arXiv subjects

Matthias Rheinhardt

Publications and source records attributed to Matthias Rheinhardt.

At least 19 recordsLinked to original sources

arXiv2026

Iterative Poisson Solvers for Self-gravity with the GPU Code Astaroth

We present the development and benchmarking of Poisson solvers for graphics processing units (GPUs). Implemented in the Astaroth platform, the solvers feature high computational efficiency. We present novel combinations of discretizations and smoothers and document practical and performance-focused implementations aimed at reducing time-to-solution for self-gravitating systems. We describe the solver architectures and validate their accuracy against known analytic solutions. We measure convergence and timing per iteration for various solver algorithms, including conjugate gradient, successive overrelaxation, and multigrid in Cartesian coordinates, along with biconjugate gradient stabilized in spherical coordinates. We also couple the solvers to the Astaroth hydrodynamics to simulate a classic time-dependent problem in star formation, measuring accuracy and time-to-solution, for self-gravity on three-dimensional structured grids. Our results demonstrate that the solvers achieve performance similar to other algorithms implemented in Astaroth, and provide a solid foundation for integration into production-scale astrophysical simulations.

astro-ph.IM↗

arXiv2023

Numerical evidence for a small-scale dynamo approaching solar magnetic Prandtl numbers

Magnetic fields on small scales are ubiquitous in the universe. Though they can often be observed in detail, their generation mechanisms are not fully understood. One possibility is the so-called small-scale dynamo (SSD). Prevailing numerical evidence, however, appears to indicate that an SSD is unlikely to exist at very low magnetic Prandtl numbers ($Pr_M$) such as are present in the Sun and other cool stars. We have performed high-resolution simulations of isothermal forced turbulence employing the lowest $Pr_M$ values so far achieved. Contrary to earlier findings, the SSD turns out to be not only possible for $Pr_M$ down to 0.0031, but even becomes increasingly easier to excite for $Pr_M$ below $\simeq\,$0.05. We relate this behaviour to the known hydrodynamic phenomenon referred to as the bottleneck effect. Extrapolating our results to solar values of $Pr_M$ indicates that an SSD would be possible under such conditions.

astro-ph.SR↗

arXiv2022

Scalable communication for high-order stencil computations using CUDA-aware MPI

Modern compute nodes in high-performance computing provide a tremendous level of parallelism and processing power. However, as arithmetic performance has been observed to increase at a faster rate relative to memory and network bandwidths, optimizing data movement has become critical for achieving strong scaling in many communication-heavy applications. This performance gap has been further accentuated with the introduction of graphics processing units, which can provide by multiple factors higher throughput in data-parallel tasks than central processing units. In this work, we explore the computational aspects of iterative stencil loops and implement a generic communication scheme using CUDA-aware MPI, which we use to accelerate magnetohydrodynamics simulations based on high-order finite differences and third-order Runge-Kutta integration. We put particular focus on improving intra-node locality of workloads. Our GPU implementation scales strongly from one to $64$ devices at $50\%$--$87\%$ of the expected efficiency based on a theoretical performance model. Compared with a multi-core CPU solver, our implementation exhibits $20$--$60\times$ speedup and $9$--$12\times$ improved energy efficiency in compute-bound benchmarks on $16$ nodes.

cs.DC↗

arXiv2022

Compressible test-field method and its application to shear dynamos

In this study we present a compressible test-field method (CTFM) for computing $α$ effect and turbulent magnetic diffusivity tensors, as well as those relevant for mean ponderomotive force and mass source, applied to the full MHD equations. We describe the theoretical background of the method, and compare it to the quasi-kinematic test-field method, and to the previously studied variant working in simplified MHD (SMHD). We present several test cases using velocity and magnetic fields of the Roberts geometry, and also compare with the imposed-field method. We show that, for moderate imposed field strengths, the nonlinear CTFM (nCTFM) gives results in agreement with the imposed-field method. Comparison of different flavors of the nCTFM in the shear dynamo case also agree up to equipartition field strengths. Some deviations between the CTFM and SMHD variants exist. As a relevant physical application, we study non-helically forced shear flows, which exhibit large-scale dynamo action, and present a re-analysis of low Reynolds number, moderate shear systems, where we previously neglected the pressure gradient in the momentum equation, and found no coherent shear-current effect. Another key difference is that in the earlier study we used magnetic forcing to mimic small-scale dynamo action, while here it is self-consistently driven by purely kinetic forcing. The kinematic CTFM with general validity forms the core of our analysis. We still find no coherent shear-current effect, but do recover strong large-scale dynamo action that, according to our analysis, is driven through the incoherent effects.

