work presents a unified numerical framework for simulating incompressible flows within the coupled fluid-porous-medium system and involving heat and solute transport and phase-changing process. A complete set of governing equations is established based on the Darcy-Brinkman equation, the advection-diffusion equations for heat and solute, and a phase field equation describing the evolution of porous medium. Phase-changing process and relevant influences are incorporated as corresponding source terms. A numerical method is then developed to solve the governing equations. Several different types of model problems are simulated with the numerical method. For the incompressible flows inside a coupled fluid-porous-medium system, the channel turbulence over a porous substrate and the thermal convection in a two-layer system are simulated. For the phase-changing flows, the one-dimensional Stefan problem and the two-dimensional flow of pure water freezing are tested. The results agree with the existing simulations. Finally, the full solver is used to simulate the growth of mushy ice during seawater freezing, which can successfully reproduce the experimental results at the exactly same conditions. Therefore, the developed framework provides a versatile and reliable tool for studying complex multiphase, multi-component transport phenomena in fluid-porous-medium systems involving solid-liquid phase change.

physics.flu-dyn↗

arXiv2025

Reinforcement-learning-assisted control of four-roll mills: geometric symmetry and inertial effect

Embedding the intrinsic symmetry of a flow system in training its machine learning algorithms has become a significant trend in the recent surge of their application in fluid mechanics. This paper leverages the geometric symmetry of a four-roll mill (FRM) to enhance its training efficiency. Stabilizing and precisely controlling droplet trajectories in a FRM is challenging due to the unstable nature of the extensional flow with a saddle point. Extending the work of Vona & Lauga, this study applies Deep Reinforcement Learning (DRL) to effectively guide a displaced droplet to the center of the FRM. Through direct numerical simulations, we explore the applicability of DRL in controlling FRM flow with moderate inertial effects, i.e., Reynolds number $\sim\mathcal{O}(1)$, a nonlinear regime previously unexplored. The FRM's geometric symmetry allows control policies trained in one of the eight sub-quadrants to be extended to the entire domain, reducing training costs. Our results indicate that the DRL-based control method can successfully guide a displaced droplet to the target center with robust performance across various starting positions, even from substantially far distances. The work also highlights potential directions for future research, particularly focusing on efficiently addressing the delay effects in flow response caused by inertia. This study presents new advances in controlling droplet trajectories in more nonlinear and complex situations, with potential applications to other nonlinear flows. The geometric symmetry used in this cutting-edge reinforcement learning approach can also be applied to other control methods.

physics.flu-dyn↗

arXiv2025

Passive scalar dispersion along porous stratum with natural convection

We investigate horizontal dispersion of a passive scalar in a porous stratum with Rayleigh-Darcy convection initiated by a geothermal gradient. While increasing Rayleigh number ($Ra$) keeps enhancing convection, the horizontal dispersion coefficient ($\hat{D}$) only scales with Ra in a narrow range, and saturates at $Ra \gtrsim 2500$. We rationalize this two-stage behavior: at low Ra, passive scalar migrates through bulk circumflex; at high Ra, boundary micro-plume layer becomes the dominant scalar pathway. Theory gives saturate $\hat{D}$ value proportional to the Lewis number $Le$ and molecular diffusivity $D_0$.

physics.flu-dyn↗

arXiv2024

From Darcy flow to convective flow: pore-scale study of density-driven currents in porous media

We conducted a series of pore-scale numerical simulations on convective flow in porous media, with a fixed Schmidt number of 400 and a wide range of Rayleigh numbers. The porous media are modeled using regularly arranged square obstacles in a Rayleigh-B\'enard (RB) system. As the Rayleigh number increases, the flow transitions from a Darcy-type regime to an RB-type regime, with the corresponding $Sh-Ra_D$ relationship shifting from sublinear scaling to the classical 0.3 scaling of RB convection. Here, $Sh$ and $Ra_D$ represent the Sherwood number and Rayleigh-Darcy number, respectively. For different porosities, the transition begins at approximately $Ra_D = 4000$, at which point the characteristic horizontal scale of the flow field is comparable to the size of a single obstacle unit. When the thickness of the concentration boundary layer is less than about one-sixth of the pore spacing, the flow finally enters the RB regime. In the Darcy regime, the scaling exponent of $Sh$ and $Ra_D$ decreases as porosity increases. Based on the Grossman-Lohse theory (J. Fluid Mech., vol. 407, 2000; Phys. Rev. Lett., vol. 86, 2001), we provide an explanation for the scaling laws in each regime and highlight the significant impact of mechanical dispersion effects within the boundary layer. Our findings provide some new insights into the validity range of the Darcy model.

