Numerical Diffusion Research Articles

Kinetically Consistent Data Assimilation for Plant PET Sparse Time Activity Curve Signals

Time activity curve (TAC) signal processing in plant positron emission tomography (PET) is a frontier nuclear science technique to bring out the quantitative fluid dynamic (FD) flow parameters of the plant vascular system and generate knowledge on crops and their sustainable management, facing the accelerating global climate change. The sparse space-time sampling of the TAC signal impairs the extraction of the FD variables, which can be determined only as averaged values with existing techniques. A data-driven approach based on a reliable FD model has never been formulated. A novel sparse data assimilation digital signal processing method is proposed, with the unique capability of a direct computation of the dynamic evolution of noise correlations between estimated and measured variables, by taking into explicit account the numerical diffusion due to the sparse sampling. The sequential time-stepping procedure estimates the spatial profile of the velocity, the diffusion coefficient and the compartmental exchange rates along the plant stem from the TAC signals. To illustrate the performance of the method, we report an example of the measurement of transport mechanisms in zucchini sprouts.

A Predictor–corrector scheme for simulation of two-phase granular flows over a moved bed with a variable topography

In this paper, we propose a numerical simulation of two-phase shallow granular flows through a moved bed with a variable irregular topography via a predictor corrector scheme. This method consists of predictor and corrector stages. The predictor stage contains a parameter to control the numerical diffusion that is performed by utilizing limiters and Riemann invariant theory. The corrector stage recovers the balance conservation equation. In the first part, we solve numerically the one-dimensional equation for two-phase shallow granular flows over a fixed bed with irregular topography. In the second part, we consider the model equations for the bed-load sediment transport, the governing model equations consist of two components, specifically, a geophysical flows part and interstitial fluid. The sediment part is described by the Exner equation when the velocity can be considered to be the solid velocity, fluid velocity or a mean value of both of them.

Breaking wave simulations for a high-speed surface vessel with hybrid THINC and HRIC schemes

To simulate the ship-induced breaking waves with high-accuracy VOF (volume of fluid) schemes, the unstructured THINC (tangent of hyperbola for interface capturing) type scheme was selected as the main interface capturing method.Particularly, an extension version of THINC/QQ (THINC method with quadratic surface representation and Gaussian quadrature), namely THINC/QQ-SF (THINC/QQ extended for split-face unstructured cells) was used. The computational domain was discretized by the trimmed meshes of STAR-CCM+. The mesh cells were categorized into three groups, including regular unstructured (i.e. hexahedral, tetrahedral, prismatic and pyramidal) cells, split-face unstructured cells and polyhedral cells. THINC/QQ-SF was applied for the first two cell groups, which take up most of the space. The algebraic VOF scheme of HRIC (high-resolution interface capturing) which has the advantage of algorithm simplicity, was implemented for the third cell group. To validate the performance of THINC/QQ-SF and HRIC, a series of testing meshes were designed for the pure VOF advection cases. Additionally, the geometric VOF scheme of isoAdvector was also involved for comparisons. In terms of the accuracy, THINC/QQ-SF is similar with isoAdvector, both of which are much better than HRIC. For the efficiency, both THINC/QQ-SF and HRIC have obvious advantages over isoAdvector under the present conditions. Then, the hull form of DTMB (David Taylor model basin) 5415 was chosen for testing, under the Froude number of 0.35. By using the combination of THINC/QQ-SF and HRIC (i.e. THINC/QQ-SF & HRIC), the compactness of the interface can be maintained. Besides, the wave elevations are well agreed with the published experiment. For the averaged calm-water resistance, the present strategy can obtain more accurate results with fewer (or much fewer) cells, compared with the previous CFD studies. To better show the advantages of the hybrid method, the simulations with pure HRIC were also conducted. Compared with pure HRIC, THINC/QQ-SF & HRIC can better capture the wave breaking details with less numerical diffusion, and the reliability of the resistance prediction is higher.

