3D Hydrodynamics Research Articles

Simulations of shock generation and propagation in laser-plasmas

AbstractWe analyze the results of a recent experiment performed at the PALS laboratory and concerning ablation pressure at 0.44 µm laser wavelength measured at irradiance up to 2 × 1014 W/cm2. Using the code “ATLANT,” we have performed two-dimensional (2D) hydrodynamics simulations. Results show that 2D effects did not affect the experiment and also give evidence of the phenomenon of delocalized absorption of laser light.

Skill assessment of an integrated modeling system for shallow coastal and estuarine ecosystems

The predictive skills of an integrated physical–biogeochemical modeling system (CH3D-IMS) for shallow estuarine and coastal ecosystems are assessed using available field data in the Indian River Lagoon estuarine system, Florida during 1998–2000. The cornerstone of the modeling system is the circulation model CH3D (Curvilinear-grid Hydrodynamics in 3D), which is coupled to models of wave (SMB), sediment transport, water quality (nutrients: N, P, and Si, three phytoplankton species, zooplankton, and dissolved oxygen), light attenuation, and seagrass. To resolve the complex geometry and bathymetry of the estuarine system, the modeling system uses a boundary-fitted non-orthogonal curvilinear grid in the horizontal direction and a terrain-following sigma grid in the vertical direction. While water level and salinity data were collected continuously (at 15-min intervals) at 10 fixed stations, most water quality data were collected at much longer time scales (bi-weekly to quarterly) during ship surveys at more than 30 stations. Sediment-water quality data were collected at 24 stations once in 1998. Model skills for hydrodynamic and water quality simulations are assessed in terms of the absolute relative errors and the relative operating characteristic (ROC) scores. Both methods indicate that the modeling system has skills in simulating water level, salinity, dissolved oxygen, chlorophyll, and dissolved nutrients, with the ROC score between 0.6 and 0.862, indicating skills for most of the variables. Skills for simulating total suspended solids (TSS) and particulate nutrients are lacking, with ROC score and: between 0.5–0.6. Simulated diffuse attenuation coefficient, which depends on TSS, chlorophyll a, and dissolved organic matter, has an ROC of 0.55. Using high frequency time-varying field data collected during two episodic events in the study period, the skills of CH3D-IMS improved significantly for both TSS and particulate nutrients. Model skills for particulate nutrients are found to be very sensitive to nutrient concentrations in the sediment column which were sampled in 1998. Sensitivity tests were conducted to determine the sensitivity of model skill to bottom boundary condition, open boundary condition, and model parameters/coefficients. Results suggest that model skills can be improved with more detailed sediment-water quality data, addition of a coastal ocean domain, and improved knowledge of model parameters/coefficients. Parameter estimation method (e.g., modified Gauss–Newton method) can be used to reduce the effort required to select optimal model coefficients for the baseline simulation.

Saguenay fjord entrance whale feeding ground: Acoustic study of sill dynamics and tidal aggregation of forage fish

The Saguenay fjord entrance in the St. Lawrence Estuary at Tadoussac is a world famous site where beluga and minke whales can be regularly observed from the coast. Strong tidal upwelling over the shallow sill of the fjord controls the exchanges with the St. Lawrence. In May 2005, an intensive oceanographic and acoustic survey was conducted to understand how the complex 3D hydrodynamics may contribute to concentrating whale preys. High time-space resolution acoustics (38 and 120 kHz split-beam), ADCP (acoustic Doppler current profilers), CTD profiles, plankton and micronekton sampling were used to track the 3D movements of water masses, zooplankton and forage fish. During flood, the dense cold waters that jump over the sill block the Saguenay outflow and subduct into the fjord with their fish and zooplankton content. This complex 3D circulation generates fronts and convergence zones where biomass is concentrating until current reversal occurs during ebb. These concentrations are then advected and dispersed downstream over the sill with the Saguenay surface plume. This whale prey tidal concentrating process depends on the existence of sufficient forage fish densities in the mesoscale neighbourhood. It is likely at the basis of the persistent high frequentation of this area by whales.

A new two-columns description for convective transport in stars

AbstractAssuming that the largest convective patterns generate the majority of convective transport, we devise a numerical scheme simplifying the convective velocity field using two parallel radial columns to represent up- and downstream flows. Horizontal exchange is described by fluid flow and radiation over the interface between those two columns. The main parameters of this convective description have a straightforward geometrical meaning, namely the diameter of the columns (representing the size of the convective cells) and the ratio of cross section between up- and downdrafts. For this geometrical setup, the equations of radiation hydrodynamics are solved time-dependently using an implicit scheme which has the advantage of being devoid of any time step limits. In order to demonstrate our approach, we present comparisons with detailed 2D hydrodynamics computations for the example of convection zones in Cepheids.