physics.flu-dyn↗

arXiv2022

On the wall-bounded model of fingering double diffusive convection

Fingering double diffusive convection with real seawater properties is studied by two-dimensional direct numerical simulations for the wall-bounded domain and compared with the results for fully periodic domain. For fixed unstable salinity difference between two horizontal plates, dominant flow structures change from convection rolls to salt fingers as the stable temperature difference increases. Meanwhile the bulk density ratio calculated by the mean scalar gradients exceeds unity. When the bulk thermal Rayleigh number, which is defined by the mean temperature gradient in the bulk and the domain height, is larger than $10^7$, the characteristic height of salt fingers is much smaller than the domain height and the flow enters the free salt-finger regime. In this regime the transport properties agree quantitatively with those obtained in the fully periodic domain (e.g. Traxler et al. J. Fluid Mech., 677, 530-553, 2011). The salt-finger bulk does not spontaneously break into multi-layer staircases probably due to the fact that solid boundary prevents the development of large-scale secondary instabilities. For the limited range of density ratio at the highest salinity Rayleigh number considered here, the multi-layer state is directly established from the initial condition with uniform salinity distribution and vertically linear temperature distribution.

physics.flu-dyn↗

arXiv2021

Flow structures and vertical transport in tilting salt finger with a background shear

In this work we study the fingering double diffusive convection, namely the buoyancy-driven convection flow within a fluid layer experiencing an unstable salinity gradient and a stable thermal gradient. Especially, we investigate the influences from a background shear with uniform strength. Linear stability analysis indicates that the unstable modes shift from a circular shape to a sheet-like shape as the shear becomes stronger. Three dimensional direction numerical simulations are conducted for five groups of cases, each of which has the same combination of thermal and salinity gradients (measured by corresponding Rayleigh numbers), and gradually increasing shear strength. Simulation results reveal that a very weak shear organizes the salt fingers into a very regular pattern, which can enhance the salinity flux. This enhancement effect, however, reduces as the Rayleigh number increases. As the shear further strengthens, the dominant structures change from salt fingers to salt sheets, and the coherence length scale increases in the streamwise direction. Meanwhile, salinity and heat fluxes decrease. These results suggest that even a weak shear can notably alter the morphology and transport properties of fingering double diffusive convection.

physics.flu-dyn↗

arXiv2021

Layering and vertical transport in sheared double diffusive convection in the diffusive regime

A sequence of two and three-dimensional simulations is conducted for the double diffusive convection (DDC) flows in the diffusive regime subjected to an imposed shear. The flow is confined between two horizontal plates which are maintained at different constant temperature, salinity, and different velocity, thus setting up a shear across the flow. The lower plate is fixed at higher temperature and salinity, while the overall (unperturbed) density gradient is statically stable. For a wide range of control parameters, and for sufficiently strong perturbation of the conductive initial state, we find that staircase-like structures spontaneously develop, with relatively well-mixed layers separated by sharp interfaces of enhanced scalar gradient. Such staircases appear to be robust even in the presence of strong shear over very long times, although we typically observe early time coarsening of the number of observed layers. For the same set of control parameters, different asymptotic layered states, with markedly different vertical scalar fluxes, can arise for different initial perturbation structures. The imposed shear does significantly spatio-temporally modify the vertical transport of the various scalars. The flux ratio (i.e., the ratio between the density fluxes due to the total (convective and diffusive) salt flux and the total heat flux) is found, at steady state, to be essentially equal to the square root of the ratio of the salt diffusivity to the thermal diffusivity, consistently with the physical model originally proposed by Linden and Shirtcliffe (1978) and the variational arguments presented by Stern (1982) for unsheared double diffusive convection.

physics.flu-dyn↗

arXiv2021

An explicit and non-iterative moving-least-squares immersed-boundary method with low boundary velocity error

In this work, based on the moving-least-squares immersed boundary method, we proposed a new technique to improve the calculation of the volume force representing the body boundary. For boundary with simple geometry, we theoretically analyse the error between the desired volume force at boundary and the actual force given by the original method. The ratio between the two forces is very close to a constant. Numerical experiments reveal that for complex geometry, this ratio exhibits very narrow distribution around certain value. A spatially uniform coefficient is then introduced to correct the force and fixed by the least-square method over all boundary markers. Such method is explicit and non-iterative, and can be easily implemented into the existing scheme. Several test cases have been simulated with stationary and moving boundaries. Our new method can reduce the residual boundary velocity to the level comparable to that given by the iterative method, but requires much less computing time. Moreover, the new method can be readily combined with the iterative method and further reduces the residual boundary velocity.

math.NA↗

arXiv2021

Realizing the ultimate scaling of the convection turbulence by spatially decoupling the thermal and viscous boundary layers

