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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Mixing across stable density interfaces in forced stratified turbulence

Understanding how turbulence enhances irreversible scalar mixing in density-stratified fluids is a central problem in geophysical fluid dynamics. While isotropic overturning regions are commonly the focus of mixing analyses, we here investigate whether significant mixing may arise in anisotropic statically stable regions of the flow. Focusing on a single forced direct numerical simulation of stratified turbulence, we analyse spatial correlations between the vertical density gradient $\partial \rho /\partial z$ and the dissipation rates of kinetic energy $\epsilon$ and scalar variance $\chi$ , the latter quantifying scalar mixing. The domain is characterized by relatively well-mixed density layers separated by sharp stable interfaces that are correlated with high vertical shear. While static instability is most prevalent within the mixed layers, much of the scalar mixing is localized to the intervening interfaces, a phenomenon not apparent if considering local static instability or $\epsilon$ alone. While the majority of the domain is characterized by the canonical flux coefficient $\varGamma \equiv \chi /\epsilon =0.2$ , often assumed in ocean mixing parametrizations, extreme values of $\chi$ within the statically stable interfaces, associated with elevated $\varGamma$ , strongly skew the bulk statistics. Our findings suggest that current parametrizations of turbulent mixing may be biased by undersampling, such that the most common, but not necessarily the most significant, mixing events are overweighted. Having focused here on a single simulation of stratified turbulence, it is hoped that our results motivate a broader investigation into the role played by stable density interfaces in mixing, across a wider range of parameters and forcing schemes representative of ocean turbulence.

Couchman, Miles M. P. (ORCID:0000000246676829)↗
DOE OSTI2022

Analysis of scale-dependent kinetic and potential energy in sheared, stably stratified turbulence

Budgets of turbulent kinetic energy (TKE) and turbulent potential energy (TPE) at different scales $\ell$ in sheared, stably stratified turbulence are analysed using a filtering approach. Competing effects in the flow are considered, along with the physical mechanisms governing the energy fluxes between scales, and the budgets are used to analyse data from direct numerical simulation at buoyancy Reynolds number $Re_b=O(100)$ . The mean TKE exceeds the TPE by an order of magnitude at the large scales, with the difference reducing as $\ell$ is decreased. At larger scales, buoyancy is never observed to be positive, with buoyancy always converting TKE to TPE. As $\ell$ is decreased, the probability of locally convecting regions increases, though it remains small at scales down to the Ozmidov scale. The TKE and TPE fluxes between scales are both downscale on average, and their instantaneous values are correlated positively, but not strongly so, and this occurs due to the different physical mechanisms that govern these fluxes. Moreover, the contributions to these fluxes arising from the sub-grid fields are shown to be significant, in addition to the filtered scale contributions associated with the processes of strain self-amplification, vortex stretching and density gradient amplification. Probability density functions (PDFs) of the $Q,R$ invariants of the filtered velocity gradient are considered and show that as $\ell$ increases, the sheared-drop shape of the PDF becomes less pronounced and the PDF becomes more symmetric about $R=0$ .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Impact of inland boundary conditions on seawater intrusion modeling in stratified coastal aquifers under sea-level rise

This study systematically examines the impact of inland boundary conditions on seawater intrusion modeling in general stratified coastal aquifers under sea-level rise (SLR). We derived analytical solutions for seawater wedge toe positions in stratified aquifers with general head boundary (GHB) conditions and compiled solutions for constant head boundary (CHB), constant flux boundary (CFB), and GHB conditions in both homogeneous and stratified aquifers. Additionally, we introduced the concept of equivalent boundary conditions and developed equations to ensure consistent steady-state toe positions across different boundary types. Unlike previous studies focusing on specific layering configurations, we conducted a comprehensive sensitivity analysis of seawater intrusion in general stratified aquifers using transmissivity centroid elevation (TCE). Our results show that SLR generally exacerbates seawater intrusion, with unconfined aquifers exhibiting higher sensitivity across all boundary conditions. Among boundary types, CHB conditions were the most sensitive to SLR, CFB the least, and GHB showed an intermediate response depending on its distance from the model boundary. Furthermore, seawater intrusion increases with the TCE of the stratified aquifer under SLR, suggesting that high-permeability or preferential flow layers near the surface amplify the impact of SLR. These findings emphasize the importance of selecting appropriate boundary conditions when evaluating SLR-driven seawater intrusion in stratified coastal aquifers.

