3D Direct Numerical Simulations Research Articles

Rivulet cascade from falling liquid films with side contact lines

We investigate the dynamics of films of partially wetting liquids falling down a vertical plane in the presence of air. We focus on the little-studied case where the film is not in contact with lateral walls and thus has two side contact lines. By way of 3D direct numerical simulations, we study the fingering instability and the distribution of rivulets. Our results show that the instability develops as a cascade: two twin rivulets first develop at the free sides, followed by a series of twin rivulets growing closer to the center. This self-sustained fall is caused by the formation of stagnation zones at the front contact line as the liquid behind the ridge escapes toward a newly created rivulet. We also show that the established rivulet distance follows the prediction of linear instability, despite the cascade. The dynamics of the cascade is modified by inertial and film thickness effects, as well as by initial shape perturbations of the contact line. On the contrary, varying the contact angle does not affect the development of the cascade, apart from the average wavelength.

Dynamics of an elastoviscoplastic droplet in a Newtonian medium under shear flow

The dynamics of a single elastoviscoplastic (EVP) drop immersed in plane shear flow of a Newtonian fluid is studied by 3D direct numerical simulations using a finite-difference and level-set method combined with the Saramito model for the EVP fluid. This model gives rise to a yield stress behavior, where the unyielded state of the material is described as a Kelvin-Voigt viscoelastic solid and the yielded state as a viscoelastic Oldroyd-B fluid. Yielding of an initially solid drop of Carbopol is simulated under successively increasing shear rates. We proceed to examine the roles of nondimensional parameters on the yielding process; in particular, the Bingham number ($Bi$), capillary number ($Ca$), Weissenberg number ($Wi$), and ratio of solvent and total drop viscosity. We find that all of these parameters, and not only $Bi$, have a significant influence on the drop dynamics. Numerical simulations predict that the volume of the unyielded region inside the droplet increases with $Bi$ and $Wi$, while it decreases with $Ca$ at low $Wi$ and $Bi$. A new regime map is obtained for the prediction of the yielded, unyielded, and partly yielded modes as a function of $Bi$ and $Wi$. The drop deformation is studied and explained by examining the stresses in the vicinity of the drop interface. The deformation has a complex dependence on $Bi$ and $Wi$. At low $Bi$, the droplet deformation shows a nonmonotonic behavior with an increasing $Wi$. In contrast, at moderate and high $Bi$, droplet deformation always increases with $Wi$. Moreover, it is found that the deformation increases with $Ca$ and with the solvent to total drop viscosity ratio. A simple ordinary differential equation model is developed to explain the various behaviours observed numerically. The presented results are in contrast with the heuristic idea that viscoelasticity in the dispersed phase always inhibits deformation.

Numerical simulations of a falling film on the inner surface of a rotating cylinder.

A flow in which a thin film falls due to gravity on the inner surface of a vertical, rotating cylinder is investigated. This is performed using two-dimensional (2D) and 3D direct numerical simulations, with a volume-of-fluid approach to treat the interface. The problem is parameterized by the Reynolds, Froude, Weber, and Ekman numbers. The variation of the Ekman number (Ek), defined to be proportional to the rotational speed of the cylinder, has a strong effect on the flow characteristics. Simulations are conducted over a wide range of Ek values (0≤Ek≤484) in order to provide detailed insight into how this parameter influences the flow. Our results indicate that increasing Ek, which leads to a rise in the magnitude of centrifugal forces, produces a stabilizing effect, suppressing wave formation. Key flow features, such as the transition from a 2D to a more complex 3D wave regime, are influenced significantly by this stabilization and are investigated in detail. Furthermore, the imposed rotation results in distinct flow characteristics such as the development of angled waves, which arise due to the combination of gravitationally and centrifugally driven motion in the axial and azimuthal directions, respectively. We also use a weighted residuals integral boundary layer method to determine a boundary in the space of Reynolds and Ekman numbers that represents a threshold beyond which waves have recirculation regions.

