This paper presents the two-dimensional numerical study of mixed convection evaporation from an inclined corrugated wet plate subjected to a constant heat flux density. Assumptions were adopted and boundary conditions are imposed so as to neglect certain terms in the continuity, momentum, heat and diffusion equations that govern the phenomenon on the boundary layers. The homotopic transformation then allows the equation of the curve to be transformed from a corrugation to that of a straight line. Adimensionnalization allowed us not only to link physical parameters together but also to obtain equations that no longer depend on the measurement systems. From the dimensionless equations, we were able to apply the implicit finite difference method. The numerical resolution of the obtained discretized equations was programmed on MATLAB. We have examined and presented the influences of wavelength, wave amplitude, and plate inclination on the dimensionless velocity, temperature, and concentration fields, as well as on the corresponding friction coefficient, Nusselt number, and Sherwood number. Depending on the dimensionless quantity or the exchange coefficient studied, the effects of the inclination of the plate, the wavelength and the wave amplitude can be similar, or two variables cause the same effect, but the third variable generates the opposite effect. Results for unstable numerical schemes on the dimensionless velocity distribution were obtained when we increased the value of the Reynolds number, the x-step, the y-step or when we decreased the value of the Richardson number indicating that the supposed laminar flow tends towards a turbulent regime.

In this work, a high-order meshless framework is developed for the numerical resolution of the temporal–fractional Black–Scholes equation arising in option pricing with long-memory effects. The spatial discretization is carried out with a local radial basis function produced finite difference (RBF–FD) method on seven-node stencils. Analytical differentiation weights are constructed by employing closed-form second integrations of a variant of the inverse multiquadric kernel, which yields sparse differentiation matrices. Explicit formulas are derived for both first- and second-order operators, and a detailed truncation error analysis confirms sixth-order convergence in space. Numerical experiments for European options discuss better accuracy per spatial node than standard finite difference schemes.

Abstract Observations in the Galaxy and nearby spirals have established that the H i -to-H 2 transition at solar metallicity occurs at gas weight of P DE / k B ≈ 10 4 K cm −3 , similar to solar neighborhood conditions. Even so, state-of-the-art models of a self-regulated interstellar medium (ISM) underproduce the molecular fraction ( R mol ≡ M H 2 / M H I ) at solar neighborhood conditions by a factor of ≈2–4. We use the GHOSDT suite of simulations at a mass resolution range of 100–0.25 M ⊙ (effective spatial resolution range of ∼20–0.05 pc) run for 500 Myr to show how this problem is affected by modeling choices such as the inclusion of photoionizing radiation, assumed supernova energy, numerical resolution, inclusion of magnetic fields, and including a model for subgrid clumping. We find that R mol is not converged even at a resolution of 1 M ⊙ , with R mol increasing by a factor of 2 when resolution is improved from 10 to 1 M ⊙ . Models excluding either photoionization or magnetic fields result in a factor 2 reduction in R mol . The only model that agrees with the observed value of R mol includes our subgrid clumping model, which enhances R mol by a factor of ∼3 compared with our fiducial model. This increases the time-averaged R mol to 0.25, in agreement with the solar circle value, and closer to the observed median value of 0.42 in regions comparable to the solar neighborhood in nearby spirals. Our findings show that small-scale clumping in the ISM plays a significant role in H 2 formation even in high-resolution numerical simulations.

Abstract Gravitational instability (GI) has long been considered a viable pathway for giant planet formation in protoplanetary disks (PPDs), especially at wide orbital separations or around low-mass stars where core accretion faces significant challenges. However, a primary drawback is that disk fragmentation from GI is generally found to produce overmassive clumps, typically in the mass range of brown dwarfs, although most numerical studies adopt simplified cooling prescriptions or those with limited numerical resolution. We conduct a suite of global three-dimensional radiation hydrodynamics simulations of self-gravitating PPDs using the meshless finite-mass method. By implementing radiation transport via the M1 closure and systematically varying disk mass and opacity, we show that increasing disk mass and lowering opacity promote fragmentation by enhancing radiative cooling. Nonfragmenting disks settle into a gravitoturbulent state with low-order spiral structures and effective angular momentum transport characterized by α ∼ β cool − 1 . In fragmenting disks, a subset of gravitationally bound clumps survives as long-lived fragments. Their initial masses form a consistent distribution around Σ · λ T · 2( c s /Ω K ) (with λ T denoting the Toomre wavelength), corresponding to ∼0.3–10 M J in our simulations, consistent with the masses of gas giants. These results demonstrate that GI can produce planet-mass fragments under more realistic conditions, reinforcing it as a viable gas giant formation pathway and motivating further studies of fragment evolution and observational signatures.