Boundary condition↗
DOE OSTI2026

A New 1D Model for Thermal Mixing and Stratification in Advanced Reactor Transients

Thermal mixing and stratification in large pools and enclosures play a critical role in the safety and performance of pool-type nuclear reactors, particularly during transient scenarios involving significant temperature differences between incoming and bulk coolant. Accurate modeling of these phenomena is essential for predicting system behavior and supporting passive safety features such as natural circulation. Here, this paper presents a new 1D model for thermal mixing and stratification, developed and implemented in the SAM code. The model represents a large pool as 1D coolant jet channels and zero-dimensional bulk pool volumes, enabling the simulation of a wide range of flow configurations, including hot and cold jet interactions, stratified layers, and the influence of complex geometries such as ceilings, free surfaces, and internal obstacles. Heat exchange between jet and pool regions is governed by closure relations calibrated against 3D computational fluid dynamics (CFD) simulations. The model improves upon earlier approaches by incorporating time-dependent jet characteristics and capturing the associated delay effects more accurately. Code-to-code comparisons and validation against experimental data from the Thermal Stratification Test Facility demonstrate the model’s accuracy and flexibility. This work offers two key contributions: (1) an efficient and robust method for simulating thermal mixing and stratification at the system level, eliminating the need for external coupling between system analysis codes and CFD, and (2) a significant enhancement of SAM’s capabilities to analyze thermal stratification phenomena in advanced reactor systems.

SAM↗
DOE OSTI2026

Shear-free, inhomogeneous turbulence in a stably stratified fluid

High-resolution large eddy simulations are conducted of locally forced, shear-free turbulence in the presence of an initially sharp density interface. The simulations are reminiscent of oscillating grid turbulence experiments used to isolate the effect of turbulent diffusion and entrainment from background shear. By simulating such a flow we avoid common challenges of the experiments such as secondary-flow contamination due to sidewall effects and the inevitable interaction of the stratifying agent and forcing region. To address the latter concern, we add a heating term (potential energy sink) to the governing equations in the forcing layer, thereby preventing a heat flux through the source region. This modification sets up a continuous stratification in the mixed layer that is often assumed to be negligible in experiments. Despite this difference, we are able to make meaningful comparisons in terms of the overall entrainment rate, which varies as a power law with a turbulent Richardson number. Two exponents, −2 and −1, are measured depending on the definition of the Richardson number and entrainment rate used. The definition leading to −1 is consistent with most experiments, and we argue it is the superior choice if one is able to measure the relevant quantities. We also verify the self-similar scaling of turbulence velocity and length scales in the homogeneous fluid and propose ‘inner’ and ‘outer’ scalings for the stratified cases based on a local Froude number. The detailed scaling results are useful for turbulence model validation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Low-Reynolds-number oscillating boundary layers on adiabatic slopes

We investigate the instabilities and transition mechanisms of Boussinesq stratified boundary layers on sloping boundaries when subjected to oscillatory body forcing parallel to the slope. We examine idealized forms of boundary layers on hydraulically smooth abyssal slopes in tranquil mid- to low-latitude regions, where low-wavenumber internal tides gently heave isopycnals up and down adiabatic slopes in the absence of mean flows, high-wavenumber internal tides, shelf breaks, resonant tide–bathymetry interactions (critical slopes) and other phenomena associated with turbulence ‘hot spots’. In non-rotating low-Reynolds-number flow, increased stratification on the downslope phase has a relaminarizing effect, while on the upslope phase we find transition-to-turbulence pathways arise from shear production triggered by gravitational instabilities. When rotation is significant (low slope Burger numbers) we find that boundary layer turbulence is sustained throughout the oscillation period, resembling stratified Stokes–Ekman layer turbulence. Simulation results suggest that oscillating boundary layers on smooth slopes at low Reynolds number ($Re\leqslant 840$), unity Prandtl number and slope Burger numbers greater than unity do not cause significant irreversible turbulent buoyancy flux (mixing), and that flat-bottom dissipation rate models derived from the tide amplitude are accurate within an order of magnitude.

