Lagrangian Code Research Articles

Chemical complexity in astrophysical simulations: optimization and reduction techniques

Chemistry plays a key role in the evolution of the interstellar medium, so it is highly important to follow its evolution in numerical simulations. However, it could easily dominate the computational cost when applied to large systems. In this paper we discuss two approaches to reduce these costs: (i) based on computational strategies, and (ii) based on the properties and on the topology of the chemical network. The first methods are more robust, while the second are meant to be giving important information on the structure of large, complex networks. We first discuss the numerical solvers for integrating the system of ordinary differential equations (ODE) associated with the chemical network, and then we propose a buffer method that decreases the computational time spent in solving the ODE system. We further discuss a flux-based method that allows one to determine and then cut on the fly the less active reactions. In addition we also present a topological approach for selecting the most probable species that will be active during the chemical evolution, thus gaining information on the chemical network that otherwise would be difficult to retrieve. This topological technique can also be used as an a priori reduction method for any size network. We implemented these methods into a 1D Lagrangian hydrodynamical code to test their effects: both classes lead to large computational speed-ups, ranging from ×2 to ×5. We have also tested some hybrid approaches finding that coupling the flux method with a buffer strategy gives the best trade-off between robustness and speed-up of calculations.

Grain evolution analysis and experimental validation in the extrusion of 6XXX alloys by use of a lagrangian FE code

The grain size and shape evolution of 6XXX aluminum alloys during hot metal forming processes are investigated by experimental observations and numerical analysis. A unified model is developed to simulate the grain evolution during deformation and subsequent static recrystallization. First, an experimental set reproducing a small scale direct extrusion was realized in order to identify the grain deformation modes and the empirical equations that model the evolution. The equations were then linked with modified formulations of static recrystallization available in literature and then implemented in the lagrangian FE code Deform through user-routines. The developed model innovatively computes all the phases of the phenomena by considering not only the static recrystallization but also the previous deformation phase. Effects of geometric dynamic recrystallization, influence of subgrain size, the dislocation densities distribution and the stored energy on subsequent grain static recrystallization were considered. Then, a reduced scale backward extrusion experiment was performed at different Zener–Hollomon levels, in order to check the model after deformation and after a fully static recrystallization. The model properly predicts both the deformed state of the grains (immediate quenching) and the fully recrystallized state but still miss to predict abnormal grain growth.

Modeling Spray Formation in Gas Turbines—A New Meshless Approach

A new meshless Lagrangian particle code has been developed to tackle the challenging numerical modeling of primary atomization. In doing so the correct treatment and representation of the interfacial physics are crucial prerequisites. Grid based codes using interface tracking or interface capturing techniques, such as the volume of fluid or level set method, exhibit difficulties regarding mass conservation, curvature capturing and interface diffusion. The objective of this work is to overcome these shortcomings of common state-of-the-art grid based approaches. Our multidimensional meshless particle code is based on the smoothed particle hydrodynamics (SPH) method. Various test cases have been conducted, by which the capability of accurately capturing the physics of single and multiphase flows is verified and the future potential of this approach is demonstrated. Compressible as well as incompresssible fluids can be modeled. Surface tension effects are taken into account by two different models. Solid walls as well as periodic boundary conditions offer a broad variety of numerically modeling technical applications. In a first step, single phase calculations of shear driven liquid flows have been carried out. Furthermore, the disintegration of a gravity driven liquid jet emerging from a generic nozzle has been investigated in free surface simulations. The typical formation of a meniscus due to surface tension is observed. Spray formation is qualitatively in good agreement compared to experiments. Finally, the results of a two-phase simulation with a fluid density ratio of 1000, which is similar to a fuel-air fluid system as in airblast atomizers, are presented. The surface minimization and pressure jump across the droplet interface due to surface tension can be predicted accurately. The test cases conducted so far demonstrate the accuracy of the existing code and underline the promising potential of this new method for successfully predicting primary atomization.

A relaxation scheme for hybrid modelling of gas-particle flows

This paper aims at proposing a relaxation scheme that allows to obtain stable approximations for a system of partial differential equations which governs the evolution of the void fraction and the mean velocity in the particle phase of two-phase flows. This system involves the divergence of a particle kinetic tensor, which is provided by a Lagrangian code and whose components are not smooth. The simulation algorithm is based on the combined use of upwinding and relaxation techniques. The main properties of the method are given, together with the Finite Volume Godunov scheme and this approach is compared to an analogous one that was developed earlier. Some measured rates of convergence in L1-norm are provided, for a particular choice of the kinetic tensor. To complete the picture, we present some numerical results obtained when non-smooth external data are provided to the system.