Reduced chemical reaction mechanisms for simulating sodium emissions by solid-fuel combustion

Starting from a reference and comprehensive chemical mechanism for alkali metal emissions (Glarborg and Marshall, 2005), combined with an hydrocarbon oxidation described with a skeleton mechanism (Kazakov and Frenklach, 1994), reduced and optimized chemical kinetics are derived. The objective is to provide a set of chemical schemes useful for three-dimensional (3D) numerical simulations of alkali metal emissions by pulverized solid-fuel combustion systems. An automated procedure relying on one-dimensional (1D) premixed flames is applied to obtain a combined reduced mechanism, whose performance is then evaluated in one-dimensional strained diffusion flames, micro-mixing based canonical problems and three-dimensional carrier-phase direct numerical simulation (DNS) of coal combustion. Predictions of the reduced mechanism on major sodium species, i.e., Na, NaOH, NaCl and Na2SO4 agree well with that of the detail reference scheme under all the considered conditions. A parametric study with 14 two-dimensional (2D) DNS cases is then performed to better understand the reactive flow properties and estimate the prediction capabilities of the reduced mechanism for various Na/Cl/S ratio in the volatiles. After pursuing the chemistry reduction, a global sodium mechanism with only 9 species and 8 reaction-steps is also discussed. The systematic comparison between the 3D DNS results obtained with the reference chemical scheme against those with the reduced ones confirm the validity of the reduction strategy. A reduction of up to 84% in computational cost is reached with the optimized global scheme, thus allowing for addressing real pulverized-coal combustion systems.

Modeling curvature effects in turbulent autoigniting non-premixed flames using tabulated chemistry

Turbulent flames are intrinsically curved. In the presence of preferential diffusion, curvature effects either enhance or suppress molecular diffusion, depending on the diffusivity of the species and the direction of the flame curvature. When a tabulated chemistry type of modeling is employed, curvature-preferential diffusion interactions have to be taken into consideration in the construction of manifolds. In this study, we employ multistage stage flamelet generated manifolds (MuSt-FGM) method to model autoigniting non-premixed turbulent flames with preferential diffusion effects included. The conditions for the modeled flame are in MILD combustion regime. To model the above-mentioned curvature-preferential diffusion interactions, a new mixture fraction which has a non-unity Lewis number is defined and used as a new control variable in the manifold generation. 1D curved flames are simulated to create the necessary flamelets. The resulting MuSt-FGM tables are used in the simulation of 1D laminar flames, and then also applied to turbulent flames using 2D direct numerical simulations (DNS). It was observed that when the curvature effects are included in the manifold, the MuSt-FGM results agree well with the detailed chemistry results; whereas the results become unsatisfactory when the curvature effects are ignored.

Direct numerical simulation of DME auto-ignition with temperature and composition stratification under HCCI engine conditions

Two-dimensional (2D) direct numerical simulation (DNS) was used to reveal the effect of temperature and composition stratifications on the ignition characteristics of dimethyl-ether (DME)/air mixture at three initial mean temperatures. The simulation was conducted within a constant volume with an isotropic turbulence condition under 40 bar. Nine 2-D cases with temperature stratification (T′), composition stratification (Ф′) and different T-Ф correlations (negative-correlated, uncorrelated, positive-correlated) were performed under the mean initial temperature of T0 = 780 K, 840 K and 1037 K. The results show that the mean heat release rate (HRR) distribution largely depends on T0 when temperature stratification was applied. When T0 = 780 K, T′ can obviously reduce the maximum of mean HRR and prolong combustion duration compared with 0D case. However, the HRR profile is barely changed for T0 = 940 K and 1037 K. Whereas, it was found that composition stratification can reduce the peak value of mean HRR and spread out HRR distribution regardless of initial mean temperature. For first ignition stage, the temperature stratification has larger effect on reducing HRR than composition stratification. Three cases with different T-Ф correlations all reduce the peak value of HRR at first ignition stage. However, for high temperature stage, UC and PC T-Ф field can largely reduce the peak value of HRR and prolong combustion duration while NC T-Ф field shows no visible effect on HRR. In addition, two different combustion modes i.e. flame propagation mode and volumetric auto-ignition mode were distinguished according to HRR contours, budget term and volume averaged temperature gradient. And the mass fraction of YOH+HO2 and YH are the more reasonable choice to track the flame front.