42 ENGINEERING↗
DOE OSTI2023

Mass and momentum transport in the Tilted Rocket Rig experiment

Here, high-fidelity large eddy simulations of the inclined Rayleigh-Taylor instability in the Tilted Rocket Rig experimental configuration [Smeeton and Youngs, AWE Report No. O 35/87 (1987)] are performed using a tenth-order compact finite difference code. These simulations are analyzed for spatial distributions of turbulent kinetic energy, turbulent mass flux velocity, species mass fraction flux, species mass fraction variance, and Favre-averaged Reynolds stresses at two time instances, t = 37 ms and t = 52 ms. Additionally, the vertical distribution of the components of the unclosed budget equations over the center of the domain for these quantities are examined. The dominant terms of these budget equations are further decomposed to examine the principal contributions to these terms in each axis. Notably, the principal contribution to the horizontal turbulent mass flux velocity budget is found to be from a term which is commonly neglected in many Reynolds-averaged Navier-Stokes models.

42 ENGINEERING↗
DOE OSTI2023

A Perturbative Solution for Nonlinear Stratified Upwelling over a Frictional Slope

Abstract A perturbative solution of simplified primitive equations for nonlinear weakly stratified upwelling over a frictional slope is found that resolves the vertical structure of velocity fields and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The solution uses assumptions consistent with the model proposed by Lentz and Chapman, including a steady-state, constant cross-shore density gradient, no alongshore gradients, laterally inviscid, and consideration of cross-shore advection of alongshore momentum. The solution resolves the vertical structure of velocity fields (including subsurface maxima of compensational flow, not resolved by Lentz and Chapman) and can satisfy Ertel’s potential vorticity conservation in the stratified inviscid interior. The dynamics are similar to Lentz and Chapman; bottom stress balances alongshore wind stress in a homogeneous density ocean and is replaced by nonlinear cross-shore transport of alongshore momentum as the Burger number (S=αN/f, whereα,N, andfare the bottom slope, buoyancy frequency, Coriolis frequency, respectively) increases. When the solution uses the empirical relation between cross-shore and vertical density gradients proposed by Lentz and Chapman, vorticity conservation is not satisfied and the nonlinear momentum transport estimated by the solution linearly increases withS, asymptotically matching Lentz and Chapman forS< 1. When the solution conserves interior potential vorticity, the momentum transport is proportional toS 2 forS< 1 and is in better agreement with numerical simulations.

Oceanography↗
DOE OSTI2024

Numerical validation of scaling laws for stratified turbulence

Recent theoretical progress using multiscale asymptotic analysis has revealed various possible regimes of stratified turbulence. Notably, buoyancy transport can either be dominated by advection or diffusion, depending on the effective Péclet number of the flow. Two types of asymptotic models have been proposed, which yield measurably different predictions for the characteristic vertical velocity and length scale of the turbulent eddies in both diffusive and non-diffusive regimes. The first, termed a ‘single-scale model’, is designed to describe flow structures having large horizontal and small vertical scales, while the second, termed a ‘multiscale model’, additionally incorporates flow features with small horizontal scales, and reduces to the single-scale model in their absence. By comparing predicted vertical velocity scaling laws with direct numerical simulation data, we show that the multiscale model correctly captures the properties of strongly stratified turbulence within regions dominated by small-scale isotropic motions, whose volume fraction decreases as the stratification increases. Meanwhile its single-scale reduction accurately describes the more orderly, layer-like, quiescent flow outside those regions.