A LAGRANGIAN INTEGRATOR FOR PLANETARY ACCRETION AND DYNAMICS (LIPAD)

We presented the first particle based, Lagrangian code that can follow the collisional/accretional/dynamical evolution of a large number of km-sized planetesimals through the entire growth process to become planets. We refer to it as the 'Lagrangian Integrator for Planetary Accretion and Dynamics' or LIPAD. LIPAD is built on top of SyMBA, which is a symplectic $N$-body integrator. In order to handle the very large number of planetesimals required by planet formation simulations, we introduce the concept of a `tracer' particle. Each tracer is intended to represent a large number of disk particles on roughly the same orbit and size as one another, and is characterized by three numbers: the physical radius, the bulk density, and the total mass of the disk particles represented by the tracer. We developed statistical algorithms that follow the dynamical and collisional evolution of the tracers due to the presence of one another. The tracers mainly dynamically interact with the larger objects (`planetary embryos') in the normal N-body way. LIPAD's greatest strength is that it can accurately model the wholesale redistribution of planetesimals due to gravitational interaction with the embryos, which has recently been shown to significantly affect the growth rate of planetary embryos . We verify the code via a comprehensive set of tests which compare our results with those of Eulerian and/or direct N-body codes.

Tracking of Bubble Trajectories in Vertical Pipes in Bubbly Flow Regime by Coupling Lagrangian, Eulerian and 3D Random Walks Models: Validation with Experimental Data

A set of air-water experiments has been performed under isothermal upward concurrent flow conditions, in a vertical column. The interfacial velocity, the bubble interfacial area and the void fraction distributions have been measured. Numerical simulation of these experiments were performed by coupling a Lagrangian code which tracks the 3D motion of the individual bubbles, with an Eulerian one. In the Eulerian solver the velocity and turbulence fields of the liquid phase were computed by solving the time dependent conservation equations in its Reynolds Averaged Transport Equation form (RANS). The turbulent kinetic energy k, and the dissipation rate transport equations were simultaneously solved by using the k, epsilon model in a (r,z) grid by the finite volume method and the SIMPLER algorithm. Both Lagrangian and Eulerian calculations were performed in parallel and an iterative self-consistent method was developed. The turbulence induced by the bubbles is an important issue considered in this paper, in order to obtain good predictions of the void fraction distribution and the interfacial velocity at different gas and liquid flow conditions. The Eulerian Code was upgraded from an axisymmetric 2D code to a 3D code in order to improve the turbulence solution. The results of the 3D CFD code have been tested and show a good agreement with the experimental results. In this paper special attention is given to the coupling between the different models.

Experiments performed with bubbly flow in vertical pipes at different flow conditions covering the transition region: simulation by coupling Eulerian, Lagrangian and 3D random walks models

Experiments performed with bubbly flow in vertical pipes at different flow conditions covering the transition region: simulation by coupling Eulerian, Lagrangian and 3D random walks modelsTwo phase flow experiments with different superficial velocities of gas and water were performed in a vertical upward isothermal cocurrent air-water flow column with conditions ranging from bubbly flow, with very low void fraction, to transition flow with some cap and slug bubbles and void fractions around 25%. The superficial velocities of the liquid and the gas phases were varied from 0.5 to 3 m/s and from 0 to 0.6 m/s, respectively. Also to check the effect of changing the surface tension on the previous experiments small amounts of 1-butanol were added to the water. These amounts range from 9 to 75 ppm and change the surface tension. This study is interesting because in real cases the surface tension of the water diminishes with temperature, and with this kind of experiments we can study indirectly the effect of changing the temperature on the void fraction distribution. The following axial and radial distributions were measured in all these experiments: void fraction, interfacial area concentration, interfacial velocity, Sauter mean diameter and turbulence intensity. The range of values of the gas superficial velocities in these experiments covered the range from bubbly flow to the transition to cap/slug flow. Also with transition flow conditions we distinguish two groups of bubbles in the experiments, the small spherical bubbles and the cap/slug bubbles. Special interest was devoted to the transition region from bubbly to cap/slug flow; the goal was to understand the physical phenomena that take place during this transition A set of numerical simulations of some of these experiments for bubbly flow conditions has been performed by coupling a Lagrangian code, that tracks the three dimensional motion of the individual bubbles in cylindrical coordinates inside the field of the carrier liquid, to an Eulerian model that computes the magnitudes of continuous phase and to a 3D random walk model that takes on account the fluctuation in the velocity field of the carrier fluid that are seen by the bubbles due to turbulence fluctuations. Also we have included in the model the deformation that suffers the bubble when it touches the wall and it is compressed by the forces that pushes it toward the wall, provoking that the bubble rebound like a ball.