Turbulent convection plays a crucial role in many natural environments, ranging from Earth ocean, mantle and outer core, to various astrophysical systems. For such flows with extremely strong thermal driving, an ultimate scaling was proposed for the heat flux and velocity. Despite numerous experimental and numerical studies, a conclusive observation of the ultimate regime has not been reached yet. Here we show that the ultimate scaling can be perfectly realized once the thermal boundary layer is fully decoupled from the viscous boundary layer and locates inside the turbulent bulk. The heat flux can be greatly enhanced by one order of magnitude. Our results provide concrete evidences for the appearance of the ultimate state when the entire thermal boundary layer is embedded in the turbulent region, which is probably the case in many natural convection systems.

physics.flu-dyn↗

arXiv2020

Thermohaline interleaving induced by horizontal temperature and salinity gradients from above

In the Ocean, thermohaline intrusions and interleaving layers occur within the water mass fronts with horizontal temperature and salinity gradients, which provide an important horizontal mixing mechanism. Here we report a new type of thermohaline intrusion which is driven by the horizontal temperature and salinity gradients in the fluid layers at adjacent depths due to the different double diffusive mixing rates in the vertical direction. Once established, the intrusion layers share similar behaviors as those found within the gradient regions. Such intrusion process generates extra horizontal heat and salinity fluxes towards the cold and fresh side, but transfer density anomaly towards the warm and salty side. These findings greatly extend the circumstance where thermohaline intrusions may be observed.

physics.flu-dyn↗

arXiv2020

What rotation rate maximizes heat transport in rotating Rayleigh-Bénard convection with Prandtl number larger than one?

The heat transfer and flow structure in rotating Rayleigh-Bénard convection are strongly influenced by the Rayleigh ($Ra$), Prandtl ($Pr$), and Rossby ($Ro$) number. For $Pr\gtrsim 1$ and intermediate rotation rates, the heat transfer is increased compared to the non-rotating case. We find that the regime of increased heat transfer is subdivided into a low and a high $Ra$ number regime. For $Ra\lesssim 5\times10^8$ the heat transfer at a given $Ra$ and $Pr$ is highest at an optimal rotation rate, at which the thickness of the viscous and thermal boundary layer is about equal. From the scaling relations of the thermal and viscous boundary layer thicknesses, we derive that the optimal rotation rate scales as $1/Ro_\mathrm{opt} \approx 0.12 Pr^{1/2}Ra^{1/6}$. In the low $Ra$ regime the heat transfer is similar in a periodic domain and cylindrical cells with different aspect ratios, i.e.\ the ratio of diameter to height. This is consistent with the view that the vertically aligned vortices are the dominant flow structure. For $Ra\gtrsim 5\times10^8$ the above scaling for the optimal rotation rate does not hold anymore. It turns out that in the high $Ra$ regime, the flow structures at the optimal rotation rate are very different than for lower $Ra$. Surprisingly, the heat transfer in the high $Ra$ regime differs significantly for a periodic domain and cylindrical cells with different aspect ratios, which originates from the sidewall boundary layer dynamics and the corresponding secondary circulation.

physics.flu-dyn↗

arXiv2020

Subcritical behaviour in double diffusive convection within the diffusive regime

We conduct two- and three-dimensional simulations for double diffusive convection in the diffusive regime, where the fluid flow is driven by a destabilizing temperature gradient and stabilized by a stably stratified salinity gradient. We study how the heat flux, Reynolds number, and flow structures change with the density ratio $Λ$, which is the ratio of the buoyancy force induced by the salinity gradient to that by the temperature gradient. When $Λ$ increases from zero, the flow first behaves similarly as in pure Rayleigh-Bénard (RB) convection, both with respect to flow structure and to heat transport. The linear stability analysis of Baines & Gill (J. Fluid Mech., vol. 37, 1969, pp. 289-306) had estimated the critical density ratio $Λ_c$, above which the flow becomes stable. However, here we show that by using a large-scale circulation as initial condition (rather than the linear profiles assumed in the linear stability analysis), DDC in the diffusive regime can exhibit subcritical behaviour when $Λ> Λ_c$, i.e., coexistence of states at the same control parameters. Even though the density ratio becomes thousands times that of the critical value $Λ_c$, there is still convection with strongly enhanced heat transfer properties compared to the pure conduction case. We reveal the corresponding flow structures and find an unstably-stratified region sandwiched between two stably-stratified layers. Our results demonstrate the importance of the initial condition for DDC in the diffusive regime, especially in the situation of a large density ratio, which occurs in high-latitude ocean regions.

physics.flu-dyn↗

arXiv2019

Multiple equilibria in fingering double diffusive convection turbulence

We report here some intriguing properties of fingering double diffusive convection turbulence, i.e. convection flow driven simultaneously by an unstable salinity gradient and a stable temperature gradient. Multiple equilibria can be established in such flow for the same control parameters, either by setting different initial scalar distribution or different evolution history. Transition between a single finger layer and multi-layer staircase can be abrupt and hysteresis. Unlike a deep finger layer, a model widely used in literature, finger interfaces within staircases show totally different transport behaviors and seem to obey the Stern number constrain. All these findings provide important new insights to fingering double diffusive convection, and to general convection turbulence.