Abstract The unsteady tip leakage flows are accountable for aerodynamic losses that inherently hinder the performance of unshrouded turbines. Abatement of these penalties through the tightening of the operating tip clearance is highly relevant for new generations of small-core high-speed turbines, whose characteristic low aspect-ratio passages result in significant influence of secondary flow structures. A deep understanding of the development of tip leakage flows is paramount to defining a suitable transition towards tight clearance turbine configurations. In-situ experimental measurements provide insights to build such comprehension and further serve to improve the numerical resolution fidelity of these highly detached unsteady flows delivered by commercially available computational tools. This manuscript presents the experimental resolution of the unsteady pressure fields experienced in the over-tip casing of a small-core high-speed turbine. Fast response miniature pressure transducers captured at 2MHz the casing's static pressure of the TRL6 small-core turbine demonstrator “STARR”, located in the Purdue Experimental Turbine Aerothermal Laboratory. The versatility of the facility for engine-representative testing allowed identifying the independent influence of the operating pressure ratio and rotational speed on the squealer tip leakage flow structures along a 60% tip clearance reduction. Besides the pressure differential across the blade, the resulting phase-locked average fields revealed two vortical structures along the squealer tip cavity as a secondary mechanism driving the tip leakage flows, with different shifting and combination trends along the operational envelope and tip clearance reduction.

The study of star cluster evolution necessitates modeling how their density profiles develop from their natal gas distribution. Observational evidence indicates that many star clusters follow a Plummer -like density profile. However, most studies have focused on the phase after gas ejection, neglecting the influence of gas on early dynamical evolution. We investigate the development of star clusters forming within gas clouds, particularly those with a centrally concentrated gas profile. Simulations were conducted using the framework, integrating the magnetohydrodynamics code into . This permitted detailed modeling of star formation, stellar evolution, stellar dynamics, radiative transfer, and gas magnetohydrodynamics. We study the collapse of centrally concentrated, turbulent spheres with a total mass of 2.5 Torch FLASH AMUSE 10^3, M_⊙, investigating the effects of varying numerical resolution and star formation scenarios. The free-fall time is shorter at the center than at the edges of the cloud, with a minimum value of 0.55, ; (2) subclusters can initially form even in centrally concentrated gas clouds; (3) gas collapses globally toward the center on the central free-fall timescale, contradicting the assumption in analytical models of local fragmentation and star formation; and (4) The key conclusions from this study are: (1) the final stellar density profile is more centrally concentrated than was analytically predicted, reflecting the role of global gas collapse and feedback the mass of the most massive star formed is directly correlated with the cluster effective radius and inversely correlated with the velocity dispersion, while the duration of star formation correlates with the star formation efficiency.

We study the impact of fragmentation on the cosmic string loop number density, using an approach inspired by the three-scale model and a Boltzmann equation. We build a new formulation designed to be more amenable to numerical resolution and present two complementary numerical methods to obtain the full loop distribution including the effect of fragmentation and gravitational radiation. We show that fragmentation generically predicts a decay of the loop number density on large scales and a deviation from a pure power-law. We expect fragmentation to be crucial for the calibration of loop distribution models.

Abstract Physical fields within thin poroelastic interphases often vary rapidly, making numerical resolution computationally expensive. Analytical approaches address this by replacing the interphase with imperfect transmission conditions along a zero-thickness interface via asymptotic methods while preserving leading order solution properties. This work examines transmission conditions when elastic and viscous effects occur in distinct asymptotic regimes, leading to atypical coupling between the fields. Such coupling poses mathematical challenges but also enables accurate representation of multiphysics processes at leading order. We develop a method for solving problems governed by these atypical conditions and apply it to two-dimensional poroelasticity in domains with mixed interface types. Exact solutions are derived using integral transforms and expressed as convergent series, with numerical simulations validating the analysis. The results highlight the limitations of classical interface models and demonstrate the importance of atypical conditions for capturing coupling phenomena.

In this work, a numerical investigation is conducted to analyze laminar mixed convection of nanofluids in a two-dimensional horizontal channel. The lower wall of the channel dissipates heat at constant hot temperature, whereas the upper wall is adiabatic. The analysis considers five volume concentrations (φ) of copper nanoparticles (Cu), ranging from 0 to 0.2, suspended in common base fluids such as ethylene glycol, soybean oil, and sunflower oil. The effective thermal conductivity and dynamic viscosity of the nanofluid are estimated using the Maxwell-Garnett and Brinkman models, respectively. The set of governing equations is derived and solved numerically through a finite difference discretization. For numerical resolution, a line-by-line sweeping strategy in combination with the Thomas algorithm (TDMA) is implemented. The objective of this study is to investigate how viscosity and thermal conductivity influence both heat transfer and flow behavior, in order to determine the nanofluid that maximizes thermal performance. The outcomes are expected to contribute to enhancing the use of nanofluids in advanced thermal control systems.

