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Register a new userEfficient smoothed particle radiation hydrodynamics II: Radiation hydrodynamics
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The radiation hydrodynamics equations for smoothed particle hydrodynamics are derived by operator splitting the radiation and hydrodynamics terms, including necessary terms for material motion, and discretizing each of the sets of equations separately in time and space. The implicit radiative transfer discussed in the first paper of this series is coupled to explicit smoothed particle hydrodynamics. The result is a multi-material meshless radiation hydrodynamics code with arbitrary opacities and equations of state that performs well for problems with significant material motion. The code converges with second-order accuracy in space and first-order accuracy in time to the semianalytic solution for the Lowrie radiative shock problem and has competitive performance compared to a mesh-based radiation hydrodynamics code for a multi-material problem in two dimensions and an ablation problem inspired by inertial confinement fusion in two and three dimensions.
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We present a new radiative transfer method (SPH-M1RT) that is coupled dynamically with smoothed particle hydrodynamics (SPH). We implement it in the (task-based parallel) SWIFT galaxy simulation code but it can be straightforwardly implemented in other SPH codes. Our moment-based method simultaneously solves the radiation energy and flux equations in SPH, making it adaptive in space and time. We modify the M1 closure relation to stabilize radiation fronts in the optically thin limit. We also introduce anisotropic artificial viscosity and high-order artificial diffusion schemes, which allow the code to handle radiation transport accurately in both the optically thin and optically thick regimes. Non-equilibrium thermo-chemistry is solved using a semi-implicit sub-cycling technique. The computational cost of our method is independent of the number of sources and can be lowered further by using the reduced speed of light approximation. We demonstrate the robustness of our method by applying it to a set of standard tests from the cosmological radiative transfer comparison project of Iliev et al. The SPH-M1RT scheme is well-suited for modelling situations in which numerous sources emit ionising radiation, such as cosmological simulations of galaxy formation or simulations of the interstellar medium.
In this paper, we present a new formulation of smoothed particle hydrodynamics (SPH), which, unlike the standard SPH (SSPH), is well-behaved at the contact discontinuity. The SSPH scheme cannot handle discontinuities in density (e.g. the contact discontinuity and the free surface), because it requires that the density of fluid is positive and continuous everywhere. Thus there is inconsistency in the formulation of the SSPH scheme at discontinuities of the fluid density. To solve this problem, we introduce a new quantity associated with particles and density of that quantity. This density evolves through the usual continuity equation with an additional artificial diffusion term, in order to guarantee the continuity of density. We use this density or pseudo density, instead of the mass density, to formulate our SPH scheme. We call our new method as SPH with smoothed pseudo-density (SPSPH). We show that our new scheme is physically consistent and can handle discontinuities quite well.
We present a thorough numerical study on the MRI using the smoothed particle magnetohydrodynamics method (SPMHD) with the geometric density average force expression (GDSPH). We perform shearing box simulations with different initial setups and a wide range of resolution and dissipation parameters. We show, for the first time, that MRI with sustained turbulence can be simulated successfully with SPH, with results consistent with prior work with grid-based codes. In particular, for the stratified boxes, our simulations reproduce the characteristic butterfly diagram of the MRI dynamo with saturated turbulence for at least 100 orbits. On the contrary, traditional SPH simulations suffer from runaway growth and develop unphysically large azimuthal fields, similar to the results from a recent study with mesh-less methods. We investigated the dependency of MRI turbulence on the numerical Prandtl number in SPH, focusing on the unstratified, zero net-flux case. We found that turbulence can only be sustained with a Prandtl number larger than $sim$2.5, similar to the critical values of physical Prandtl number found in grid-code simulations. However, unlike grid-based codes, the numerical Prandtl number in SPH increases with resolution, and for a fixed Prandtl number, the resulting magnetic energy and stresses are independent of resolution. Mean-field analyses were performed on all simulations, and the resulting transport coefficients indicate no $alpha$-effect in the unstratified cases, but an active $alphaOmega$ dynamo and a diamagnetic pumping effect in the stratified medium, which are generally in agreement with previous studies. There is no clear indication of a shear-current dynamo in our simulation, which is likely to be responsible for a weaker mean-field growth in the tall, unstratified, zero net-flux simulation.
In this paper we investigate whether Smoothed Particle Hydrodynamics (SPH), equipped with artificial conductivity, is able to capture the physics of density/energy discontinuities in the case of the so-called shearing layers test, a test for examining Kelvin-Helmholtz (KH) instabilities. We can trace back each failure of SPH to show KH rolls to two causes: i) shock waves travelling in the simulation box and ii) particle clumping, or more generally, particle noise. The probable cause of shock waves is the Local Mixing Instability (LMI), previously identified in the literature. Particle noise on the other hand is a problem because it introduces a large error in the SPH momentum equation. We also investigate the role of artificial conductivity (AC). Including AC is necessary for the long-term behavior of the simulation (e.g. to get $lambda=1/2, 1$ KH rolls). In sensitive hydrodynamical simulations great care is however needed in selecting the AC signal velocity, with the default formulation leading to too much energy diffusion. We present new signal velocities that lead to less diffusion. The effects of the shock waves and of particle disorder become less important as the time-scale of the physical problem (for the shearing layers problem: lower density contrast and higher Mach numbers) decreases. At the resolution of current galaxy formation simulations mixing is probably not important. However, mixing could become crucial for next-generation simulations.
The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation of a sun-like star), gas dynamics (wall heating problem, collision of two streams of gas) and inertial confinement fusion (ICF, -ablative implosion of a small capsule-). New material concerning the standard SPH formalism is given. That includes the numerical handling of those mass points which move close to the singularity axis, more accurate expressions for the artificial viscosity and the heat conduction term and an easy way to incorporate self-gravity in the simulations. The algorithm developed to compute gravity does not rely in any sort of grid, leading to a numerical scheme totally compatible with the lagrangian nature of the SPH equations.
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