Comparison of Lagrangian Superdroplet and Eulerian Double-Moment Spectral Microphysics Schemes in Large-Eddy Simulations of an Isolated Cumulus Congestus Cloud

Abstract Advanced microphysics schemes (such as Eulerian bin and Lagrangian superdroplet) are becoming standard tools for cloud physics research and parameterization development. This study compares a double-moment bin scheme and a Lagrangian superdroplet scheme via large-eddy simulations of nonprecipitating and precipitating cumulus congestus clouds. Cloud water mixing ratio in the bin simulations is reduced compared to the Lagrangian simulations in the upper part of the cloud, likely from numerical diffusion, which is absent in the Lagrangian approach. Greater diffusion in the bin simulations is compensated by more secondary droplet activation (activation above cloud base), leading to similar or somewhat higher droplet number concentrations and smaller mean droplet radius than the Lagrangian simulations for the nonprecipitating case. The bin scheme also produces a significantly larger standard deviation of droplet radius than the superdroplet method, likely due to diffusion associated with the vertical advection of bin variables. However, the spectral width in the bin simulations is insensitive to the grid spacing between 50 and 100 m, suggesting other mechanisms may be compensating for diffusion as the grid spacing is modified. For the precipitating case, larger spectral width in the bin simulations initiates rain earlier and enhances rain development in a positive feedback loop. However, with time, rain formation in the superdroplet simulations catches up to the bin simulations. Offline calculations using the same drop size distributions in both schemes show that the different numerical methods for treating collision–coalescence also contribute to differences in rain formation. The stochastic collision–coalescence in the superdroplet method introduces more variability in drop growth for a given rain mixing ratio.

Sustainable synthesis and theoretical studies of polyhedral gold nanoparticles displaying high SERS activity, NIR absorption, and cellular uptake

The preparation of gold nanoparticles with multimodal properties such as near-infrared absorption, high surface-enhanced Raman scattering, cell internalization and low cytotoxicity is a challenging task. In this study, we developed a sustainable protocol to develop gold nanoparticles, using trisodium citrate as reducing, stabilizing, and shape-modulating agent at ambient conditions (25 °C). Reduction of gold salt at room temperature at a peculiar ratio R(Ccitrate/CHAuCl4) and concentration of reactants resulted in the formation of non-spherical, homogenous mixture of gold nanoparticles with polyhedral shapes. The protocol is extremely simple and does not even require stirring or mechanical shaking. The as-synthesized gold nanoparticles, even though multi-shaped, displayed a single monomodal peak in dynamic light scattering with polydispersity index of 0.098, representative of a fairly good monodisperse system. We investigated the optical properties of the nanoparticles both experimentally and by two-dimensional Finite-Difference-Time-Domain modeling. Due to the presence of shapes such as nanorods, nanotriangles, and prismatic, these nanoparticles exhibited a high surface-enhanced Raman scattering activity and a wide absorption range extending up to the near-infrared region, which makes them useful candidate for photothermal therapy too. We characterized the nanoparticles by electron microscopy, UV–vis–NIR spectroscopy, Raman spectroscopy, and X-ray photoelectron spectroscopy. We have also developed an enhanced numerical diffusion limited aggregation model to simulate the growth of the particles, including the particle interfacial energy as a parameter of the system. Numerical results matched with the experimental data, and the model revealed being effective in reproducing size, shape, and morphological characteristics of non-spherical nanoparticles obtained under real experimental conditions. Finally, in vitro studies and nanoparticles cellular uptake were performed on a model cell line of mouse brain endothelium (bEnd.3) to assess biocompatibility. The main advantage of the proposed method lies in its simplicity with no other requirement like refluxing at elevated temperature, mechanical stirring, electromagnetic radiations, ultrasound, toxic chemicals, or seed mediation.

A simplified and efficient weakly-compressible FV-WENO scheme for immiscible two-phase flows

The present paper proposes a simplified and efficient FV-WENO scheme for simulating weakly-compressible multi-phase flows. Comparing with a classic FV-WENO scheme, the computational accuracy and efficiency are improved by two choices: (i) reconstructing the primitive variables instead of the conservative ones; (ii) performing the WENO reconstruction only once per direction. Although these choices lead to a formally 2nd-order accurate scheme, it is still different from conventional 2nd-order schemes and can be expected to provide higher-order accuracies far from interfaces. An HLLC-type Riemann flux solver is proposed, which appears to be more robust than the linearized Riemann flux solver, allowing the use of smaller artificial sound speeds. The proposed scheme is proven to have the oscillation-free property in the advection of isolated interfaces. A series of validation test-cases have been carried out, in which a good agreement can be observed with references. It is shown that the proposed scheme can give accurate results with little numerical diffusion in the simulations involving weakly-compressible multi-phase flows.