Mechanics↗
DOE OSTI2023

Assessment of Sodium Thermal Stratification Models Utilizing the TSTF Benchmark

As a result of certain transient scenarios, a thermally stratified layer of liquid sodium can develop in the bulk coolant volumes of a sodium-cooled fast reactor (SFR). In addition to the effects a stratification layer has on the temperature of the heat transport system, a stratification layer can also influence the transition to and establishment of natural circulation flow, which plays an important role in passive cooling and the inherent safety of a pool-type SFR. Therefore, the ability to accurately capture thermal stratification phenomena is important when demonstrating the safety basis of a pool-type SFR during transient sequences. The present work assesses various computational models with different fidelities in their ability to predict thermal stratification in the upper plenum of an SFR. Each computational model will be assessed using the data generated at the Thermal Stratification Test Facility (TSTF) located at the University of Wisconsin-Madison. Using measured flow rate and inlet temperature data, the measured temperature distributions of the tests are compared to the predictions of the lumped volume-based models in SAS4A/SASSYS-1, a 1D-based model in SAM, and a 3-D computational fluid dynamics (CFD) model using STAR-CCM+. The relative performance of the various computational methods is assessed with respect to key metrics such as bulk coolant temperature distribution and plenum exit temperature. A total of eight tests are analyzed, covering different combinations of flow rates (3 and 10 GPM) and upper internal structure (UIS) configurations (none, solid, porous, and open) The perfect mixing model of SAS4A/SASSYS-1 provides the highest accuracy when the flow rate is high and there is no UIS in the test vessel, as high flow rate injection promotes thermal mixing of the sodium in the test vessel. For most of the analyzed tests, the stratified volume model of SAS4A/SASSYS-1 is able to predict the delay in the outlet temperature drop and temperature distribution in the test vessel by a small number of layers to represent thermal stratification. However, the stratified volume model can only simulate a maximum of three temperature layers within a volume and when a layer approaches the elevation of the outlet, the predicted outlet temperature can demonstrate rapid, non-physical changes. The 1-D axial mixing model of SAM provides results that agree reasonably well with the measured data in the prediction of the temporal evolution of the outlet temperature with the exception of the case with a high flow rate and no UIS. The SAM 1-D model has a similar level of accuracy to CFD results when it comes to predicting the outlet temperature. CFD shows overall good agreement in predicting the temperature distribution in the test vessel and outlet temperature. As CFD can model the test vessel geometry in detail, it performs well in the cases of complex geometries such as tests that included a UIS and internal flow through the UIS resulting in active mixing of the coolant in the test vessel. Each of the models discussed in the present work has the potential to be useful during the various stages of reactor design, analysis, and licensing. The lumped-volume approach can be applied for fast turnaround safety calculations to obtain overall reactor behavior during transients. The 1-D models provide improved accuracy when stratification is expected for a relatively low increase in the computational cost. The CFD model can be utilized for confirmatory analysis of the 1-D model, when experimental measurements are not available.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Immune checkpoint analysis of T‐cell responses to pp65 and IE‐1 antigens in end‐stage lung diseases

Abstract Lung transplant (LTX) patients are at high risk of cytomegalovirus (CMV) infection, which is often associated with high mortality and morbidity. Reactivation of CMV causes cell injury due to the cytopathic effect of viral replication and triggering of T cell immunity. The aim of this study was to compare expression of immune checkpoints (ICs) (PD‐1, CTLA‐4, LAG‐3 and TIGIT) in CD4, CD8 and CD56 and activation markers CD137, CD154 and CD69 of end‐stage patients awaiting lung transplant. Eighteen pre‐LTX positive for anti‐CMV IgG titres and 18 healthy subjects were enrolled. IC and activation markers have been evaluated through flow cytometric analysis in HC and pre‐LTX patients. Reactive (QF+) and unreactive (QF−) patients were stratified according to QuantiFERON‐CMV assays. ICs' and activation markers' expression were determined before and after in vitro stimulation with pp‐65 and IE‐1 antigens. Lower expression of PD‐1 was observed in CD4 and CD8 cells of pre‐LTX patients than controls, whereas CTLA4 appeared upregulated in CD56 and CD8 cells. TIGIT is increased on the surface of CD4, CD8 and NK cells after peptide stimulation in QF‐negative patients and PD‐1 is only downregulated after stimulation in the QF‐positive patients. This study provides new evidence of immune dysregulation in patients with end‐stage lung disorders, particularly in relation to immune checkpoint cell biology. The change in QF+ mostly happens on cytotoxic cells NK and CD8, while the changes in QF− were observed in adaptive immune cells, including CD4 and CD8.