physics.flu-dyn↗

arXiv2021

Investigating global convective dynamos with mean-field models: full spectrum of turbulent effects required

The role of turbulent effects for dynamos in the Sun and stars continues to be debated. Mean-field (MF) theory provides a broadly used framework to connect these effects to fundamental magnetohydrodynamics. While inaccessible observationally, turbulent effects can be directly studied using global convective dynamo (GCD) simulations. We measure the turbulent effects in terms of turbulent transport coefficients, based on the MF framework, from an exemplary GCD simulation using the test-field method. These coefficients are then used as an input into an MF model. We find a good agreement between the MF and GCD solutions, which validates our theoretical approach. This agreement requires all turbulent effects to be included, even those which have been regarded as unimportant so far. Our results suggest that simple dynamo models, as are commonly used in the solar and stellar community, relying on very few, precisely fine-tuned turbulent effects, may not be representative of the full dynamics of dynamos in global convective simulations and astronomical objects.

astro-ph.SR↗

arXiv2021

Relic gravitational waves from the chiral magnetic effect

Relic gravitational waves (GWs) can be produced by primordial magnetic fields. However, not much is known about the resulting GW amplitudes and their dependence on the details of the generation mechanism. Here we treat magnetic field generation through the chiral magnetic effect (CME) as a generic mechanism and explore its dependence on the speed of generation (the product of magnetic diffusivity and characteristic wavenumber) and the speed characterizing the maximum magnetic field strength expected from the CME. When the latter exceeds the former (regime I), the regime applicable to the early universe, we obtain an inverse cascade with moderate GW energy that scales with the third power of the magnetic energy. When the generation speed exceeds the CME limit (regime II), the GW energy continues to increase without a corresponding increase of magnetic energy. In the early kinematic phase, the GW energy spectrum (per linear wavenumber interval) has opposite slopes in both regimes and is characterized by an inertial range spectrum in regime I and a white noise spectrum in regime II. The occurrence of these two slopes is shown to be a generic consequence of a nearly monochromatic exponential growth of the magnetic field. The resulting GW energy is found to be proportional to the fifth power of the limiting CME speed and the first power of the generation speed.

astro-ph.CO↗

arXiv2021

On the existence of shear-current effects in magnetized burgulence

The possibility of explaining shear flow dynamos by a magnetic shear-current (MSC) effect is examined via numerical simulations. Our primary diagnostics is the determination of the turbulent magnetic diffusivity tensor $\boldsymbolη$. In our setup, a negative sign of its component $η_{yx}$ is necessary for coherent dynamo action by the SC effect. To be able to measure turbulent transport coefficients from systems with magnetic background turbulence, we present an extension of the test-field method (TFM), applicable to our setup where the pressure gradient is dropped from the momentum equation: the nonlinear TFM (NLTFM). Our momentum equation is related to Burgers' equation and the resulting flows are referred to as magnetized burgulence. We use both stochastic kinetic and magnetic forcings to mimic cases without and with simultaneous small-scale dynamo action (SSD). When we force only kinetically, negative $η_{yx}$ are obtained with exponential growth in both the radial and azimuthal mean magnetic field components. Using isotropic magnetic forcing, the field growth is no longer exponential, while NLTFM yields positive $η_{yx}$. By employing an alternative forcing from which wavevectors having small components are removed, the exponential growth is recovered, but the NLTFM results do not change significantly. Analyzing the dynamo excitation conditions for the coherent SC and incoherent $α$ and SC effects shows that the incoherent effects are the main drivers of the dynamo in the majority of cases. We find no evidence for MSC-effect-driven dynamos in our simulations.

physics.flu-dyn↗

arXiv2020

Interaction of large- and small-scale dynamos in isotropic turbulent flows from GPU-accelerated simulations