A Coupled Evaluation of Operational MODIS and Model Aerosol Products for Maritime Environments Using Sun Photometry: Evaluation of the Fine and Coarse Mode

Although satellite retrievals and data assimilation have progressed to where there is a good skill for monitoring maritime Aerosol Optical Depth (AOD), there remains uncertainty in achieving further degrees of freedom, such as distinguishing fine and coarse mode dominated species in maritime environments (e.g., coarse mode sea salt and dust versus fine mode terrestrial anthropogenic emissions, biomass burning, and maritime secondary production). For the years 2016 through 2019, we performed an analysis of 550 nm total AOD550, fine mode AOD (FAOD550; also known as FM AOD in the literature), coarse mode AOD (CAOD550), and fine mode fraction (η550) between Moderate Resolution Spectral Imaging Radiometer (MODIS) V6.1 MOD/MYD04 dark target aerosol retrievals and the International Cooperative for Aerosol Prediction (ICAP) core four multi-model consensus (C4C) of analyses/short term forecasts that assimilate total MODIS AOD550. Differences were adjudicated by the global shipboard Maritime Aerosol Network (MAN) and selected island AERONET sun photometer observations with the application of the spectral deconvolution algorithm (SDA). Through a series of conditional and regional analyses, we found divergence included regions of terrestrial influence and latitudinal dependencies in the remote oceans. Notably, MODIS and the C4C and its members, while having good correlations overall, have a persistent +0.04 to +0.02 biases relative to MAN and AERONET for typical AOD550 values (84th% < 0.28), with the C4C underestimating significant events thereafter. Second, high biases in AOD550 are largely associated with the attribution of the fine mode in satellites and models alike. Thus, both MODIS and C4C members are systematically overestimating AOD550 and FAOD550 but perform better in characterizing the CAOD550. Third, for MODIS, findings are consistent with previous reports of a high bias in the retrieved Ångström Exponent, and we diagnosed both the optical model and cloud masking as likely causal factors for the AOD550 and FAOD550 high bias, whereas for the C4C, it is likely from secondary overproduction and perhaps numerical diffusion. Fourth, while there is no wind-speed-dependent bias for surface winds <12 m s−1, the C4C and MODIS AOD550s also overestimate CAOD550 and FAOD550, respectively, for wind speeds above 12 m/s. Finally, sampling bias inherent in MAN, as well as other circumstantial evidence, suggests biases in MODIS are likely even larger than what was diagnosed here. We conclude with a discussion on how MODIS and the C4C products have their own strengths and challenges for a given climate application and discuss needed research.

High resolution adaptive implicit method for reactive transport in heterogeneous porous media

The Adaptive Implicit Method (AIM) reduces the computational cost related to simulations of field scale displacements in porous media. Standard AIM uses a mixed implicit/explicit time discretization that overcomes the time step size limitations of purely explicit approaches and considers single-point upwinding to approximate both the implicit and explicit numerical fluxes. Use of high-order fluxes improves accuracy but leads to increased stencil size and more complex Jacobians in the implicit regions. To reduce numerical diffusion and improve the accuracy of AIM while avoiding the larger stencils and nonlinearities introduced by an implicit treatment of high-order schemes, we introduce a scheme that in addition to blending implicit and explicit time discretizations, deliberately blends single-point upwind and a high-order flux-limited total variation diminishing approximation of the numerical fluxes. The proposed scheme does not interfere with the discretization of the implicit terms and the structure of the matrices that need to be solved is the same of standard AIM, making the scheme easy to apply in existing simulators. The details of the scheme are presented and it is applied to single-phase reactive transport problems in 1-, 2-, and 3-dimensions with simple homogeneous decay reactions, mixing-limited reactions, and the calcium carbonate system. For mixing-limited reactions, that are highly sensitive to numerical diffusion, accurate results depend on properly representing the sharp reactive fronts and a strategy to avoid an implicit treatment inside the reactive fronts is presented. The numerical results indicate significant gains in accuracy at the additional expense of slightly more involved flux computations in the explicit regions, that represent a small fraction of the total CPU cost.