Nonlinear wave propagation and reconnection at magnetic X-points in the Hall MHD regime

The highly dynamical, complex nature of the solar atmosphere naturally implies the presence of waves in a topologically varied magnetic environment. Here, the interaction of waves with topological features such as null points is inevitable and potentially important for energetics. The low resistivity of the solar coronal plasma implies that non-MHD effects should be considered in studies of magnetic energy release in this environment. This paper investigates the role of the Hall term in the propagation and dissipation of waves, their interaction with 2D magnetic X-points and the nature of the resulting reconnection. A Lagrangian remap shock-capturing code (Lare2d) is used to study the evolution of an initial fast magnetoacoustic wave annulus for a range of values of the ion skin depth in resistive Hall MHD. A magnetic null-point finding algorithm is also used to locate and track the evolution of the multiple null-points that are formed in the system. Depending on the ratio of ion skin depth to system size, our model demonstrates that Hall effects can play a key role in the wave-null interaction. In particular, the initial fast-wave pulse now consists of whistler and ion-cyclotron components; the dispersive nature of the whistler wave leads to (i) earlier interaction with the null, (ii) the creation of multiple additional, transient nulls and, hence, an increased number of energy release sites. In the Hall regime, the relevant timescales (such as the onset of reconnection and the period of the oscillatory relaxation) of the system are reduced significantly, and the reconnection rate is enhanced.

Enhancement of Lagrangian slide lines as a combined force and velocity boundary condition

Many hydrodynamical problems involve shear flows along material interfaces. If the materials move along each other but are tied to a single Lagrangian computational mesh without any sliding treatment, severe mesh distortions appear which can eventually cause the failure of the simulation. This problem is usually treated by introducing the sliding line framework into the Lagrangian code. In this paper, we revise the 2D approach described in the article E.J. Caramana, The implementation of slide lines as a combined force and velocity boundary condition, Journal of Computational Physics 228 (2009), and suggest two enhancements – interpolated interaction instead of a simple one-to-one interaction described in the previous article, and a numerical surface tension model improving the stability of the interface. Both improvements stabilize the slide line and lead to more realistic results, as shown on selected numerical examples.

Numerical investigation of magnetic Richtmyer-Meshkov instability

AbstractWe report numerical results of the linear growth of the Richtmyer-Meshkov instability (RMI) in compressible fluids and in the presence of a magnetic field. These results are obtained with the Lagrangian code LPC-MHD in which media are supposed to be compressible ideal gases. We first applied a magnetic field perpendicular to the wave vector and perpendicular to the shock wave propagation and observed no changes on the perturbation growth velocity compared to the case without magnetic field. We also considered the configuration where the magnetic field is parallel to the wave vector. We observed the stabilization of the instability with oscillations of the perturbations amplitude. Numerical results are compared to impulsive acceleration model of the RMI in the presence of a transverse magnetic field, in the non-compressible limit. A good agreement is obtained between numerical results and model for both the amplitude and the frequency of oscillations. Compressibility seems to have negligible effects.

Study of Sand Particle Trajectories and Erosion Into the First Compression Stage of a Turbofan

Aero-engines operating in dusty environments are subject to ingestion of erodent particles leading to erosion damage of blades and a permanent drop in performance. This work concerns the study of particle dynamics and erosion of the front compression stage of a commercial turbofan. Particle trajectories simulations used a stochastic Lagrangian tracking code that solves the equations of motion separately from the airflow in a stepwise manner, while the tracking of particles in different cells is based on the finite element method. As the locations of impacts and rates of erosion were predicted, the subsequent geometry deteriorations were assessed. The number of particles, sizes, and initial positions were specified conformed to sand particle distribution (MIL-E5007E, 0-1000 micrometers) and concentrations 50–700 mg/m3. The results show that the IGV blade is mainly eroded over the leading edge and near hub and shroud; also the rotor blade has a noticeable erosion of the leading and trailing edges and a rounding of the blade tip corners, whereas in the diffuser, erosion is shown to spread over the blade surfaces in addition to the leading edge and trailing edge.