Bergantini, Laura↗
DOE OSTI2022

A scale-wise analysis of intermittent momentum transport in dense canopy flows

We investigate the intermittent dynamics of momentum transport and its underlying time scales in the near-wall region of the neutrally stratified atmospheric boundary layer in the presence of a vegetation canopy. This is achieved through an empirical analysis of the persistence time scales (periods between successive zero-crossings) of momentum flux events, and their connection to the ejection–sweep cycle. Using high-frequency measurements from the GoAmazon campaign, spanning multiple heights within and above a dense canopy, the analysis suggests that, when the persistence time scales ( $t_p$ ) of momentum flux events from four different quadrants are separately normalized by $\varGamma _{w}$ (integral time scale of the vertical velocity), their distributions $P(t_p/\varGamma _{w})$ remain height-invariant. This result points to a persistent memory imposed by canopy-induced coherent structures, and to their role as an efficient momentum-transporting mechanism between the canopy airspace and the region immediately above. Moreover, $P(t_p/\varGamma _{w})$ exhibits a power-law scaling at times $t_{p}<\varGamma _{w}$ , with an exponential tail appearing for $t_{p} \geq \varGamma _{w}$ . By separating the flux events based on $t_p$ , we discover that around 80 % of the momentum is transported through the long-lived events ( $t_{p} \geq \varGamma _{w}$ ) at heights immediately above the canopy, while the short-lived ones ( $t_{p} < \varGamma _{w}$ ) only contribute marginally ( $\approx 20\,\%$ ). To explain the role of instantaneous flux amplitudes in momentum transport, we compare the measurements with newly developed surrogate data and establish that the range of time scales involved with amplitude variations in the fluxes tends to increase as one transitions from within to above the canopy.

Mechanics↗
DOE OSTI2023

High-fidelity Experiments of Turbulent Buoyant Jets from Simultaneous Particle Image Velocimetry and Laser Induced Fluorescence

Accurate models of turbulent buoyant flows are essential for the design of nuclear reactors thermal hydraulics and passive safety systems. However, available models fail to fully capture the physics of turbulent mixing when buoyancy becomes predominant with respect to momentum. Therefore, high-fidelity experiments of well-controlled fundamental flows are needed to develop and validate more accurate models. We performed experiments of positive and negative turbulent buoyant jets, both in uniform and stratified environments, with the aim of understanding the thermal hydraulics of turbulent mixing with variable density and providing high-fidelity data for the development and validation of turbulence models. Non-intrusive, simultaneous Particle Image Velocimetry and Laser Induced Fluorescence measurements were carried out to acquire instantaneous velocity and concentration fields on a vertical section parallel to the axis of a jet in the self-similar region. The Refractive Index Matching method was applied to measure high-resolution buoyant jets with up to 8.6% density difference. These data are free of the typical errors that characterize optical measurements of buoyancy driven flows (e.g., natural and mixed convection) where the refractive index of the fluid is inhomogeneous throughout the measurement domain. Turbulent statistics and entrainment of buoyant jets in uniform and stratified environments are presented. These data are compared with non-buoyant jets in uniform environment, as a reference to investigate the effects of buoyancy and stratification on turbulent mixing. The results will be used for the assessment of current turbulence models and as basis for the development of a new one that captures turbulent mixing.

42 ENGINEERING↗
DOE OSTI2024

High-Fidelity Velocity and Concentration Measurements of Turbulent Buoyant Jets

Accurate models of turbulent buoyant flows are essential for the design of the cooling circuit of nuclear reactors and passive safety systems. However, available models fail to fully capture the physics of turbulent mixing when buoyancy becomes predominant with respect to momentum. Therefore, high-fidelity experiments of well-controlled fundamental flows are needed to develop and validate more accurate models. We analyze experiments of positive and negative turbulent buoyant jets, both in uniform and stratified environments, with the aim of understanding the thermal hydraulics of turbulent mixing with variable density and providing high-fidelity data for the development and validation of turbulence models. Non-intrusive, simultaneous particle image velocimetry and laser-induced fluorescence measurements were carried out to acquire instantaneous velocity and concentration fields on a vertical section parallel to the axis of a jet in the self-similar region. The refractive index matching method was applied to measure high-resolution buoyant jets with up to 8.6% density difference. These data are free of the typical errors that characterize optical measurements of buoyancy-driven flows (e.g. natural and mixed convection) where the refractive index of the fluid is inhomogeneous throughout the measurement domain. Turbulent statistics and entrainment of buoyant jets in uniform and stratified environments are presented. These data are compared with non-buoyant jets in a uniform environment, as a reference to investigate the effects of buoyancy and stratification on turbulent mixing. The results will be used for the assessment of current turbulence models and as a basis for the development of a new model that captures turbulent mixing.

