TRAPHIC - Radiative Transfer for Smoothed Particle Hydrodynamics Simulations

We present TRAPHIC, a novel radiative transfer scheme for Smoothed Particle Hydrodynamics (SPH) simulations. TRAPHIC is designed for use in simulations exhibiting a wide dynamic range in physical length scales and containing a large number of light sources. It is adaptive both in space and in angle and can be employed for application on distributed memory machines. The commonly encountered computationally expensive scaling with the number of light sources in the simulation is avoided by introducing a source merging procedure. The (time-dependent) radiative transfer equation is solved by tracing individual photon packets in an explicitly photon-conserving manner directly on the unstructured grid traced out by the set of SPH particles. To accomplish directed transport of radiation despite the irregular spatial distribution of the SPH particles, photons are guided inside cones. We present and test a parallel numerical implementation of TRAPHIC in the SPH code GADGET-2, specified for the transport of mono-chromatic hydrogen-ionizing radiation. The results of the tests are in excellent agreement with both analytic solutions and results obtained with other state-of-the-art radiative transfer codes.Comment: 31 pages, 20 figures. Accepted for publication in MNRAS. Revised version includes many clarifications and a new time-dependent radiative transfer calculation (fig. 19

A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations

Lattice Boltzmann models that recover a macroscopic description of multiphase flow of immiscible liquids typically represent the boundaries between phases using a scalar function, the phase field, that varies smoothly over several grid points. Attempts to tune the model parameters to minimise the thicknesses of these interfaces typically lead to the interfaces becoming fixed to the underlying grid instead of advecting with the fluid velocity. This phenomenon, known as lattice pinning, is strikingly similar to that associated with the numerical simulation of conservation laws coupled to stiff algebraic source terms. We present a lattice Boltzmann formulation of the model problem proposed by LeVeque and Yee [J. Comput. Phys. 86, 187] to study the latter phenomenon in the context of computational combustion, and offer a volume-conserving extension in multiple space dimensions. Inspired by the random projection method of Bao and Jin [J. Comput. Phys. 163, 216] we further generalise this formulation by introducing a uniformly distributed quasi-random variable into the term responsible for the sharpening of phase boundaries. This method is mass conserving and the statistical average of this method is shown to significantly delay the onset of pinning

Flux form Semi-Lagrangian methods for parabolic problems

A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and convergence analysis are proposed. Numerical examples validate the proposed method and display its potential for consistent semi-Lagrangian discretization of advection--diffusion and nonlinear parabolic problems

The Athena Astrophysical MHD Code in Cylindrical Geometry

A method for implementing cylindrical coordinates in the Athena magnetohydrodynamics (MHD) code is described. The extension follows the approach of Athena's original developers and has been designed to alter the existing Cartesian-coordinates code as minimally and transparently as possible. The numerical equations in cylindrical coordinates are formulated to maintain consistency with constrained transport, a central feature of the Athena algorithm, while making use of previously implemented code modules such as the Riemann solvers. Angular-momentum transport, which is critical in astrophysical disk systems dominated by rotation, is treated carefully. We describe modifications for cylindrical coordinates of the higher-order spatial reconstruction and characteristic evolution steps as well as the finite-volume and constrained transport updates. Finally, we present a test suite of standard and novel problems in one-, two-, and three-dimensions designed to validate our algorithms and implementation and to be of use to other code developers. The code is suitable for use in a wide variety of astrophysical applications and is freely available for download on the web

Low-diffusivity scalar transport using a WENO scheme and dual meshing

Interfacial mass transfer of low-diffusive substances in an unsteady flow environment is marked by a very thin boundary layer at the interface and other regions with steep concentration gradients. A numerical scheme capable of resolving accurately most details of this process is presented. In this scheme, the fourth-order accurate WENO method developed by Liu et al. (1994) was implemented on a non-uniform staggered mesh to discretize the scalar convection while for the scalar diffusion a fourth-order accurate central discretization was employed. The discretization of the scalar convection-diffusion equation was combined with a fourth-order Navier-Stokes solver which solves the incompressible flow. A dual meshing strategy was employed, in which the scalar was solved on a finer mesh than the incompressible flow. The solver was tested by performing a number of two-dimensional simulations of an unstably stratified flow with low diffusivity scalar transport. The unstable stratification led to buoyant convection which was modelled using a Boussinesq approximation with a linear relationship between flow temperature and density. The order of accuracy for one-dimensional scalar transport on a stretched and uniform grid was also tested. The results show that for the method presented above a relatively coarse mesh is sufficient to accurately describe the fluid flow, while the use of a refined mesh for the low-diffusive scalars is found to be beneficial in order to obtain a highly accurate resolution with negligible numerical diffusion