Hamiltonian description of dipoles on the plane and sphere

Abstract Poisson bracket for dipoles of ideal 2D hydrodynamics reduces to Zakharov–Faddeev–Gardner bracket by introducing new variables: coordinates of the vorticity extrema and geodesical distances from the poles to the vorticity lines. The new Hamiltonian equations include the well-known two point-vortex system and a decoupled pair of monopoles as asymptotical cases.

Numerical Astrophysics

AbstractE119 3D Simulations of Weakly Magnetized Accretion DisksE147 The MRI in stratified accretion discsE212 Comparison between observed and simulated globular clustersE219 Presentation of simulation results of our 3D PIC CodeE244 MAGMA: A 3D Lagrangian hydrodynamics codeE254 FEARLESS – A new modelling approach for turbulent astrophysical flowsE256 Cosmic ray transport in MHD turbulence: Numerical calculation of Dμμ (μ) and Dμμ (p)E261 FEARLESS modeling of turbulent flows applied to numerical simulations of galaxy clustersE264 FEARLESS – Subgrid Scale Turbulence modeling and Applications to Star Formation

Hydrodynamic description of heavy ion collisions

We give a short review of hydrodynamic models at heavy ion collisions from the point of view of initial conditions, an equation of states (EoS) and a freezeout process. Then we show our latest results of a combined fully three-dimensional macroscopic/microscopic transport approach. In this model for the early, dense, deconfined stage relativistic 3D hydrodynamics of the reaction and a microscopic non-equilibrium model for the later hadronic stage where the equilibrium assumptions are no longer valid are employed. Within this approach we study the dynamics of hot, bulk QCD matter, which is being created in ultra-relativistic heavy ion collisions at RHIC.

The stability of poloidal magnetic fields in rotating stars

The stability of large-scale magnetic fields in rotating stars is explored, using 3D numerical hydrodynamics to follow the evolution of an initial poloidal field. It is found that the field is subject to an instability, located initially on the magnetic equator, whereby the gas is displaced in a direction parallel to the magnetic axis. If the magnetic axis is parallel to the rotation axis, the rotation does not affect the initial linear growth of the instability, but does restrict the growth of the instability outside of the equatorial zone. The magnetic energy decays on a timescale which is a function of the Alfven crossing time and the rotation speed, but short compared to any evolutionary timescale. No evidence is found for a possible stable end state to evolve from an initial axisymmetric poloidal field. The field of an oblique rotator is similarly unstable, in both cases regardless of the rotation speed.

Numerical transport of an arbitrary number of components

This paper deals with the numerical transport of an arbitrary number of materials having the same velocity. One difficulty is to derive numerical algorithms that are conservative for the mass of each component and that satisfy some inequality and equality constraints: each mass fraction has to stay in [0, 1] and the sum of all mass fractions should be 1. These constraints are satisfied by the classical upwind scheme (which is very dissipative) but not for most of nonlinear (high-order or anti-dissipative) schemes. Here we propose local conditions of inequality type for the finite volume fluxes of mass fractions to ensure the aforementioned constraints. More precisely, we give explicit stability intervals for each flux. This is done in the manner of Després and Lagoutière [B. Després, F. Lagoutière, Contact discontinuity capturing schemes for linear advection and compressible gas dynamics, J. Sci. Comput. 16 (4) (2002) 479–524] for hyperbolic systems, Després and Lagoutière [B. Després, F. Lagoutière, Numerical resolution of a two-component compressible fluid model with interfaces, Progress Comput. Fluid Dyn., to appear] for the transport of 2 components; see also Bouchut [F. Bouchut, An anti-diffusive entropy scheme for monotone scalar conservation laws, J. Sci. Comput. 21 (1) (2004) 1–30] for the same type of inequality constraints for nonlinear conservation laws. Comparisons on two dimensional test-cases with the Youngs’ interface reconstruction algorithm [D.L. Youngs, An interface tracking method for a 3D eulerian hydrodynamics code, Technical Report 44/92/35, AWRE, 1984] show that results are qualitatively comparable. The advantages of this approach are its simplicity, its low computational cost, and its flexibility since it can deal with interfaces as well as mixing zones.

Numerical solution of a variational data assimilation problem for a 3D ocean thermohydrodynamics model with a nonlinear vertical heat exchange

We consider a variational data assimilation problem with the aim to reconstruct the initial condition for a 3D ocean hydrodynamics problem with the inclusion of a quasilocal model of vertical heat exchange in the ocean, which is described by a nonstationary heat conduction equation with a nonlinear diffusion coefficient. We develop and justify algorithms for the numerical solution of the problem. We give the results of test calculations using the Indian Ocean as example.