Context. Turbulence is one of the key processes that control the spatial and temporal evolution of matter and energy of many astrophysical systems. Aims. This paper investigates the statistical properties of isothermal turbulence in both the subsonic and supersonic regimes. The focus is on the influence of the Mach number ( Ma ) and the Reynolds number ( Re ) on both the space-local and scale-dependent fluctuations of relevant gas variables, the density, velocity, their derivatives, and the kinetic energy. Methods. We carried out hydrodynamical simulations of driven turbulence with explicit viscosity and therefore controlled Re , at converged numerical resolutions up to 1920 3 grid cells. Results. We confirm previous work that the probability density functions (PDFs) of the gas density are approximately log-normal and depend on Ma . We provide a new detailed quantification of the dependence of the PDFs of density and velocity on Re , finding a relatively weak dependence, provided Re > 200. In contrast, derivatives of the density and velocity field are sensitive to Re , with the probability of extreme events (the tails of the PDFs) growing with Re . The PDFs of the density gradient and velocity divergence (dilatation) exhibit increasingly heavy tails with growing Ma , signalling enhanced internal intermittency. At sufficiently high Ma , the statistics of dilatation are observed to saturate at a level determined solely by Re , suggesting that turbulent dilatation becomes limited by viscous effects. We also examine the scale-by-scale distribution of kinetic energy through a compressible form of the Kármán-Howarth-Monin (KHM) equation that incorporates density variations. In the intermediate range of scales, a marked difference is found between subsonic and supersonic turbulence: while Kolmogorov-like scaling applies in the sub- and transonic regimes, supersonic turbulence aligns more closely with Burgers turbulence predictions. The analysis of individual terms in the KHM equation highlights the role of the pressure-velocity coupling as an additional mechanism for converting and transferring kinetic energy from large to small scales. Moreover, the contributions of the KHM terms exhibit non-monotonic behaviour with increasing Ma , with dilatational effects becoming more pronounced and acting to oppose the cascade of kinetic energy.

ABSTRACT This paper is devoted to a numerical resolution of spectral shape optimization problems governed by the Robin ‐Laplacian operator under a volume constraint. We deal notably with the numerical computation of optimal shapes and corresponding higher eigenvalues of the problem governed by the ‐Laplacian operator with Robin boundary conditions, in two and three dimensions. In this regard, it is worth mentioning that to our knowledge, no existing work has yet addressed this numerical investigation. So, we establish first the existence of the shape derivative for simple eigenvalues, providing both volume and boundary shape derivative formulas. Then we develop a numerical approach using gradient descent methods to approximate minimizers of higher Robin eigenvalues. This is based on a finite element discretization, combined with a Picard iteration scheme, designed to compute higher order Robin eigenvalues for various values of . Finally, several numerical experiments in 2D and 3D are presented to demonstrate the effectiveness and robustness of the proposed approaches, and new conjectures are stated, based on these numerical simulations.

Abstract Cosmological hydrodynamical simulations have become an indispensable tool to understand galaxies. However, computational constraints still severely limit their numerical resolution. This not only restricts the sampling of the stellar component and its direct comparison to detailed observations, but also the precision with which it is evolved. To overcome these problems we introduce the Superstars method. This method increases the stellar mass resolution in cosmological galaxy simulations in a computationally inexpensive way for a fixed dark matter and gas resolution without altering any global properties of the simulated galaxies. We demonstrate the Superstars method for a Milky Way-like galaxy of the Auriga project, improving the stellar mass resolution by factors of 8 and 64 at an additional cost of only 10% and 500%, respectively. We show and quantify that this improves the sampling of the stellar population in the disc and halo without changing the properties of the central galaxy or its satellites, unlike simulations that change the resolution of all components (gas, dark matter, stars). Moreover, the better stellar mass resolution reduces numerical heating of the stellar disc in its outskirts and keeps substructures in the stellar disc and inner halo more coherent. It also makes lower mass and lower surface brightness structures in the stellar halo more visible. The Superstars method is straightforward to incorporate in any cosmological galaxy simulation that does not resolve individual stars.