Ash deposition modeling using a visco-elastic approach

In pulverized fuel (PF) combustors and gasifiers, ash particles may deposit on heat exchangers reducing efficiency, performance and, in some cases, damaging boilers and gasifiers. In general, ash particle composition, size (fragmentation) and mechanical properties (hardness and stickiness) are affected by the history of each particle along their trajectory. In the present work, visco-elastic models are used to predict the Young Modulus according to time, temperature and ash composition. In commercial CFD programs, particle adhesion is usually modeled either as fully trapped or bouncing off according to a specific restitution coefficient usually given as input to the wall boundary surface. The authors apply the mechanical adhesion approach proposed by Johnson (JKR theory) which takes into account the surface energy, particle size and the hardness of both the particle and the impacted surface. The energy restitution coefficients are calculated as the remaining kinetic energy after elastic–plastic particle deformation and work of adhesion due to inertia impaction. To implement this approach, a specific Lagrangian particle tracking code was developed to track particle and predict their fate post-processing CFD flow data fields. Numerical results are validated against hollow glass particle and biomass ash experiments carried out in the entrained flow reactor in use at The Energy Research Center of The Netherlands (ECN). Hollow glass particle were used to mimic the high silica content ash obtained from co-firing biomass facilities. The final goal of this work is to present a comprehensive approach to mathematically describe deposition and deposit build-up by means of mechanical and rheological models for visco-elastic solids. Numerical results compare fairly well to available experimental data of the average particle dispersion.

Shock and mechanical response of 2139-T8 aluminum

Planar shock wave experiments were performed on 2139-T8 aluminum to determine its response to dynamic loading. A Hugoniot was determined to 12 GPa. Lateral stress measurements along with a study of the release behavior indicate that this material retains its shear strength to at least 8 GPa. Spall strength was measured for ∼1 μs compressive pulse durations and found to be approximately constant at 1.45 GPa up to shock stresses of 10 GPa. Beyond 10 GPa, spall strength decreases considerably. Uniaxial stress compression tests were conducted with a servo-hydraulic load frame and the Kolsky bar method to obtain stress-strain curves at strain-rates from 0.001/s to 85k/s. This data shows the material is rate independent. The shock experiments were simulated using a Lagrangian finite element code using a polynomial equation of state, the Johnson-Cook strength law, and the Cochran and Banner spall model. The ability of the simulations to reproduce the experimentally measured data is mixed, with significant deviations in modeling the plastic wave front, plastic release, and the spall pull-back signals.

RADIATION-HYDRODYNAMICAL MODELING OF CORE-COLLAPSE SUPERNOVAE: LIGHT CURVES AND THE EVOLUTION OF PHOTOSPHERIC VELOCITY AND TEMPERATURE

We have developed a relativistic, radiation-hydrodynamics Lagrangian code, specifically tailored to simulate the evolution of the main observables (light curve and the evolution of photospheric velocity and temperature) in core-collapse supernova (CC-SN) events. The distinctive features of the code are an accurate treatment of radiative transfer coupled to relativistic hydrodynamics, a self-consistent treatment of the evolution of the innermost ejecta taking into account the gravitational effects of the central compact remnant, and a fully implicit Lagrangian approach to the solution of the coupled nonlinear finite difference system of equations. Our aim is to use it as a numerical tool to perform calculations of a grid of models to be compared with observations of CC-SNe. In this paper, we present some testcase simulations and a comparison with observations of SN 1987A, as well as with the results obtained with other numerical codes. We also briefly discuss the influence of the main physical parameters (ejected mass, progenitor radius, explosion energy, amount of 56Ni) on the evolution of the ejecta, and the implications of our results in connection with the possibility to "standardize" hydrogen-rich CC-SNe for using them as candles to measure cosmological distances.

Numerical Simulation for the Excavation in Tunnel Construction

Tunnel excavation is often done in underground engineering such as civil tunnel construction and mine excavation. The numerical simulation can output colorful results to interpret the tunnel excavation effect more easier. Among all the numerical simulation methods, fast lagrangian explicit finite difference code of continua (FLAC3D) is widely used to solve practical problems, especially in field of elasto-plastic characteristic and construction procedure. So in the present paper, 3 steps of excavations in a tunnel is modeled by FLAC3D to present the stress and displacement distribution, and give guidance for the real practice.

Calibrating Hydrogen-Rich Core-Collapse Supernovae for their Use as Distance Indicators Independent of Type Ia Supernovae

AbstractUsing our new general-relativistic, radiation hydrodynamics, Lagrangian code, we computed a rather extended grid of hydrogen-rich core-collapse supernovae (CC-SNe) models and explored the potentials of their “standardization” as distance indicators. We discuss the properties of some calibrations previously reported in the literature, and present new correlations based on the behavior of the light curve that can be employed for calibrating hydrogen-rich CC-SNe using only photometric data.

