We compare the performance of energy-based and entropy-conserving schemes for modeling nonthermal energy components, such as unresolved turbulence and cosmic rays, using idealized fluid dynamics tests and isolated galaxy simulations. While both methods are aimed to model advection and adiabatic compression or expansion of different energy components, the energy-based scheme numerically solves the nonconservative equation for the energy density evolution, while the entropy-conserving scheme uses a conservative equation for modified entropy. Using the standard shock tube and Zel’dovich pancake tests, we show that the energy-based scheme results in a spurious generation of nonthermal energy on shocks, while the entropy-conserving method evolves the energy adiabatically to machine precision. We also show that, in simulations of an isolated
- Award ID(s):
- 1911111
- NSF-PAR ID:
- 10284526
- Date Published:
- Journal Name:
- The astrophysical journal
- ISSN:
- 2041-8213
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
more » « less
Abstract L ⋆galaxy, switching between the schemes results in ≈20%–30% changes of the total star formation rate and a significant difference in morphology, particularly near the galaxy center. We also outline and test a simple method that can be used in conjunction with the entropy-conserving scheme to model the injection of nonthermal energies on shocks. Finally, we discuss how the entropy-conserving scheme can be used to capture the kinetic energy dissipated by numerical viscosity into the subgrid turbulent energyimplicitly , without explicit source terms that require calibration and can be rather uncertain. Our results indicate that the entropy-conserving scheme is the preferred choice for modeling nonthermal energy components, a conclusion that is equally relevant for Eulerian and moving-mesh fluid dynamics codes. -
more » « less
ABSTRACT Modelling self-gravity of collisionless fluids (e.g. ensembles of dark matter, stars, black holes, dust, and planetary bodies) in simulations is challenging and requires some force softening. It is often desirable to allow softenings to evolve adaptively, in any high-dynamic range simulation, but this poses unique challenges of consistency, conservation, and accuracy, especially in multiphysics simulations where species with different ‘softening laws’ may interact. We therefore derive a generalized form of the energy-and-momentum conserving gravitational equations of motion, applicable to arbitrary rules used to determine the force softening, together with consistent associated time-step criteria, interaction terms between species with different softening laws, and arbitrary maximum/minimum softenings. We also derive new methods to maintain better accuracy and conservation when symmetrizing forces between particles. We review and extend previously discussed adaptive softening schemes based on the local neighbour particle density, and present several new schemes for scaling the softening with properties of the gravitational field, i.e. the potential or acceleration or tidal tensor. We show that the ‘tidal softening’ scheme not only represents a physically motivated, translation and Galilean invariant and equivalence-principle respecting (and therefore conservative) method but also imposes negligible time-step or other computational penalties, ensuring that pairwise two-body scattering is small compared to smooth background forces and can resolve outstanding challenges in properly capturing tidal disruption of substructures (minimizing artificial destruction) while also avoiding excessive N-body heating. We make all of this public in the GIZMO code.
-
Simulation of flow and transport in petroleum reservoirs involves solving coupled systems of advection-diffusion-reaction equations with nonlinear flux functions, diffusion coefficients, and reactions/wells. It is important to develop numerical schemes that can approximate all three processes at once, and to high order, so that the physics can be well resolved. In this paper, we propose an approach based on high order, finite volume, implicit, Weighted Essentially NonOscillatory (iWENO) schemes. The resulting schemes are locally mass conservative and, being implicit, suited to systems of advection-diffusion-reaction equations. Moreover, our approach gives unconditionally L-stable schemes for smooth solutions to the linear advection-diffusion-reaction equation in the sense of a von Neumann stability analysis. To illustrate our approach, we develop a third order iWENO scheme for the saturation equation of two-phase flow in porous media in two space dimensions. The keys to high order accuracy are to use WENO reconstruction in space (which handles shocks and steep fronts) combined with a two-stage Radau-IIA Runge-Kutta time integrator. The saturation is approximated by its averages over the mesh elements at the current time level and at two future time levels; therefore, the scheme uses two unknowns per grid block per variable, independent of the spatial dimension. This makes the scheme fairly computationally efficient, both because reconstructions make use of local information that can fit in cache memory, and because the global system has about as small a number of degrees of freedom as possible. The scheme is relatively simple to implement, high order accurate, maintains local mass conservation, applies to general computational meshes, and appears to be robust. Preliminary computational tests show the potential of the scheme to handle advection-diffusion-reaction processes on meshes of quadrilateral gridblocks, and to do so to high order accuracy using relatively long time steps. The new scheme can be viewed as a generalization of standard cell-centered finite volume (or finite difference) methods. It achieves high order in both space and time, and it incorporates WENO slope limiting.more » « less
-
A nondispersive, conservative regularisation of the inviscid Burgers equation is proposed and studied. Inspired by a related regularisation of the shallow water system recently introduced by Clamond and Dutykh, the new regularisation provides a family of Galilean-invariant interpolants between the inviscid Burgers equation and the Hunter-Saxton equation. It admits weakly singular regularised shocks and cusped traveling-wave weak solutions. The breakdown of local smooth solutions is demonstrated, and the existence of two types of global weak solutions, conserving or dissipating an H1 energy, is established. Dissipative solutions satisfy an Oleinik inequality like entropy solutions of the inviscid Burgers equation. As the regularisation scale parameter tends to zero or infinity, limits of dissipative solutions are shown to satisfy the inviscid Burgers or Hunter-Saxton equation respectively, forced by an unknown remaining term.more » « less
-
more » « less
Abstract The ability of collisionless shocks to efficiently accelerate nonthermal electrons via diffusive shock acceleration (DSA) is thought to require an injection mechanism capable of preaccelerating electrons to high enough energy where they can start crossing the shock front potential. We propose, and show via fully kinetic plasma simulations, that in high-Mach-number shocks electrons can be effectively injected by scattering in kinetic-scale magnetic turbulence produced near the shock transition by the ion Weibel, or current filamentation, instability. We describe this process as a modified DSA mechanism where initially thermal electrons experience the flow velocity gradient in the shock transition and are accelerated via a first-order Fermi process as they scatter back and forth. The electron energization rate, diffusion coefficient, and acceleration time obtained in the model are consistent with particle-in-cell simulations and with the results of recent laboratory experiments where nonthermal electron acceleration was observed. This injection model represents a natural extension of DSA and could account for electron injection in high-Mach-number astrophysical shocks, such as those associated with young supernova remnants and accretion shocks in galaxy clusters.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- The DOI is not currently available.