ABSTRACT The aim of this work is to characterize the thermodynamic state of fuel mixed into the turbulent flame brush in the context of the Zel’dovich deflagration-to-detonation transition (ZDDT) mechanism of Type Ia supernovae (SNe Ia). We perform a series of three-dimensional computer simulations of thermonuclear deflagrations subject to the Rayleigh–Taylor instability (RTI) for conditions found in model explosions of centrally ignited realistic, Chandrasekhar mass white dwarf progenitors. These conditions correspond to explosion times when the flame reaches low density progenitor regions where DDT is expected to occur. The flame database is constructed using a thickened flame model. High numerical resolution is achieved with the help of the adaptive mesh refinement (AMR) approach allowing, for the first time, to resolve mesoscale buoyancy-driven flame turbulence. The system is evolved to a quasi-steady state, and flow properties in the turbulent region, where turbulence is most isotropic, is analysed in a co-moving frame of reference. We find evidence for strong buoyancy-driven adiabatic heating of fuel layers adjacent to the flame front. The heating results in a dramatic reduction of fuel ignition times by between $\approx$2 and more than about 5 orders of magnitude. The heating increases with the RTI forcing. The observed shortening of fuel burning time-scales suggests a new source of energy is important inside fuel penetrating the flame brush. These regions are up to several hundred meters wide. On the basis of the previous results of turbulent combustion in SNe Ia, preconditioning required by the ZDDT mechanism can occur there.

Abstract Recent observations have revealed slow, coherent temperature fluctuations in AGN disks that propagate both inward and outward at velocities of ∼0.01–0.1c, a kind of variability that is distinct from reverberation (mediated by the reprocessing of light) between different regions of the disk. We investigate the origin and nature of these fluctuations using global 3D radiation–magnetohydrodynamic simulations of radiation- and magnetic-pressure-dominated AGN accretion disks. Disks with a significant turbulent Maxwell stress component exhibit wave-like temperature perturbations, most evident close to the midplane, whose propagation speeds exactly match the local fast magnetosonic speed and are consistent with the speeds inferred in observations. These fluctuations have amplitudes of 2%–4% in gas temperature, which are also consistent with observational constraints. Disks that are dominated by mean-field Maxwell stresses do not exhibit such waves. While waves may be present in the body of the disk, we do not find them to be present in the photosphere. Although this may in part be due to low numerical resolution in the photosphere region, we discuss the physical challenges that must be overcome for the waves to manifest there. In particular, the fact that such waves are observed implies that the disk photospheres must be magnetically dominated, since radiative damping from photon diffusion smooths out radiation pressure fluctuations. Furthermore, the gas and radiation fluctuations must be out of local thermodynamic equilibrium.

ABSTRACT Numerical simulations have become an indispensable tool in astrophysics. To interpret their results, it is critical to understand their intrinsic variability, i.e. how much the results change with numerical noise or inherent stochasticity of the physics model. We present a set of seven realizations of high-resolution cosmological zoom-in simulations of a Milky Way-like galaxy with the Auriga galaxy formation model. All realizations share the same initial conditions and code parameters, but draw different random numbers for the inherently stochastic parts of the model. We show that global galaxy properties at $z=0$, including stellar mass, star formation history, masses of stellar bulge and stellar disc, the radius and height of the stellar disc change by less than $10{{\, \rm per\, cent}}$ between the different realizations, and that magnetic field structures in the disc and the halo are very similar. In contrast, the star formation rate today can vary by a factor of 2, and the internal morphological structure of the stellar disc can change. The time and orbit of satellite galaxies and their galaxy properties when falling into the main halo are again very similar, but their orbits start to deviate after the first pericentre passage. Finally, we show that changing the mass resolution of all matter components by a factor of 8 in the Auriga model changes galaxy properties significantly more than the intrinsic variability of the model, and that these changes are systematic. This limits detailed comparisons between simulations at different numerical resolutions.

The oscillatory properties of pendular motion, along with the associated energetic conditions, are used to induce analytical functions capable of simultaneously describing the angular position and velocity. To describe the angular position of a generic pendulum, for very large amplitudes of oscillation, we used the numerical solutions obtained from the numerical resolution of the differential equation of motion. The solver software needed was built using the LabView 2019 platform, but any other ODE solver containing peak and valley detectors can be used. The fitting software and plots were performed with the ORIGIN 7.0 program, but also other equivalent programs can be used. For a non-damped pendulum, an analytical model is proposed, built from simple trigonometric functions, but containing the important physical information of the dependence between the period and amplitude of oscillation. The application of the proposed model, using the numerical solutions of the non-approximated differential equation of motion, shows very good agreement, less than 0.01%, for large amplitudes, up to 3π/4.