Computer Aided Design for Safety Analysis of Excavation in Stratified Rock Tunnel

Stratified rock mass is widely existing in tunnel engineering. The most relevant feature of stratified rocks is the occurrence of very persistent bedding, which makes the rock-mass highly non-isotropic. A number of techniques for designing underground excavations in stratified media have been described in the literature, like theoretical method and laboratory test, which can only be applied in analyzing the problem with simple geometry and costs much expense. Recently, with rapid development of computer technique, numerical simulation methods have been widely applied in engineerin. Among all the numerical simulation methods, fast lagrangian explicit finite difference code of continua (FLAC3D) is widely used to solve practical problems, especially in field of elasto-plastic characteristic, large deformation analysis and construction procedure. So in the present paper, numerical simulation for the failure mode of stratified rock mass after tunnel excavation is done by FLAC3D, which can give further guidance to understand the anisotropic characteristic of stratified rock mass.

Magnetoacoustic shock formation near a magnetic null point

We investigate the interaction of nonlinear fast magnetoacoustic waves with a magnetic null point in connection with the triggering of solar flares. Methods. We model the propagation of fast, initially axisymmetric waves towards a two-dimensional isothermal magnetic null point in terms of ideal magnetohydrodynamic equations. The numerical simulations are carried out with the Lagrangian remap code Lare2D. Results. Dynamics of initially axisymmetric fast pulses of small amplitude is found to be consistent with a linear analytical solution proposed earlier. The increase in the amplitude leads to the nonlinear acceleration of the compression pulse and deceleration of the rarefaction pulse and hence the distortion of the wave front. The pulse experiences nonlinear steepening in the radial direction either on the leading or the back slopes for the compression and rarefaction pulses, respectively. This effect is most pronounced in the directions perpendicular to the field. Hence, the nonlinear evolution of the fast pulse depends on the polar angle. The nonlinear steepening generates the sharp spikes of the electric current density. As in the uniform medium, the position of the shock formation also depends on the initial width of the pulse. Only sufficiently smooth and low-amplitude initial pulses can reach the vicinity of the null point, create there current density spikes, and initiate magnetic reconnection by seeding anomalous electrical resistivity. Steeper and higher amplitude initial pulses overturn at larger distance from the null point, and cannot trigger reconnection.

GRAVITATIONAL FRAGMENTATION OF EXPANDING SHELLS. II. THREE-DIMENSIONAL SIMULATIONS

We investigate the gravitational fragmentation of expanding shells driven by HII regions using the three-dimensional Lagrangian simulation codes based on the Riemann solver, called Godunov smoothed particle hydrodynamics. The ambient gas is assumed to be uniform. In order to attain high resolution to resolve the geometrically thin dense shell, we calculate not the whole but a part of the shell. We find that perturbations begin to grow earlier than the prediction of the linear analysis under the thin-shell approximation. The wavenumber of the most unstable mode is larger than that in the thin-shell linear analysis. The development of the gravitational instability is accompanied by the significant deformation of the contact discontinuity. These results are consistent with a linear analysis presented by Iwasaki et al. (2011) that have taken into account the density profile across the thickness and approximate shock and contact discontinuity boundary conditions. We derive useful analytic formulae for the fragment scale and the epoch when the gravitational instability begins to grow.

HYDRODYNAMICAL MODELS OF TYPE II PLATEAU SUPERNOVAE

We present bolometric light curves of Type II-plateau supernovae (SNe II-P) obtained using a newly developed, one-dimensional Lagrangian hydrodynamic code with flux-limited radiation diffusion. Using our code we calculate the bolometric light curve and photospheric velocities of SN1999em obtaining a remarkably good agreement with observations despite the simplifications used in our calculation. The physical parameters used in our calculation are E=1.25 foe, M= 19 M_\odot, R= 800 R_\odot and M_{Ni}=0.056 M_\odot. We find that an extensive mixing of 56Ni is needed in order to reproduce a plateau as flat as that shown by the observations. We also study the possibility to fit the observations with lower values of the initial mass consistently with upper limits that have been inferred from pre-supernova imaging of SN1999em in connection with stellar evolution models. We cannot find a set of physical parameters that reproduce well the observations for models with pre-supernova mass of \leq 12 M_\odot, although models with 14 M_\odot cannot be fully discarded.