Fast Multiple-Fluid Simulation Using Helmholtz Free Energy

Multiple-fluid interaction is an interesting and common visual phenomenon we often observe. In this paper, we present an energybased Lagrangian method that expands the capability of existing multiple-fluid methods to handle various phenomena, such as extraction, partial dissolution, etc. Based on our user-adjusted Helmholtz free energy functions, the simulated fluid evolves from high-energy states to low-energy states, allowing flexible capture of various mixing and unmixing processes. We also extend the original Cahn-Hilliard equation to be better able to simulate complex fluid-fluid interaction and rich visual phenomena such as motionrelated mixing and position based pattern. Our approach is easily integrated with existing state-of-the-art smooth particle hydrodynamic (SPH) solvers and can be further implemented on top of the position based dynamics (PBD) method, improving the stability and incompressibility of the fluid during Lagrangian simulation under large time steps. Performance analysis shows that our method is at least 4 times faster than the state-of-the-art multiple-fluid method. Examples are provided to demonstrate the new capability and effectiveness of our approach

Relativistic particle transport in extragalactic jets: I. Coupling MHD and kinetic theory

Multidimensional magneto-hydrodynamical (MHD) simulations coupled with stochastic differential equations (SDEs) adapted to test particle acceleration and transport in complex astrophysical flows are presented. The numerical scheme allows the investigation of shock acceleration, adiabatic and radiative losses as well as diffusive spatial transport in various diffusion regimes. The applicability of SDEs to astrophysics is first discussed in regards to the different regimes and the MHD code spatial resolution. The procedure is then applied to 2.5D MHD-SDE simulations of kilo-parsec scale extragalactic jets. The ability of SDE to reproduce analytical solutions of the diffusion-convection equation for electrons is tested through the incorporation of an increasing number of effects: shock acceleration, spatially dependent diffusion coefficients and synchrotron losses. The SDEs prove to be efficient in various shock configuration occurring in the inner jet during the development of the Kelvin-Helmholtz instability. The particle acceleration in snapshots of strong single and multiple shock acceleration including realistic spatial transport is treated. In chaotic magnetic diffusion regime, turbulence levels $\eta_T=/(B^2+)$ around $0.2-0.3$ are found to be the most efficient to enable particles to reach the highest energies. The spectrum, extending from 100 MeV to few TeV (or even 100 TeV for fast flows), does not exhibit a power-law shape due to transverse momentum dependent escapes. Out of this range, the confinement is not so efficient and the spectrum cut-off above few hundreds of GeV, questioning the Chandra observations of X-ray knots as being synchrotron radiation. The extension to full time dependent simulations to X-ray extragalactic jets is discussed.Comment: Astronomy & Astrophysics (in press), 18 page

Fluid and solid phases of the Gaussian core model

We study the structural and thermodynamic properties of a model of point particles interacting by means of a Gaussian pair potential first introduced by Stillinger [Stillinger F H 1976 J. Chem. Phys. 65, 3968]. By employing integral equation theories for the fluid state and comparing with Monte Carlo simulation results, we establish the limits of applicability of various common closures and examine the dependence of the correlation functions of the liquid on the density and temperature. We employ a simple, mean-field theory for the high density domain of the liquid and demonstrate that at infinite density the mean-field theory is exact and that the system reduces to an `infinite density ideal gas', where all correlations vanish and where the hypernetted chain (HNC) closure becomes exact. By employing an Einstein model for the solid phases, we subsequently calculate quantitatively the phase diagram of the model and find that the system possesses two solid phases, face centered cubic and body centered cubic, and also displays reentrant melting into a liquid at high densities. Moreover, the system remains fluid at all densities when the temperature exceeds 1% of the strength of the interactions.Comment: 22 pages, 10 figure

Acoustic and Large Eddy Simulation studies of azimuthal modes in annular combustion chambers

The objectives of this paper are the description of azimuthal instability modes found in annular combus- tion chambers using two numerical tools: (1) Large Eddy Simulation (LES) methods and (2) acoustic solv- ers. These strong combustion instabilities are difficult to study experimentally and the present study is based on a LES of a full aeronautical combustion chamber. The LES exhibits a self-excited oscillation at the frequency of the first azimuthal eigenmode. The mesh independence of the LES is verified before ana- lysing the nature of this mode using various indicators over more than 100 cycles: the mode is mostly a pure standing mode but it transitions from time to time to a turning mode because of turbulent fluctu- ations, confirming experimental observations and theoretical results. The correlation between pressure and heat release fluctuations (Rayleigh criterion) is not verified locally but it is satisfied when pressure and heat release are averaged over sectors. LES is also used to check modes predicted by an acoustic Helmholtz solver where the flow is frozen and flames are modelled using a Flame Transfer Function (FTF) as done in most present tools. The results in terms of mode structure compare well confirming that the mode appearing in the LES is the first azimuthal mode of the chamber. Moreover, the acoustic solver provides stability maps suggesting that a reduction of the time delay of the FTF would be enough to sta- bilise the mode. This is confirmed with LES by increasing the flame speed and verifying that this modi- fication leads to a damped mode in a few cycles

Effect of dust on Kelvin-Helmholtz instabilities

Dust is present in a large variety of astrophysical fluids, from tori around supermassive black holes to molecular clouds, protoplanetary discs, and cometary outflows. In many such fluids, shearing flows are present, leading to the formation of Kelvin-Helmholtz instabilities (KHI) and changing the properties and structures of the fluid through processes such as mixing and clumping of dust. We investigate how dust changes the growth rates of the KHI in 2D and 3D and how the it redistributes and clumps dust. We investigate if similarities can be found between the structures in 3D KHI and those seen in observations of molecular clouds. We do this by performing numerical hydrodynamical dust+gas simulations with in addition to gas a number of dust fluids. Each dust fluid represents a portion of the particle size-distribution. We study how dust-to-gas mass density ratios between 0.01 and 1 alter the growth rate in the linear phase of the KHI. We do this for a wide range of perturbation wavelengths, and compare these values to the analytical gas-only growth rates. As the formation of high-density dust structures is of interest in many astrophysical environments, we scale our simulations with physical quantities similar to values in molecular clouds. Large differences in dynamics are seen for different grain sizes. We demonstrate that high dust-to-gas ratios significantly reduce the growth rate of the KHI, especially for short wavelengths. We compare the dynamics in 2D and 3D simulations, where the latter demonstrates additional full 3D instabilities during the non-linear phase, leading to increased dust densities. We compare the structures formed by the KHI in 3D simulations with those in molecular clouds and see how the column density distribution of the simulation shares similarities with log-normal distributions with power-law tails sometimes seen in observations of molecular clouds.Comment: 14 pages, 20 figure

Generating functionals, consistency, and uniqueness in the integral equation theory of liquids

We discuss and illustrate through numerical examples the relations between generating functionals, thermodynamic consistency (in particular the virial-free energy one), and uniqueness of the solution, in the integral equation theory of liquids. We propose a new approach for deriving closures automatically satisfying such characteristics. Results from a first exploration of this program are presented and discussed.Comment: 27 pages, 5 figure