laser induced fluorescence↗
DOE OSTI2020

Direct numerical simulations of turbulent reacting flows with shock waves and stiff chemistry using many-core/GPU acceleration

Compressible reacting flows may display sharp spatial variation related to shocks, contact discontinuities or reactive zones embedded within relatively smooth regions. The presence of such phenomena emphasizes the relevance of shock-capturing schemes such as the weighted essentially non-oscillatory (WENO) scheme as an essential ingredient of the numerical solver. However, these schemes are complex and have more computational cost than the simple high-order compact or non-compact schemes. In this paper, we present the implementation of a seventh-order, minimally-dissipative mapped WENO (WENO7M) scheme in a newly developed direct numerical simulation (DNS) code called KAUST Adaptive Reactive Flows Solver (KARFS). In order to make efficient use of the computer resources and reduce the solution time, without compromising the resolution requirement, the WENO routines are accelerated via graphics processing unit (GPU) computation. The performance characteristics and scalability of the code are studied using different grid sizes and block decomposition. Furthermore, the performance portability of KARFS is demonstrated on a variety of architectures including NVIDIA Tesla P100 GPUs and NVIDIA Kepler K20X GPUs. In addition, the capability and potential of the newly implemented WENO7M scheme in KARFS to perform DNS of compressible flows is also demonstrated with model problems involving shocks, isotropic turbulence, detonations and flame propagation into a stratified mixture with complex chemical kinetics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Multi-spatio-temporal scales PIV in a turbulent buoyant jet discharging in a linearly stratified environment

Time-resolved particle image velocimetry is implemented with a camera array and several laser sheets; this results in a multi-spatio-temporal scale system that is modular and flexible. The setup is optimized to capture global flow features, while locally resolving in space and time near the Kolmogorov scale. The apparatus relies extensively on machine vision CMOS cameras; they are inexpensive and stream to computer hard drive with virtually continuous time-resolved records (up to one hour for the current system). This leads to statistically converged data and also helps in minimizing down time between experimental runs. Details of the implementation and design of experiment are reported. The system instruments a vertical buoyant jet discharging in a linearly stratified environment. Refractive index matched aqueous solutions enable precise optical deployment. The density difference is 3% and the fluids have similar dynamic viscosity. The jet Reynolds number is 2.00 x 10 4 and is above the mixing transition. Such flows are typically challenging to instrument and few velocity field data are available to date. The velocity statistics are reported as well as first insights gained from the campaign.

42 ENGINEERING↗
DOE OSTI2022

A finite-volume scheme for modeling compressible magnetohydrodynamic flows at low Mach numbers in stellar interiors

Fully compressible magnetohydrodynamic (MHD) simulations are a fundamental tool for investigating the role of dynamo amplification in the generation of magnetic fields in deep convective layers of stars. The flows that arise in such environments are characterized by low (sonic) Mach numbers ($\mathscr{M}$ son ≲ 10 –2 ). In these regimes, conventional MHD codes typically show excessive dissipation and tend to be inefficient as the Courant–Friedrichs–Lewy (CFL) constraint on the time step becomes too strict. In this work we present a new method for efficiently simulating MHD flows at low Mach numbers in a space-dependent gravitational potential while still retaining all effects of compressibility. The proposed scheme is implemented in the finite-volume SEVEN-LEAGUE HYDRO (SLH) code, and it makes use of a low-Mach version of the five-wave Harten–Lax–van Leer discontinuities (HLLD) solver to reduce numerical dissipation, an implicit–explicit time discretization technique based on Strang splitting to overcome the overly strict CFL constraint, and a well-balancing method that dramatically reduces the magnitude of spatial discretization errors in strongly stratified setups. The solenoidal constraint on the magnetic field is enforced by using a constrained transport method on a staggered grid. We carry out five verification tests, including the simulation of a small-scale dynamo in a star-like environment at $\mathscr{M}$ son ~ 10 –3 . We demonstrate that the proposed scheme can be used to accurately simulate compressible MHD flows in regimes of low Mach numbers and strongly stratified setups even with moderately coarse grids.

79 ASTRONOMY AND ASTROPHYSICS↗