Space-time evolution of bulk QCD matter

We introduce a combined, fully three-dimensional macroscopic/microscopic transport approach employing relativistic 3D hydrodynamics for the early, dense, deconfined stage of the reaction and a microscopic nonequilibrium model for the later hadronic stage where the equilibrium assumptions are no longer valid. Within this approach, we study the dynamics of hot bulk QCD matter, which is being created in ultrarelativistic heavy-ion collisions at the BNL Relativistic Heavy-Ion Collider. Our work is an extension of the well-known hybrid macro+micro approach in 1+1 and 2+1 dimensions, which is capable of self-consistently calculating the freeze-out of the hadronic system while accounting for the collective flow on the hadronization hypersurface generated by the quark-gluon plasma expansion. In particular, we perform a detailed analysis of the reaction dynamics, hadronic freeze-out, and transverse flow.

Numerical Simulations and Astrophysical Applications of Laboratory Jets at Omega

We have conducted experiments on the Omega laser at the University of Rochester that have produced jets of supersonic Ti impacting and being deflected by a ball of high density plastic. These mm-sized jets of dense plasma are highly complex, have large Reynolds numbers, and, given sufficient time and shear, should produce a fully turbulent flow. The experiments are diagnosed with a point-projection backlighter, resulting in a single image per shot. Simulations of the 3D hydrodynamics capture the large-scale features of the experimental data fairly well while missing some of the smaller scale turbulent-like phenomena. This is to be expected given the limited characterization of the targets as well as the finite resolution of the 3D simulations. If Euler scaling holds, these experiments should model larger astrophysical jets in objects such as HH 110 where an outflow can be seen colliding with a molecular cloud. However, Euler scaling demands that not only the isothermal internal Mach numbers of the two systems be similar but also that any dissipative mechanisms, such as radiative cooling or viscous dissipation, be of equal importance relative to each other. Similar equations of state are required as well. We discuss such issues in the context of these experiments and simulations.

Photospheric modeling through spectral line inversion

Aims.We aim to determine average radial stratifications of various physical parameters throughout the solar photosphere at high angular resolution for non-magnetic and magnetic areas and to compare these with standard semiempirical 1D modeling and with 3D hydrodynamics (HD) and magnetohydrodynamics (MHD) simulations.

A physical hydrodynamic 2D model for simulation and scaling of InP/InGaAs(P) DHBTs and circuits with limited complexity

In this paper we demonstrate a physical two-dimensional hydrodynamic (2D HD) model which simulates the DC and AC characteristics of vertically and laterally scaled InP/InGaAs(P) type I double heterojunction bipolar transistors (DHBTs) with state-of-the-art accuracy when compared to experimental data. For the first time, a physical model clearly shows good agreement between simulated and measured circuit data, for example the gate delay of current mode logic (CML) or emitter coupled logic (ECL) ring oscillators of laterally and vertically scaled devices. The deviation of the simulated gate delays of these digital circuits is smaller than 10%. Additionally, the model successfully predicts the circuit performance of experimental frequency dividers and multiplexers. This experimentally verified model can be used to predict and optimize AC and switching characteristics of future generations of aggressively downscaled DHBTs and is a significant advancement in the art of physical and scalable DHBT and circuit modeling. We demonstrate that optimized type I DHBTs approach bit rates towards 235Gb/s with realistic scaling parameters in the near future.

The role of Kelvin-Helmholtz instability in the internal structure of relativistic outflows. The case of the jet in 3C 273

Context. Relativistic outflows represent one of the best-suited tools to probe the physics of AGN. Numerical modelling of internal structure of the relativistic outflows on parsec scales provides important clues about the conditions and dynamics of the material in the immediate vicinity of the central black holes in AGN. Aims. We investigate possible causes of the structural patterns and regularities observed in the parsec-scale jet of the well-known quasar 3C 273. Methods. We present here the results from a 3D relativistic hydrodynamics numerical simulation based on the parameters given for the jet by Lobanov & Zensus (2001, Science, 294, 128), and one in which the effects of jet precession and the injection of discrete components have been taken into account. We compare the model with the structures observed in 3C 273 using very long baseline interferometry and constrain the basic properties of the flow. Results. We find growing perturbation modes in the simulation with similar wavelengths to those observed, but with a different set of wave speeds and mode identification. If the observed longest helical structure is produced by the precession of the flow, longer precession periods should be expected. Conclusions. Our results show that some of the observed structures could be explained by growing Kelvin-Helmholtz instabilities in a slow moving region of the jet. However, we point towards possible errors in the mode identification that show the need of more complete linear analysis in order to interpret the observations. We conclude that, with the given viewing angle, superluminal components and jet precession cannot explain the observed structures.