Air injection in vertical water column: Experimental test and numerical simulation using volume of fluid and two-fluid methods

• VOF model was used to reproduce the interaction of two fluids in an experiment. • Eulerian model was used to reproduce the interaction of two fluids in an experiment. • Comparisons of numerical results using VOF and Eulerian model were made. • Results of different models based on VOF were compared with the traditional VOF. • The effect of turbulence was studied with different RANS turbulence models. A novel test consisting on fast air injection into a vertical water column was experimentally and numerically studied. Measurements were focused on capturing the air–water interface as well as the volume of water evicted by the air, for a wide range of air flow rates. The numerical simulations, were performed with the Eulerian Two-Fluid (TF) and the Volume of Fluid (VOF) methods.For the TF method three topologies were considered: bubbly flow, dropUNR Universidad Nacional de Rosario flow, and blending. The last is a more smart methodology to automatically handle with the different flow regimes. For the VOF method, the standar VOF (SVOF), the Adaptive Mesh Refinement (AMR), and the high order Piecewise Linear Interface Calculation (PLIC) methods were assessed. SVOF and TF blending methods were choice to study the mesh convergence and turbulence modeling. Two-dimensional (2D) meshes of 2, 1 and 0.5 mm, and three-dimensional (3D) meshes of 2, 1 and 0.75 mm were considered. In all cases the standard VOF (SVOF) formulation showed mesh convergence and good agreement with experiments. The error for the finest 3D mesh was around 1 % , but increased up to 20% for the finest 2D mesh. On the other hand, for the TF method mesh convergence was only evidenced for the 2D meshes. Regard the TF method, the bubbly and drop topology cases led to unacceptable solutions both in terms of inteface capturing as well as liquid evicted. On the other hand, the blending methodology clearly improved the estimations, although the interface was only partially captured because of the numerical diffusion. On the other hand, all the VOF methods were in relative good agreement both in terms of the liquid evicted as well as interface capturing. Errors were were reduced by refining the mesh. The initial swelling, with small bubbles and large slugs around the air injector was well captured, and the ligaments and drops spilled for high air flow rates were quite well estimated. The SVOF method showed low computational cost for coarse grids, but the computing time increased more than linearly with the mesh size. The AMR method showed accurate solutions, but the computing cost was largely increased with the refining level. Finally, the use of PLIC method for the coarser mesh reduced the error from 15% (SVOF) to 3.5% keeping low the computing cost.

An enthalpy-based cascaded lattice Boltzmann method for solid-liquid phase-change heat transfer

• The CLB method is extended to simulate solid-liquid phase-change problems. • The unphysical numerical diffusion can be effectively eliminated by the CLB method. • The CLB method can achieve better numerical stability due to the enhanced Galilean invariance. In this paper, a cascaded lattice Boltzmann (CLB) method for investigating solid-liquid phase-change heat transfer is developed. In the CLB method, the enthalpy methodology is adopted to capture the solid-liquid phase interface implicitly. Mesoscopically, the enthalpy is defined as the basic evolution variable of the CLB equation of the temperature field so as to consider the phase-change effect in simulations without iteration procedure, and to achieve this purpose, the cascaded collision process is artfully designed by modifying the shifting procedure. Numerical results demonstrate that the enthalpy-based CLB method can serve as an accurate and reliable numerical tool for simulating solid-liquid phase-change heat transfer.

The modified Rusanov scheme for solving the phonon-Bose model

Abstract This paper considers the one-dimensional model of heat conduction in solids at low temperature, the so called phonon-Bose model. The nonlinear model consists of a conservation equation for the energy density e and the heat flux Q with ∣Q∣ < e. We present a simple and accurate class of finite volume schemes for numerical simulation of heat flow in arteries. This scheme consists of predictor and corrector steps, the predictor step contains a parameter of control of the numerical diffusion of the scheme, which modulate by using limiter theory and Riemann invariant, the corrector step recovers the balance conservation equation, the scheme can compute the numerical flux corresponding the real state of solution without relying on Riemann problem solvers and it can thus be turned to order 1 in the regions where the flow has a strong variation and to order 2 in the regions where the flow is regular. The numerical test cases demonstrate high resolution of the proposed finite volume scheme (modified Rusanov) and confirm its capability to provide accurate simulations for heat flow under flow regimes with strong shocks.