DNS-studies on flame front markers for turbulent premixed combustion

Flame front identification and analysis in premixed turbulent combustion often relies on some scalar iso-surface as a flame marker, and the quest for a suitable scalar, and an appropriate flame-identifying iso-value, then becomes important. In an effort to contribute to this field, we study the suitability of various flame front identification approaches using the concept of ridge analysis. This serves to mark the central region of a given scalar field. In combustion, an essential scalar field is the heat release rate (HRR). Ridge analysis applied to the HRR-field therefore delivers a central region of combustion, which we identify with the flame front. Similar to iso-surfaces, ridges can define sheet-like objects that track the flame front in a given combustion data set. Ridges bear the advantage of being universal, intrinsic flame identifiers, because they do not depend on user-defined parameters like thresholds, iso-values or similar, and they can be applied to premixed as well as to diffusion flames. We determine flame fronts by ridge analysis of the heat release rate field in turbulent premixed combustion data sets obtained by 3D Direct Numerical Simulation (DNS). The suitability of other, iso-surface based flame identifiers is evaluated using the ridge-based, intrinsic flame front as a reference. Iso-surfaces of various scalars (several species and temperature) are compared to the ridges. The study shows that for a methane flame, iso-surfaces of several scalars can serve as good flame front markers, and suitable iso-values for these scalars can be derived from ridge-conditioned statistics. However, different fuel/air mixtures (we study two fuels, hydrogen and methane) exhibit different characteristics. For the hydrogen/air flame, none of the studied scalars was a suitable flame marker. This flame featured ‘holes’ (regions of vanishing chemical heat release). These are correctly detected as non-flame regions by the ridge method, but not by the iso-surfaces of classical flame marker scalars like temperature.

Machine learning for detailed chemistry reduction in DNS of a syngas turbulent oxy-flame with side-wall effects

A novel chemistry reduction strategy based on convolutional neural networks (CNNs) is developed and applied to direct numerical simulation (DNS) of a turbulent non-premixed flame interacting with a cooled wall. The fuel syngas mixture is burning in pure oxygen. The training and the subsequent application of the CNN rely on the processing of two-dimensional (2D) images built from species mass fractions and temperature (CNN input), to predict the corresponding chemical sources at the center of the image (CNN output). This image-type treatment of chemistry is found to efficiently capture intermediate radicals species highly sensitive to the local flame topology. To reduce the CPU cost, a simplified 2D DNS database with detailed chemistry serves as reference and is used for training and testing the neural network. Comparisons are also made a posteriori against the same 2D DNS with a reduced chemical scheme specialized for syngas. Then, three-dimensional (3D) DNS are conducted either with CNN or the reduced chemistry for more a posteriori tests. The CNN reduced chemistry outperforms the reduced Arrhenius based mechanism in the prediction of radical species, such as monoatomic hydrogen, and also in terms of CPU cost.

Transitions in overstable rotating magnetoconvection.

The classical Rayleigh-Bénard convection (RBC) system is known to exhibit either subcritical or supercritical transition to convection in the presence or absence of rotation and/or magnetic field. However, the simultaneous exhibition of subcritical and supercritical branches of convection in plane layer RBC depending on the initial conditions, to the best of our knowledge, has not been reported so far. Here, we report the phenomenon of simultaneous occurrence of subcritical and supercritical branches of convection in overstable RBC of electrically conducting low Prandtl number fluids (liquid metals) in the presence of an external uniform horizontal magnetic field and rotation about the vertical axis. Extensive three-dimensional (3D) direct numerical simulations (DNS) and low-dimensional modeling of the system, performed in the ranges 750≤Ta≤3000 and 0<Q≤1000 of the Taylor number (Ta, strength of the Coriolis force) and the Chandrasekhar number (Q, strength of the Lorenz force), respectively, establish the phenomenon convincingly. Detailed bifurcation analysis of a simple 3D model derived from the DNS data reveals that a supercritical Hopf bifurcation and a subcritical pitchfork bifurcation of the conduction state are responsible for this. The effect of Prandtl number on these transitions is also explored in detail.

Dynamics of co-rotating vortices in a flow around a bio-inspired corrugated airfoil

Bio-inspired corrugated airfoils show favourable aerodynamic characteristics such as high coefficient of lift and delayed stall at low Reynolds numbers. Two-dimensional (2D) direct numerical simulation has been performed here on a corrugated airfoil at various angles of attack (0°, +5°, -5°) and Reynolds number of 280 to 6700. The objective is to analyse the pressure variation inside the corrugations and correlate it to the vortex movement across the corrugations and the overall aerodynamic characteristics of the corrugated airfoil. The flow characteristics have been examined based on the local Strouhal numbers in the corrugations of the airfoil. It is observed that the pressure variation in each corrugation is the result of vortex merging and separation in the corrugation which plays a major role in changing the flow characteristics. The Strouhal number of the flow is dictated by the most dominant local Strouhal number. The numerical results are further compared with experimental results obtained using particle image velocimetry, and the two set of results are found to match well. These results are significant because they elucidate the effect of corrugation, angle of attack, and Reynolds number on flow over a corrugated airfoil.