Analysis of core plasma heating in fast ignition target by two-dimensional Fokker-Planck-Hydro code

To investigate the core plasma heating in fast ignition targets, we recently developed a two-dimensional relativistic Fokker-Planck code for fast electron transport in dense plasmas. In the present study, we have coupled RFP-2D with a 2D hydrodynamics code for bulk plasma and analyzed the core plasma heating by assuming a condition similar to that in the GXII-PW laser experiments at ILE. It was found that when the source beam electrons enter the dense core region with low (< 1 MeV) average energy and a Super-Gaussian spatial distribution, the core plasma can be heated above 0.8 keV at maximum, which is almost the same temperature as measured in the experiments.

Runaway collisions in young star clusters - II. Numerical results

We present a new study of the collisional runaway scenario to form an intermediate-mass black hole (IMBH, M-BH greater than or similar to 100M(circle dot)) at the centre of a young, compact stellar cluster. The first phase is the formation of a very dense central core of massive stars (M-* similar or equal to 30-120M(circle dot)) through mass segregation and gravothermal collapse. Previous work established the conditions for this to happen before the massive stars evolve off the main sequence ( MS). In this and a companion paper, we investigate the next stage by implementing direct collisions between stars. Using a Monte Carlo stellar dynamics code, we follow the core collapse and subsequent collisional phase in more than 100 models with varying cluster mass, size, and initial concentration. Collisions are treated either as ideal, 'sticky-sphere' mergers or using realistic prescriptions derived from 3D hydrodynamics computations. In all cases for which the core collapse happens in less than the MS lifetime of massive stars (similar or equal to 3 Myr), we obtain the growth of a single very massive star (VMS, M-* similar or equal to 400-4000M(circle dot)) through a runaway sequence of mergers. Mass loss from collisions, even for velocity dispersions as high as sigma(v) similar to 1000 km s(-1), does not prevent the runaway. The region of cluster parameter space leading to runaway is even more extended than predicted in previous work because, in clusters with sigma(v) > 300 km s(-1), collisions accelerate (and, in extreme cases, drive) core collapse. Although the VMS grows rapidly to greater than or similar to 1000M(circle dot) in models exhibiting runaway, we cannot predict accurately its final mass. This is because the termination of the runaway process must eventually be determined by a complex interplay between stellar dynamics, hydrodynamics, and the stellar evolution of the VMS. In the vast majority of cases, we find that the time between successive collisions becomes much shorter than the thermal time-scale of the VMS. Therefore, our assumption that all stars return quickly to the MS after a collision must eventually break down for the runaway product, and the stellar evolution of the VMS becomes very uncertain. For the same reason, the final fate of the VMS, including its possible collapse to an IMBH, remains unclear.

Hamiltonian description of monopoles on a rotating sphere

The Poisson bracket for 2D hydrodynamics on a Riemann manifold is considered. For a special class of vorticities a general method is suggested for reducing this bracket to Gardner–Zakharov–Faddeev bracket by changing the functional variable. When applying to a rotating sphere, new Hamiltonian equations are obtained for Rossby monopoles in terms of the vorticity extremum coordinates and the distance from it to the vorticity lines. The equations have clear physical meaning and may be used as a split-up scheme for numerical solution.

Solutions of the 2D quasi-geostrophic equation in Hölder spaces

The 2D quasi-geostrophic equation ∂ t θ + u · ∇ θ + κ ( - Δ ) α θ = 0 , u = R ⊥ ( θ ) is a two-dimensional model of the 3D hydrodynamics equations. When α ⩽ 1 2 , the issue of existence and uniqueness concerning this equation becomes difficult. It is shown here that this equation with either κ = 0 or κ > 0 and 0 ⩽ α ⩽ 1 2 has a unique local in time solution corresponding to any initial datum in the space C r ∩ L q for r > 1 and q > 1 .

Towards a reasoned 1D river model calibration

Model calibration remains a critical step in numerical modelling. After many attempts to automate this task in water-related domains, questions about the actual need for calibrating physics-based models are still open. This paper proposes a framework for good model calibration practice for end-users of 1D hydraulic simulation codes. This framework includes a formalisation of objects used in 1D river hydraulics along with a generic conceptual description of the model calibration process. It was implemented within a knowledge-based system integrating a simulation code and expert knowledge about model calibration. A prototype calibration support system was then built up with a specific simulation code solving subcritical unsteady flow equations for fixed-bed rivers. The framework for model calibration is composed of three independent levels related, respectively, to the generic task, to the application domain and to the simulation code itself. The first two knowledge levels can thus easily be reused to build calibration support systems for other application domains, like 2D hydrodynamics or physics-based rainfall–runoff modelling.