Global spectral analysis of the Lax–Wendroff-central difference scheme applied to Convection–Diffusion equation

In this work, the Global Spectral Analysis (GSA) is applied to the convective Lax–Wendroff based discretization of linear convection–diffusion problem in both 1D and 2D. Contrary to standard numerical analysis approaches, two important physical processes (convection and diffusion) are treated together, thus making GSA a function of multiple non-dimensional numerical parameters, namely, the non-dimensional wavenumber (kh), the Courant–Friedrich–Lewy number (Nc) and the Peclet number (Pe). All the three quantities impact the stability of the numerical scheme by affecting both numerical amplification factor as well as numerical diffusion. Likewise, numerical phase speed and numerical group velocity all become expressions of all three non-dimensional parameters. Leveraging the GSA, an accurate map (property charts) of acceptable range of parameter space is evidenced to obtain the spatio-temporal numerical solution that is stable as well as Dispersion Relation Preserving (DRP). The numerical property charts are shown to be useful to calibrate numerical solutions of both 1D and the 2D convection–diffusion equations on uniform meshes. Finally, as demonstrated while solving the Navier–Stokes equation for a Taylor–Green vortex problem, property charts allow to explain numerical behaviors often observed with real complex flow problems.

Numerical Investigation of 3D Flow Properties around Finite Emergent Vegetation by Using the Two-Phase Volume of Fluid (VOF) Modeling Technique

This study predicts how the Free Surface Level (FSL) variations around finite length vegetation affect flow structure by using a numerical simulation. The volume of fluid (VOF) technique with the Reynolds stress model (RSM) was used for the simulation. Multizone Hexahedral meshing was adopted to accurately track the free surface level with minimum numerical diffusion at the water–air interface. After the validation, finite length emergent vegetation patches were selected based on the aspect ratio (AR = vegetation width-length ratio) under constant subcritical flow conditions for an inland tsunami flow. The results showed that the generation of large vortices was predominated in wider vegetation patches (AR > 1) due to the increase and decrease in the FSL at the front and back of the vegetation compared to longer vegetation patches (AR ≤ 1), as this offered more resistance against the approaching flow. The wider vegetation patches (AR > 1) are favorable in terms of generating a large area of low velocity compared to the longer vegetation patch (AR < 1) directly downstream of the vegetation patch. On the other hand, it has a negative impact on the adjacent downstream gap region, where a 14.3–34.9% increase in velocity was observed. The longer vegetation patches (AR < 1) generate optimal conditions within the vegetation region due to great velocity reduction. Moreover, in all the AR vegetation cases, the water turbulent intensity was maximum in the vegetation region compared to the adjacent gap region and air turbulent intensity above the FSL, suggesting strong air entrainment over this region. The results of this study are important in constructing vegetation layouts based on the AR of the vegetation for tsunami mitigation.

On numerical broadening of particle-size spectra: a condensational growth study using PyMPDATA 1.0

Abstract. This work discusses the numerical aspects of representing the condensational growth of particles in models of aerosol systems such as atmospheric clouds. It focuses on the Eulerian modelling approach, in which fixed-bin discretisation is used for the probability density function describing the particle-size spectrum. Numerical diffusion is inherent to the employment of the fixed-bin discretisation for solving the arising transport problem (advection equation describing size spectrum evolution). The focus of this work is on a technique for reducing the numerical diffusion in solutions based on the upwind scheme: the multidimensional positive definite advection transport algorithm (MPDATA). Several MPDATA variants are explored including infinite-gauge, non-oscillatory, third-order terms and recursive antidiffusive correction (double-pass donor cell, DPDC) options. Methodologies for handling coordinate transformations associated with both particle-size spectrum coordinate choice and with numerical grid layout choice are expounded. Analysis of the performance of the scheme for different discretisation parameters and different settings of the algorithm is performed using (i) an analytically solvable box-model test case and (ii) the single-column kinematic driver (“KiD”) test case in which the size-spectral advection due to condensation is solved simultaneously with the advection in the vertical spatial coordinate, and in which the supersaturation evolution is coupled with the droplet growth through water mass budget. The box-model problem covers size-spectral dynamics only; no spatial dimension is considered. The single-column test case involves a numerical solution of a two-dimensional advection problem (spectral and spatial dimensions). The discussion presented in the paper covers size-spectral, spatial and temporal convergence as well as computational cost, conservativeness and quantification of the numerical broadening of the particle-size spectrum. The box-model simulations demonstrate that, compared with upwind solutions, even a 10-fold decrease in the spurious numerical spectral broadening can be obtained by an apt choice of the MPDATA variant (maintaining the same spatial and temporal resolution), yet at an increased computational cost. Analyses using the single-column test case reveal that the width of the droplet size spectrum is affected by numerical diffusion pertinent to both spatial and spectral advection. Application of even a single corrective iteration of MPDATA robustly decreases the relative dispersion of the droplet spectrum, roughly by a factor of 2 at the levels of maximal liquid water content. Presented simulations are carried out using PyMPDATA – a new open-source Python implementation of MPDATA based on the Numba just-in-time compilation infrastructure.