Wake events during early three-dimensional transition of a circular cylinder placed in shear flow

Three-dimensional (3D) direct numerical simulations are carried out for shear flows past a circular cylinder in the early 2D (two-dimensional)–3D transition regime. The effect of incoming shear is buried in a source term employing a velocity transformation. Wake transition events are inspected for both planar and span-wise shear flows. Parallel, time-mean-symmetric shedding for planar shear and oblique vortex shedding for span-wise shear are observed with a near wake roll-up vortical structure. Vortex splits and dislocations are found without any order in time for moderate shear, while they give way to visibly higher levels of instabilities at higher shear rates. Mode “B” instabilities are noted for planar shear, while opposite streamwise vortices align in parallel horizontal layers for span-wise shear. Local Strouhal frequency (Stz) drops inside a span-wise cell for span-wise shear with finite jumps across cell boundaries. Wavelet multiresolution analysis indicates a strong flushing effect, triggered by vortex dislocations, which gives rise to a new frequency event. The dominant span-wise mode indicates periodic forcing of mode “A” instabilities at a rate close to the inverse of local Strouhal number. In contrast, the streamwise velocity modes result in a global span-wise similarity. Intrinsic secondary instabilities play a vital role in span-wise shear cases. The addition of planar shear makes the downstream defect layer nearly span-wise-invariant. However, the velocity defect is entirely controlled by the span-wise shear. The momentum thickness exhibits streamwise growth, similar to the Blasius profile. The shape factor of such profiles indicates a delay in laminar–turbulent transition for span-wise shear.

Direct numerical simulation of a spatially developing n-dodecane jet flame under Spray A thermochemical conditions: Flame structure and stabilisation mechanism

We present results from a three-dimensional (3D) direct numerical simulation (DNS) of a spatially developing n-dodecane round jet flame. The thermochemical conditions (i.e. pressure, temperature and oxidiser composition) correspond to those of Spray A, an experimental target flame of the Engine Combustion Network (ECN). To make the DNS computationally tractable, we consider a gas jet with a reduced Reynolds number of 17,000 and a shorter lifted length of 11 times the jet diameter. The flame structure and stabilisation mechanism of the statistically steady jet flame are discussed. Overall the flame structure is similar to that identified from experimental observations, i.e. a region of high formaldehyde (CH2O) concentration, which marks the low-temperature chemistry (LTC), is present upstream of the main flame and persists downstream in the central region of the jet where the mixture is rich. A high-temperature (HTC) nonpremixed flame marked by OH radicals shrouds the jet. Ignition kernels are observed upstream of the flame base, some of which are convected downstream and join with the main flame. At the flame base, a three-branch structure is observed, namely an LTC branch upstream of the flame, a rich HTC branch attached to the flame base and a trailing nonpremixed flame anchored at the stoichiometric mixture fraction. A detailed analysis of the flame stabilisation mechanism is reported, employing structural comparisons to two-dimensional (2D) reference cases, transport budgets, and flame speeds. It is concluded from these analyses that the flame is stabilised principally by flame propagation. The role of autoignition kernels is also analysed and found to be secondary.

Evaluation of electrostatic properties of electret filters for aerosol deposition

Electret filter media are nonwovens with electrostatically charged fibers and are commonly applied for separation of fine particles from gases. However, the distribution of the electrostatic charge on the fiber surfaces – which dependens on the applied charging method – could not be completely clarified so far. The aim of this work is to determine the amount of electrostatic charge and its distribution in the porous structure of the nonwoven by comparison of experiments and 3D DirectNumerical Simulations coupling the gas flow and electrostatic field to the particle movement.As example, corona and triboelectrically charged filter media were investigated. The charge distributions on the fibrous structure were estimated by comparison of the numerically and experimentally obtained fractional deposition efficiencies. Furthermore, the simulations showed that different charge distributions led to significant differences in the fractional deposition efficiency up to 15%, even if the amount of charge and the area ratio of positive and negative charges were constant.