Abstract In this study, the static bending and free vibration of a bilaterally coated magneto electro elastic (MEE) functionally graded (FG) microbeam is analysed by using a high order quasi-3D beam theory, along with a Differential Quadrature Finite Element Method (DQ-FEM). The power formulation for FG gradation through the thickness direction is considered. The microbeam consists of two materials, one possessing piezo-magneto-electric characteristics and the other without them. The material characteristics are progressively graded from the outermost surfaces to the innermost core. In order to localize the microstructural effect of the beam, the modified couple stress theory (MCST) is incorporated. By the application of Lagrange's theorem and Gauss-Lobato node scheme, the general governing equation are established. Through the implementation of the established model, “the static bending and free vibration” analysis are determined. To illustrate the effectiveness and accuracy of this particular numerical resolution method, the obtained results are validated with similar outcomes in existing literature. The effects of the material gradation volume fraction index, and the length-thickness ratio on the natural frequencies and static bending are investigated. The results reveal that the material distribution plays a significant role in influencing both static bending and free vibration behavior. Material composition plays a critical role, with higher proportions of MEE material enhancing the piezoelectric effect and magnetostrictive response, respecting the material gradation with optimized combinations of MEE material for higher deflection and optimal electric and magnetic potentials. This study provides a comprehensive framework for optimizing MEE microbeams in applications requiring precise control of mechanical, electrical, and magnetic responses.

The dust settling instability (DSI) is a member of the resonant drag instability (RDI) family, and is thus related to the streaming instability (SI). Linear calculations found that the unstratified monodisperse DSI has growth rates much higher than the SI even with lower initial dust-to-gas ratios. However, recent non-linear investigation found no evidence of strong dust clumping at the saturation level. We seek to investigate the non-linear saturation of the mono- and polydisperse DSI. We examine the convergence behaviour with regard to both the numerical resolution as well as the number of species. By characterising the morphology of the dust evolution triggered by the DSI, we can shed more light on its role in planetesimal formation. We performed a suite of 2D shearing box hydrodynamic simulations with the code Idefix both in the mono- and polydisperse regimes. We focussed on the time evolution of the maximum dust density, noting the time at which the instability is triggered, and analysed the morphology of the resultant structure. In our monodisperse DSI simulations, the maximum dust density increases and the instability saturates earlier with a higher spatial resolution, with no signs of convergence yet. The polydisperse simulations do seem to converge with the number of species and produce maximum dust densities that are comparable to, albeit lower than, the monodisperse simulations. Different dust species tend to form adjacent but separate dust filaments, which may have implications on dust growth and further clumping. The monodisperse DSI produces dust structure at densities high enough to likely lead to clumping. The polydisperse DSI produces lower but comparable dust densities at the same spatial resolution. Our idealised treatment suggests that the DSI is important for planetesimal formation, as it is less affected by the inclusion of a dust size distribution than the SI.

This study employs Mie's scattering theory and van de Hulst's mixing model to predict the refractive indices (n,k) of silver nanowire (AgNW) networks in the visible and near-infrared wavelengths, allowing the comparison to the experimentally determined k spectra. Transmittance spectra calculated via the numerical resolution of Fresnel's equations are compared to experimental data, showing excellent agreement, particularly for nanowires with larger diameters and at shorter wavelengths. These findings, both theoretical and empirical, pave the way for accurate optical simulations of metallic nanowire networks, supporting their integration into complex multilayer systems and devices such as displays or smart windows. Notably, our work proposes the first demonstration of the dominance of the metallic character of AgNW networks over their dielectric behavior in terms of optical response.

Geophysical flows in the atmosphere and oceans encompass rich dynamics across a wide range of scales, making their physical representation and interpretation an essential element for advancing the state of the science of climate modeling and weather forecasting. This is particularly the case at spatial scales smaller than the numerical resolution of contemporary earth system models (∼ 25–100 km), where the physics of turbulence in the atmospheric boundary layer and ocean mixed layer, convection and clouds, air–sea interactions, wildfires, and urban flows are all but complex geophysical flows that continue to present challenges toward improved physical parameterization. Buoyancy effects stand out as a distinguishing and critical feature in such contexts. This special issue is comprised of 15 papers that advance the theory, modeling, simulation, and observation of a variety of problems relevant to the physics of atmospheric and oceanic flows, hence bridging the knowledge gap between fundamental aspects of geophysical fluid dynamics and weather/climate modeling.