Doubly Monotonic Constraint on Interpolators: Bridging Second-Order to Singularity Preservation to Cancel “Numerical Wetting” in Transport Schemes

Monotonic interpolation and its avatars are major ingredients of many numerical schemes for solving partial differential equations (PDEs) under total variation diminishing (TVD) or similar constraints. However, despite over forty years of extensive study of principles and applications, a key aspect of monotonic interpolant design can still appear somewhat empirical: how does a monotonic interpolator connect the limiting cases of smooth (differentiable) and singular (limited) functions in a consistent and possibly canonical way? The present study aims at providing understanding in the basic but important case of per-cell monotonic one-dimensional scalar reconstruction and at applying it to second-order accurate transport. First, a general mapping of bounded monotonic functions in elliptic coordinates is built. Then, the usual “single-slope” second-order monotonic interpolants are continued into “slope-and-bound” monotonic interpolants. Finally, a critical constraint is introduced, the “double monotonicity,” in order to build various slope-and-bound monotonic interpolators from this set of interpolants. With these slope-and-bound interpolators, standard numerical tests show a complete cancellation of the “numerical wetting” that usual TVD transport schemes produce. When transporting scalar fields of compact support, this effect---not to be confused with usual numerical diffusion---is the low-level contamination that spreads linearly in time over all the regions of the computational domain where nonvanishing transport is present. Removal of numerical wetting is of particular importance in many industrial and academic applications, notably at “phase disappearance” episodes in multiphase flows or “wet-dry” transitions in shallow water flows. Improvement of the “numerical erosion” of extrema is also observed. The general principles exposed here can be extended to multidimensional settings, high-order schemes, and other PDEs.

Large‐Eddy Simulations of a Convection Cloud Chamber: Sensitivity to Bin Microphysics and Advection

AbstractBin microphysics schemes are useful tools for cloud simulations and are often considered to provide a benchmark for model intercomparison. However, they may experience issues with numerical diffusion, which are not well quantified, and the transport of hydrometeors depends on the choice of advection scheme, which can also change cloud simulation results. Here, an atmospheric large‐eddy simulation model is adapted to simulate a statistically steady‐state cloud in a convection cloud chamber under well‐constrained conditions. Two bin microphysics schemes, a spectral bin method and the method of moments, as well as several advection methods for the transport of the microphysical variables are employed for model intercomparison. Results show that different combinations of microphysics and advection schemes can lead to considerable differences in simulated cloud properties, such as cloud droplet number concentration. We find that simulations using the advection scheme that suffers more from numerical diffusion tends to have a smaller droplet number concentration and liquid water content, while simulation with the microphysics scheme that suffers more from numerical diffusion tends to have a broader size distribution and thus larger mean droplet sizes. Sensitivities of simulations to bin resolution, spatial resolution, and temporal resolution are also tested. We find that refining the microphysical bin resolution leads to a broader cloud droplet size distribution due to the advection of hydrometeors. Our results provide insight for using different advection and microphysics schemes in cloud chamber simulations, which might also help understand the uncertainties of the schemes used in atmospheric cloud simulations.

A strongly coupled Eulerian Lagrangian method applied in unsteady 3D external flows around Wind Turbine rotors

This paper presents a hybrid CFD solver that couples a standard Eulerian approach that solves the compressible Navier-Stokes equations under a cell-centered finite volume discretization, with a Lagrangian one, based on particles representation which carry mass, pressure, dilatation and vorticity. The velocity field is calculated using the Helmholtz’s decomposition theorem. Computational performance is enhanced by employing the Particle Mesh (PM) technique in order to solve the Poisson equations for the scalar potential ϕ and the stream function ψ. Even though validated for 2D flows over airfoils, this specific solver is used for the first time in order reproduce the flow around a wind turbine rotor. The validation simulations concern axial flow over the wind turbine model rotor used in the New MEXICO experimental campaign. Results of the hybrid solver, presented as blade pressure distribution and axial flow velocities are compared against the ones produced by its pure Eulerian counterpart and experimental measurements. PM grids of up to 5 points per chord of the blade section at 75% radius have been used. Comparison with the standard Eulerian solver suggest that the produced blade loads are over-predicted by approximately 7% near the tip and 14% near the root. However, the calculated velocity field is much closer to the experimental measurements as compared to the one produced by the Eulerian approach, which is attributed to the reduced numerical diffusion of the Lagrangian-vorticity formulation.