physics.flu-dyn↗

arXiv2019

Solving Differential Equation with Constrained Multilayer Feedforward Network

In this paper, we present a novel framework to solve differential equations based on multilayer feedforward network. Previous works indicate that solvers based on neural network have low accuracy due to that the boundary conditions are not satisfied accurately. The boundary condition is now inserted directly into the model as boundary term, and the model is a combination of a boundary term and a multilayer feedforward network with its weight function. As the boundary condition becomes predefined constraintion in the model itself, the neural network is trained as an unconstrained optimization problem. This leads to both ease of training and high accuracy. Due to universal convergency of multilayer feedforward networks, the new method is a general approach in solving different types of differential equations. Numerical examples solving ODEs and PDEs with Dirichlet boundary condition are presented and discussed.

math.NA↗

arXiv2018

Flow induced dissolution of femtoliter surface droplet arrays

The dissolution of liquid nanodroplets is a crucial step in many applied processes, such as separation and dispersion in food industry, crystal formation of pharmaceutical products, concentrating and analysis in medical diagnosis, and drug delivery in aerosols. In this work, using both experiments and numerical simulations, we \textit{quantitatively} study the dissolution dynamics of femtoliter surface droplets in a highly ordered array under a uniform flow. Our results show that the dissolution of femoliter droplets strongly depends on their spatial positions relative to the flow direction, drop-to-drop spacing in the array, and the imposed flow rate. In some particular case, the droplet at the edge of the array can dissolve about 30% faster than the ones located near the centre. The dissolution rate of the droplet increases by 60% as the inter-droplet spacing is increased from 2.5 $\mu$m to 20 $\mu$m. Moreover, the droplets close to the front of flow commence to shrink earlier than those droplets in the center of the array. The average dissolution rate is faster for faster flow. As a result, the dissolution time $T_{i}$ decreases with the Reynolds number Re of the flow as $T_{i}\propto Re^{-3/4}$. The experimental results are in good agreement with numerical simulations where the advection-diffusion equation for the concentration field is solved and the concentration gradient on the surface of the drop is computed. The findings suggest potential approaches to manipulate nanodroplet sizes in droplet arrays simply by dissolution controlled by an external flow. The obtained droplets with varying curvatures may serve as templates for generating multifocal microlens in one array.

cond-mat.soft↗

arXiv2017

Two-Scalar Turbulent Rayleigh-Benard Convection: Numerical Simulations and Unifying Theory

We conduct direct numerical simulations for turbulent Rayleigh-Bénard (RB) convection, driven simultaneously by two scalar components (say, temperature and salt concentration) with different molecular diffusivities, and measure the respective fluxes and the Reynolds number. To account for the results, we generalize the Grossmann-Lohse theory for traditional RB convections~(Grossmann and Lohse, J. Fluid Mech., 407, 27-56; Phys. Rev. Lett., 86, 3316-3319; Stevens et al., J. Fluid Mech., 730, 295-308) to this two-scalar turbulent convection. Our numerical results suggest that the generalized theory can successfully predict the overall trends for the fluxes of two scalars and the Reynolds number. In fact, for most of the parameters explored here, the theory can even predict the absolute values of the fluxes and the Reynolds number with good accuracy. The current study extends the generality of the Grossmann-Lohse theory in the area of the buoyancy-driven convection flows.

physics.flu-dyn↗

arXiv2017

AFiD-GPU: a versatile Navier-Stokes Solver for Wall-Bounded Turbulent Flows on GPU Clusters

The AFiD code, an open source solver for the incompressible Navier-Stokes equations ({\color{blue}\burl{http://www.afid.eu}}), has been ported to GPU clusters to tackle large-scale wall-bounded turbulent flow simulations. The GPU porting has been carried out in CUDA Fortran with the extensive use of kernel loop directives (CUF kernels) in order to have a source code as close as possible to the original CPU version; just a few routines have been manually rewritten. A new transpose scheme, which is not limited to the GPU version only and can be generally applied to any CFD code that uses pencil distributed parallelization, has been devised to improve the scaling of the Poisson solver, the main bottleneck of incompressible solvers. The GPU version can reduce the wall clock time by an order of magnitude compared to the CPU version for large meshes. Due to the increased performance and efficient use of memory, the GPU version of AFiD can perform simulations in parameter ranges that are unprecedented in thermally-driven wall-bounded turbulence. To verify the accuracy of the code, turbulent Rayleigh-Bénard convection and plane Couette flow are simulated and the results are in good agreement with the experimental and computational data that published in previous literatures.

physics.flu-dyn↗