Magnetohydrodynamical (MHD) dynamos emerge in many different astrophysical situations where turbulence is present, but the interaction between large-scale (LSD) and small-scale dynamos (SSD) is not fully understood. We performed a systematic study of turbulent dynamos driven by isotropic forcing in isothermal MHD with magnetic Prandtl number of unity, focusing on the exponential growth stage. Both helical and non-helical forcing was employed to separate the effects of LSD and SSD in a periodic domain. Reynolds numbers (Rm) up to $\approx 250$ were examined and multiple resolutions used for convergence checks. We ran our simulations with the Astaroth code, designed to accelerate 3D stencil computations on graphics processing units (GPUs) and to employ multiple GPUs with peer-to-peer communication. We observed a speedup of $\approx 35$ in single-node performance compared to the widely used multi-CPU MHD solver Pencil Code. We estimated the growth rates both from the averaged magnetic fields and their power spectra. At low Rm, LSD growth dominates, but at high Rm SSD appears to dominate in both helically and non-helically forced cases. Pure SSD growth rates follow a logarithmic scaling as a function of Rm. Probability density functions of the magnetic field from the growth stage exhibit SSD behaviour in helically forced cases even at intermediate Rm. We estimated mean-field turbulence transport coefficients using closures like the second-order correlation approximation (SOCA). They yield growth rates similar to the directly measured ones and provide evidence of $α$ quenching. Our results are consistent with the SSD inhibiting the growth of the LSD at moderate Rm, while the dynamo growth is enhanced at higher Rm.

physics.flu-dyn↗

arXiv2020

Turbulent viscosity and effective magnetic Prandtl number from simulations of isotropically forced turbulence

(abridged) Context: Turbulent diffusion of large-scale flows and magnetic fields play major roles in many astrophysical systems. Aims: Our goal is to compute turbulent viscosity and magnetic diffusivity, relevant for diffusing large-scale flows and magnetic fields, respectively, and their ratio, the turbulent magnetic Prandtl number, ${\rm Pm}_{\rm t}$, for isotropically forced homogeneous turbulence. Methods: We use simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow. Turbulent viscosity is computed either from the resulting Reynolds stress or from the decay rate of the large-scale flow. Turbulent magnetic diffusivity is computed using the test-field method. The scale dependence of the coefficients is studied by varying the wavenumber of the imposed sinusoidal shear and test fields. Results: We find that turbulent viscosity and magnetic diffusivity are in general of the same order of magnitude. Furthermore, the turbulent viscosity depends on the fluid Reynolds number (${\rm Re}$) and scale separation ratio of turbulence. The scale dependence of the turbulent viscosity is found to be well approximated by a Lorentzian. The results for the turbulent transport coefficients appear to converge at sufficiently high values of ${\rm Re}$ and the scale separation ratio. However, a weak decreasing trend is found even at the largest values of ${\rm Re}$. The turbulent magnetic Prandtl number converges to a value that is slightly below unity for large ${\rm Re}$ whereas for small ${\rm Re}$, we find values between 0.5 and 0.6. Conclusions: The turbulent magnetic diffusivity is in general consistently higher than the turbulent viscosity. The actual value of ${\rm Pm}_{\rm t}$ found from the simulations ($\approx0.9\ldots0.95$) at large ${\rm Re}$ and scale separation ratio is higher than any of the analytic predictions.

astro-ph.SR↗

arXiv2019

$f$-mode strengthening from a localized bipolar subsurface magnetic field

Recent numerical work in helioseismology has shown that a periodically varying subsurface magnetic field leads to a fanning of the $f$-mode, which emerges from the density jump at the surface. In an attempt to model a more realistic situation, we now modulate this periodic variation with an envelope, giving thus more emphasis on localized bipolar magnetic structures in the middle of the domain. Some notable findings are: (i) compared to the purely hydrodynamic case, the strength of the $f$-mode is significantly larger at high horizontal wavenumbers $k$, but the fanning is weaker for the localized subsurface magnetic field concentrations investigated here than the periodic ones studied earlier; (ii) when the strength of the magnetic field is enhanced at a fixed depth below the surface, the fanning of the $f$-mode in the $kω$ diagram increases proportionally in such a way that the normalized $f$-mode strengths remain nearly the same in different such cases; (iii) the unstable Bloch modes reported previously in case of harmonically varying magnetic fields are now completely absent when more realistic localized magnetic field concentrations are imposed beneath the surface, thus suggesting that the Bloch modes are unlikely to be supported during most phases of the solar cycle; (iv) the $f$-mode strength appears to depend also on the depth of magnetic field concentrations such that it shows a relative decrement when the maximum of the magnetic field is moved to a deeper layer. We argue that detections of $f$-mode perturbations such as those being explored here could be effective tracers of solar magnetic fields below the photosphere before these are directly detectable as visible manifestations in terms of active regions or sunspots.