Theoretical reassessment of the first Stefan diffusion column experiment with a two-component liquid phase, consisting of a high-density volatile solvent and a low-density nonvolatile diluent

The Stefan column was designed in the 19th century to allow the experimental estimation of binary gas diffusion coefficients starting with a pure volatile liquid A placed at the bottom overlaid with a stagnant/inert gas B. A sweeping B stream was provided at the top to remove the diffused gas A. In 1959, Richardson first studied a two-component liquid mixture in the Stefan column. One of his systems, a high-density volatile liquid A (carbon tetrachloride) dissolved in a low-density nonvolatile liquid O (dibutyl phthalate), is of interest to our ongoing research efforts. He collected interfacial descent-time data in his single isothermal Stefan column experiment, and analyzed them with a diffusion transport model, which contained unnecessary assumptions and simplifications, to obtain the binary liquid diffusivity of A in O, D AO. The present study removes the major restrictions of the previous model, reanalyzing the reported data with an improved numerical diffusion model that includes realistic features of the one-dimensional transport problem and statistical information on the estimated D AO. The average ± standard deviation of D AO were 8.82E-10 ± 1.85E-15 m2/s (12 data points), with an error of −13.3% relative to the Richardson value. The new model also provides detailed insight on the diffusive transport dynamics of liquid A by predicting interfacial descent rates, instantaneous concentration profiles in the liquid phase, and the time-dependent fraction of the mass of A lost from the original solution. The model is valuable to chemical engineering researchers studying diffusion–evaporation phenomena and multicomponent distillation processes.

Anti‐diffusive alternate‐directions schemes for the transport of step functions

AbstractThe purpose in this article is to design finite‐volume schemes on structured grids for the transport of piecewise‐constant functions (typically, indicator functions) with as low diffusion as possible. We first propose an extension of the so‐called Lagrange‐projection algorithm, or downwind scheme with an Ultrabee limiter, for the transport equation in one space dimension with a non‐constant velocity; as its constant velocity counterpart, this scheme is designed to capture the discontinuities separating two plateaus in only one cell, and is referred to as “anti‐diffusive.” It is shown to preserve the bounds of the solution. Then, for two and three dimensional problems, we introduce a conservative alternate‐directions algorithm, an show that this latter enjoys a discrete maximum principle, provided that the underlying one‐dimensional schemes satisfy a property which may be seen as a flux limitation, possibly incorporated a posteriori in any explicit scheme. Numerical tests of this alternate‐directions algorithm are performed, with a variety of one‐dimensional embedded schemes including the anti‐diffusive scheme developed here and the so called THINC scheme. The observed numerical diffusion is indeed very low. With the anti‐diffusive scheme, the above‐mentioned a posteriori limitation is necessary to preserve the solution bounds, but, in the performed tests, does not introduce any visible additional diffusion.

A Direct Ghost Fluid Method for Modeling Explosive Gas and Water Flows

This work presents a Direct Ghost Fluid Method (DGFM) as part of a two-fluid numerical framework suitable to model explosive gas and water flows resulting from underwater explosion (UNDEX). Due to the presence of explosive gas and water with shock waves in the modeling domain, classic Eulerian methods with inherent diffusion may not be effective. Numerical diffusion occurs due to nonphysical diffused density at material interfaces, which creates spurious pressure oscillations and significantly degrades the quality of the numerical results. To eliminate or minimize numerical diffusion, sharp interface methods having no mixed elements may be used in multifluid flow computations. The Direct Ghost Fluid Method (DGFM) described in this paper uses direct extrapolation of density (vice pressure) and tangential velocity from real to ghost fluid. The spurious pressure oscillations near the material interface are therefore minimized. One-, two-, and three-dimensional computational fluid dynamics (CFD) solvers that have DGFM as an essential part in their framework to model UNDEX interface conditions are developed, explored, and applied to the simulation of a series of benchmark problems. Excellent agreement is obtained among the simulations, the analytical solutions, and the experiments.