Assessment of Tabulated Premixed Conditional Moment Closure Model Using Direct Numerical Simulation

ABSTRACT The Conditional Moment Closure (CMC) is a proven methodology to model non-premixed flames, but an emerging technique for analyzing turbulent premixed flames. However, solving a full set of CMC equations is a time-consuming process. The Tabulated Premixed CMC (TPCMC) model is a modification of the premixed CMC model that seeks to reduce the time consumed in solving equations by making the premixed CMC model amenable to the tabulation of chemistry. TPCMC model considers the effect of small scale mixing of reactants and products using the scalar dissipation rate and effect of large scale turbulence on the flame using the beta probability density function. The validation of TPCMC model using Direct Numerical Simulation (DNS) data has been attempted in this paper. DNS of growth of an ignition kernel in a turbulent medium was performed for this purpose. Two sets of simulations, namely 3D DNS with three-step reduced chemistry and 2D DNS with multi-step chemistry, have been carried out in this study using PENCIL code. The Favre averaging of this DNS data was performed on the surfaces of constant radius to assess the accuracy of TPCMC model. The variations in turbulence intensity and integral length scale were considered to generate DNS database. TPCMC model accurately predicted the variation of fuel mass fraction and temperature for all the cases considered in this study and captured the qualitative trends in the CO mass fraction where a negligible deviation from the actual values was observed. The influence of initial parameters related to turbulence considered in this study was negligible on the accuracy of predictions obtained from the model.

Rayleigh–Taylor unstable flames at higher Reynolds number

ABSTRACT Rayleigh–Taylor (RT) unstable flames are a key component of Type Ia and Iax supernovae explosions, but their complex hydrodynamics is still not well understood. These flames are affected not only by the RT instability, but also by the turbulence it generates. Both processes can increase the flame speed by stretching and wrinkling the flame. This makes it hard to choose a subgrid model for the flame speed in full star Type Ia or Iax simulations. Commonly used subgrid models get around this difficulty by assuming that either the RT instability or turbulence is dominant and sets the flame speed. In previous work, we evaluated the physical assumptions and predictive abilities of these two types of models by analysing a large parameter study of 3D direct numerical simulations of RT unstable flames. Surprisingly, we found that the flame dynamics is dominated by the RT instability and that RT unstable flames are very different from turbulent flames. In particular, RT unstable flames are thinner rather than thicker when turbulence is strong. In addition, none of the turbulent flame speed models adequately predicted the flame speed. We also showed that the RT flame speed model failed when the RT instability was strong, suggesting that geometrical burning effects also influence the flame speed. However, these results depended on simulations with Re ≲ 720. In this paper, we extend the parameter study to higher Reynolds number and show that the basic conclusions of our previous study still hold when the RT-generated turbulence is stronger.

Upscaled model for diffusion and serial reduction pathways in porous ​electrodes

Multiscale modelling of coupled diffusion and serial reduction reactions in porous micro-electrodes is developed in this work. The governing coupled equations at the pore scale in the case of two reduction reactions, as for instance, the serial reaction pathway for oxygen reduction to hydrogen peroxide and subsequently to water, are upscaled to obtain a macroscopic model describing the process in an effective medium at the electrode scale. This new macroscopic model, obtained from the volume averaging technique, is validated through comparisons with results of 3D Direct Numerical Simulations of the pore-scale model. The excellent agreement between the two approaches proves the relevance of the macroscale model which reduces to a 1D problem in the configuration under concern, providing a drastic speedup in the computation of the solution. Numerical results obtained with the macroscopic model are successfully compared to experimental data obtained by voltammetry with porous gold electrodes of different thicknesses operating the serial pathway of oxygen reduction to water. Results highlight the ability of this new macroscopic model to predict the electrode behavior and show that the second reduction reaction of hydrogen peroxide plays an important role in the current production.

Structure of strongly turbulent premixed n-dodecane–air flames: Direct numerical simulations and chemical explosive mode analysis

Structure of strongly turbulent premixed n-dodecane/air flames with high Karlovitz numbers (Ka) is studied based on three-dimensional (3D) direct numerical simulation (DNS) datasets. Heat release and fuel consumption rates in these flames are observed to be enhanced compared to what can be conventionally described as increases in flame surface area. To explain the cause for the burning rate enhancement, temperature and species mass fractions are first investigated to reveal the overall flame structure. The chemical explosive mode analysis (CEMA) is then employed to identify local combustion modes, including local assisted ignition, auto-ignition, and extinction, each of which is found to play a role in the overall burning rates. The spatial distribution of the local modes is found to be drastically different from that in comparable laminar flames where the local extinction mode is mostly absent. For the high-Ka cases (Ka = 103 and 104), the extinction mode is shown to be comparable to or more important than the auto-ignition mode for heat release and fuel consumption rates. In contrast, the auto-ignition mode plays a more important role in heat release than the extinction mode in laminar and the relatively low-Ka flames (Ka = 102). In addition, two types of mixture pockets are identified by CEMA: pockets of reactants in bulk products and pockets of hot products in bulk reactants. The dynamics of these pockets are strongly affected by the local modes of the spatially adjacent mixtures. While the pockets of reactants in bulk products are almost always consumed by auto-ignition and/or inward flame propagation, the pockets of products in bulk reactants may either grow themselves due to outward flame propagation or contract volumetrically due to local extinction. In contrast to the conventional understanding, local extinction can promote the overall burning process, as it enables mixing of the radicals and sensible energy from the product pockets into the surrounding reactants, thus facilitating their ignition. Clearly, such effects must be considered in order to closely model these flames.