astro-ph.SR↗

arXiv2018

Turbulent transport coefficients in spherical wedge dynamo simulations of solar-like stars

We investigate dynamo action in global compressible solar-like convective dynamos in the framework of mean-field theory. We simulate a solar-type star in a wedge-shaped spherical shell, where the interplay between convection and rotation self-consistently drives a large-scale dynamo. To analyze the dynamo mechanism we apply the test-field method for azimuthally ($ϕ$) averaged fields to determine the 27 turbulent transport coefficients of the electromotive force, of which six are related to the $α$ tensor. This method has previously been used either in simulations in Cartesian coordinates or in the geodynamo context and is applied here for the first time to fully compressible simulations of solar-like dynamos. We find that the $ϕϕ$-component of the $α$ tensor does not follow the profile expected from that of kinetic helicity. The turbulent pumping velocities significantly alter the effective mean flows acting on the magnetic field and therefore challenge the flux transport dynamo concept. All coefficients are significantly affected by dynamically important magnetic fields. Quenching as well as enhancement are being observed. This leads to a modulation of the coefficients with the activity cycle. The temporal variations are found to be comparable to the time-averaged values and seem to be responsible for a nonlinear feedback on the magnetic field generation. Furthermore, we quantify the validity of the Parker-Yoshimura rule for the equatorward propagation of the mean magnetic field in the present case.

astro-ph.SR↗

arXiv2017

Extended subadiabatic layer in simulations of overshooting convection

We present numerical simulations of hydrodynamic overshooting convection in local Cartesian domains. We find that a substantial fraction of the lower part of the convection zone (CZ) is stably stratified according to the Schwarzschild criterion while the enthalpy flux is outward directed. This occurs when the heat conduction profile at the bottom of the CZ is smoothly varying, based either on a Kramers-like opacity prescription as a function of temperature and density or a static profile of a similar shape. We show that the subadiabatic layer arises due to nonlocal energy transport by buoyantly driven downflows in the upper parts of the CZ. Analysis of the force balance of the upflows and downflows confirms that convection is driven by cooling at the surface. We find that the commonly used prescription for the convective enthalpy flux being proportional to the negative entropy gradient does not hold in the stably stratified layers where the flux is positive. We demonstrate the existence of a non-gradient contribution to the enthalpy flux, which is estimated to be important throughout the convective layer. A quantitative analysis of downflows indicates a transition from a tree-like structure where smaller downdrafts merge into larger ones in the upper parts to a structure in the deeper parts where a height-independent number of strong downdrafts persist. This change of flow topology occurs when a substantial subadiabatic layer is present in the lower part of the CZ.

astro-ph.SR↗

arXiv2015

Properties of $p$- and $f$-modes in hydromagnetic turbulence

With the ultimate aim of using the fundamental or $f$-mode to study helioseismic aspects of turbulence-generated magnetic flux concentrations, we use randomly forced hydromagnetic simulations of a piecewise isothermal layer in two dimensions with reflecting boundaries at top and bottom. We compute numerically diagnostic wavenumber-frequency diagrams of the vertical velocity at the interface between the denser gas below and the less dense gas above. For an Alfvén-to-sound speed ratio of about 0.1, a 5% frequency increase of the $f$-mode can be measured when $k_xH_{\rm p}=3$-$4$, where $k_x$ is the horizontal wavenumber and $H_{\rm p}$ is the pressure scale height at the surface. Since the solar radius is about 2000 times larger than $H_{\rm p}$, the corresponding spherical harmonic degree would be 6000-8000. For weaker fields, a $k_x$-dependent frequency decrease by the turbulent motions becomes dominant. For vertical magnetic fields, the frequency is enhanced for $k_xH_{\rm p}\approx4$, but decreased relative to its nonmagnetic value for $k_xH_{\rm p}\approx9$.