Close Nozzle Spray Characteristics of a Prefilming Airblast Atomizer

The formation of pollutant emissions in jet engines is closely related to the fuel distribution inside the combustor. Hence, the characteristics of the spray formed during primary breakup are of major importance for an accurate prediction of the pollutant emissions. Currently, an Euler–Lagrangian approach for droplet transport in combination with combustion and pollutant formation models is used to predict the pollutant emissions. The missing element for predicting these emissions more accurately is well defined starting conditions for the liquid fuel droplets as they emerge from the fuel nozzle. Recently, it was demonstrated that the primary breakup can be predicted from first principles by the Lagrangian, mesh-free, Smoothed Particle Hydrodynamics (SPH) method. In the present work, 2D Direct Numerical Simulations (DNS) of a planar prefilming airblast atomizer using the SPH method are presented, which capture most of the breakup phenomena known from experiments. Strong links between the ligament breakup and the resulting spray in terms of droplet size, trajectory and velocity are demonstrated. The SPH predictions at elevated pressure conditions resemble quite well the effects observed in experiments. Significant interdependencies between droplet diameter, position and velocity are observed. This encourages to employ such multidimensional interdependence relations as a base for the development of primary atomization models.

Analytical and numerical study of Soret mixed convection in two sided lid-driven horizontal cavity: Optimal species separation

The coupling between shear-driven convection and thermo-diffusion is a complex phenomenon due to the interactions between the different forces inside the fluid mixture. This paper studies the species separation that may appear in a parallelepipedic cell filled by a binary mixture. Dirichlet boundary conditions are imposed with differentially heated horizontal walls. Each wall can be animated with a uniform velocity. More precisely, two velocities UPex→,andfUPex→ are applied at the upper and the lower horizontal walls respectively. An analytical solution, based on the parallel flow approximation in the core region of the cavity of large aspect ratio, is obtained as a function of the dimensionless parameters of the problem. The species separation is optimized according to the multiple control parameters of the problem. The velocity field obtained is the superposition of the flow generated by the velocity of the walls under weightless conditions and thermoconvective flow under gravity only. The combination of these two flows leads to a mixed convection flow with a single convective cell for f∈-1,0 and two superposed cells for f∈0,1. Only unicellular flow leads to a notable species separation. This study shows that the effective species separation admits a partial optimum as a function of f and Up. As in the case of thermogravitational columns, there is no optimum species separation with respect to parameters ΔT and H but, for a fixed temperature difference ΔT, there is a thickness H that optimizes the separation and vice versa. 2D and 3D direct numerical simulations are performed using a finite element method in order to corroborate the analytical results. The influence of mass Péclet number on the diffusive relaxation time is determined numerically. Taking into account the confinement of the medium in the third dimension, perpendicular to a vertical plane, we show that the aspect ratio in the y-direction has an influence on the species separation.

A fast multi-layer boundary element method for direct numerical simulation of sound propagation in shallow water environments

Direct three-dimensional (3D) numerical simulations of acoustic fields in range-dependent shallow water environments remains a challenge due to environmental complexities and large computational cost. We develop an efficient 3D boundary element method (BEM) to solve the Helmholtz equation for shallow water acoustic propagation, which utilizes a Pre-corrected Fast Fourier Transform (PFFT) approach to reduce the computational effort from O(N2∼3) to O(Nlog⁡N) where N is the total number of boundary unknowns. To account for inhomogeneous media, the method allows for arbitrary number of coupled multi-layer BEM sub-domains. With O(Nlog⁡N) efficiency and the use of massively parallel high-performance computing platforms, we are able to conduct multi-layer 3D direct numerical simulations of low-mid frequency acoustics over kilometer ranges. We perform extensive validations of the method and provide two shallow water waveguide examples benchmarked against theoretical solutions. To illustrate the efficacy and usefulness of the PFFT-BEM method, we perform 3D large-scale direct numerical simulations to assess the performance of two established canonical models: axisymmetric coupled mode model for 3D seamount; and Kirchhoff approximation and perturbation theory for 3D rough surface scattering.