astro-ph.SR↗

arXiv2014

Quenching and anisotropy of hydromagnetic turbulent transport

Hydromagnetic turbulence affects the evolution of large-scale magnetic fields through mean-field effects like turbulent diffusion and the $α$ effect. For stronger fields, these effects are usually suppressed or quenched, and additional anisotropies are introduced. Using different variants of the test-field method, we determine the quenching of the turbulent transport coefficients for the forced Roberts flow, isotropically forced non-helical turbulence, and rotating thermal convection. We see significant quenching only when the mean magnetic field is larger than the equipartition value of the turbulence. Expressing the magnetic field in terms of the equipartition value of the {\it quenched} flows, we obtain for the quenching exponents of the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced turbulence, and convection, respectively. However, when the magnetic field is expressed in terms of the equipartition value of the unquenched flows these quenching exponents become about 4, 1.5, and 2.3, respectively. For the $α$ effect, the exponent is about 1.3 for the Roberts flow and 2 for convection in the first case, but 4 and 3, respectively, in the second. In convection, the quenching of turbulent pumping follows the same power law as turbulent diffusion, while for the coefficient describing the $\bf Ω\times \bf J$ effect nearly the same quenching exponent is obtained as for $α$. For forced turbulence, turbulent diffusion proportional to the second derivative along the mean magnetic field is quenched much less, especially for larger values of the magnetic Reynolds number. However, we find that in corresponding axisymmetric mean-field dynamos with dominant toroidal field the quenched diffusion coefficients are the same for the poloidal and toroidal field constituents.

astro-ph.SR↗

arXiv2014

Fanning out of the $f$-mode in presence of nonuniform magnetic fields

We show that in the presence of a harmonically varying magnetic field the fundamental or $f$-mode in a stratified layer is altered in such a way that it fans out in the diagnostic $kω$ diagram, but with mode power also within the fan. In our simulations, the surface is defined by a temperature and density jump in a piecewise isothermal layer. Unlike our previous work (Singh et al. 2014) where a uniform magnetic field was considered, we employ here a nonuniform magnetic field together with hydromagnetic turbulence at length scales much smaller than those of the magnetic fields. The expansion of the $f$-mode is stronger for fields confined to the layer below the surface. In some of those cases, the $kω$ diagram also reveals a new class of low frequency vertical stripes at multiples of twice the horizontal wavenumber of the background magnetic field. We argue that the study of the $f$-mode expansion might be a new and sensitive tool to determining subsurface magnetic fields with longitudinal periodicity.

astro-ph.SR↗

arXiv2014

Mean-field dynamo action from delayed transport

We analyze the nature of dynamo action that produces horizontally averaged magnetic fields in two particular flows that were studied by Roberts (1972, Phil. Trans. R. Soc. A 271, 411), namely his flows II and III. They have zero kinetic helicity either pointwise (flow II), or on average (flow III). Using direct numerical simulations, we determine the onset conditions for dynamo action at moderate values of the magnetic Reynolds number. Using the test-field method, we show that the turbulent magnetic diffusivity is then positive for both flows. However, we demonstrate that for both flows large-scale dynamo action occurs through delayed transport. Mathematically speaking, the magnetic field at earlier times contributes to the electromotive force through the off-diagonal components of the alpha tensor such that a zero mean magnetic field becomes unstable to dynamo action. This represents a qualitatively new mean-field dynamo mechanism not previously described.

astro-ph.SR↗

arXiv2011

Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows

Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the Pèclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to non-local and non-instantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves.

astro-ph.GA↗

arXiv2011

Spontaneous chiral parity breaking by hydromagnetic buoyancy

Evidence for a parity-breaking nature of the magnetic buoyancy instability in a stably stratified gas is reported. In the absence of rotation, no helicity is produced, but the non-helical state is found to be unstable to small helical perturbations during the development of the instability. The parity-breaking nature of an instability in magnetohydrodynamics appears to be the first of its kind and is similar to chiral symmetry breaking in biochemistry. Applications to the production of mean fields in galaxy clusters are being discussed.

astro-ph.SR↗