Lagrangian particle method for compressible fluid dynamics. A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order. The method is generalizable to coupled hyperbolic-elliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.

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This dissertation presents the development and validation of the One Dimensional Turbulence ODT multiphase model in the Lagrangian reference frame. ODT is a stochastic model that captures the full range of length and time scales and provides statistical information on fine-scale turbulent- particle mixing and transport at low computational cost.

The flow evolution is governed by a deterministic solution of the viscous processes and a stochastic representation of advection through stochastic domain mapping processes.

The three algorithms for Lagrangian particle transport are presented within the context of the ODT approach. The Type-I and -C models consider the particle -eddy interaction as instantaneous and continuous change of the particle position and velocity, respectively.

The models are applied to the multi-phase flows in the homogeneous decaying turbulence and turbulent round jet. Particle dispersion, dispersion coefficients, and velocity statistics are predicted and compared with experimental data. The models accurately reproduces the experimental data sets and capture particle inertial effects and trajectory crossing effect.

A new adjustable particle parameter is introduced into the ODT model, and sensitivity analysis is performed to facilitate parameter estimation and selection. A novel algorithm of the two-way momentum coupling between the particle and carrier phases is developed in the ODT multiphase model.

Momentum exchange between the phases is accounted for through particle source terms in the viscous diffusion. The source term is implemented in eddy events through a new kernel transformation and an iterative procedure is required for eddy selection. This model is applied to a particle -laden turbulent jet flow, and simulation results are compared with experimental measurements.

The effect of particle addition on the velocities of the gas phase is investigated. The development of. Stochastic modeling of Lagrangian accelerations.

It is shown how Sawford's second-order Lagrangian stochastic model Phys. Fluids A 3, , for fluid- particle accelerations can be combined with a model for the evolution of the dissipation rate Pope and Chen, Phys. Fluids A 2, , to produce a Lagrangian stochastic model that is consistent with both the measured distribution of Lagrangian accelerations La Porta et al. The later condition is found not to be satisfied when a constant dissipation rate is employed and consistency with prescribed acceleration statistics is enforced through fulfilment of a well-mixed condition.

The main objective of this study was to investigate the capabilities of the receptor-oriented inverse mode Lagrangian Stochastic Particle Dispersion Model LSPDM with the km resolution Mesoscale Model 5 MM5 wind field input for the assessment of source identification from seven regions impacting two receptors located in the eastern United States.

The analysis included four 7-day summertime events in ; residence times in the modeling domain were computed from the inverse LSPDM runs and HYPSLIT-simulated backward trajectories started from receptor-source heights of , , , , and m. The improvement of using the LSPDM is also seen in the overall normalized root mean square error values of 0. The HYSPLIT backward trajectories generally tend to underestimate near-receptor sources because of a lack of stochastic dispersion of the backward trajectories and to overestimate distant sources because of a lack of treatment of dispersion.

Additionally, the HYSPLIT backward trajectories showed a lack of consistency in the results obtained from different single vertical levels for starting the backward trajectories. Target Lagrangian kinematic simulation for particle -laden flows. The target Lagrangian kinematic simulation method was motivated as a stochastic Lagrangian particle model that better synthesizes turbulence structure, relative to stochastic separated flow models. By this method, the trajectories of particles are constructed according to synthetic turbulent-like fields, which conform to a target Lagrangian integral timescale.

In addition to recovering the expected Lagrangian properties of fluid tracers, this method is shown to reproduce the crossing trajectories and continuity effects, in agreement with an experimental benchmark. Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows. In this paper, we establish a set of criteria which are applied to discuss various formulations under which Lagrangian stochastic models can be found.

These models are used for the simulation of fluid particles in single-phase turbulence as well as for the fluid seen by discrete particles in dispersed turbulent two-phase flows. The purpose of the present work is to provide guidelines, useful for experts and non-experts alike, which are shown to be helpful to clarify issues related to the form of Lagrangian stochastic models.

A central issue is to put forward reliable requirements which must be met by Lagrangian stochastic models and a new element brought by the present analysis is to address the single- and two-phase flow situations from a unified point of view.

For that purpose, we consider first the single-phase flow case and check whether models are fully consistent with the structure of the Reynolds-stress models. In the two-phase flow situation, coming up with clear-cut criteria is more difficult and the present choice is to require that the single-phase situation be well-retrieved in the fluid-limit case, elementary predictive abilities be respected and that some simple statistical features of homogeneous fluid turbulence be correctly reproduced.

This analysis does not address the question of the relative predictive capacities of different models but concentrates on their formulation since advantages and disadvantages of different formulations are not always clear. Indeed, hidden in the changes from one structure to another are some possible pitfalls which can lead to flaws in the construction of practical models and to physically unsound numerical calculations.

A first interest of the present approach is illustrated by considering some models proposed in the literature and by showing that these criteria help to assess whether these Lagrangian stochastic models can be regarded as acceptable descriptions. A second interest is to indicate how future. Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics. In Holm Holm Proc.

A , Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map.

We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation.

To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow. PubMed Central. Numerical considerations for Lagrangian stochastic dispersion models: Eliminating rogue trajectories, and the importance of numerical accuracy.

When Lagrangian stochastic models for turbulent dispersion are applied to complex flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behavior in the numerical solution. This paper discusses numerical considerations when solving the Langevin-based particle velo Lagrangian particles with mixing. Simulating scalar transport. The physical similarity and mathematical equivalence of continuous diffusion and particle random walk forms one of the cornerstones of modern physics and the theory of stochastic processes.

The randomly walking particles do not need to posses any properties other than location in physical space. However, particles used in many models dealing with simulating turbulent transport and turbulent combustion do posses a set of scalar properties and mixing between particle properties is performed to reflect the dissipative nature of the diffusion processes.

We show that the continuous scalar transport and diffusion can be accurately specified by means of localized mixing between randomly walking Lagrangian particles with scalar properties and assess errors associated with this scheme.

Particles with scalar properties and localized mixing represent an alternative formulation for the process, which is selected to represent the continuous diffusion. Simulating diffusion by Lagrangian particles with mixing involves three main competing requirements: minimizing stochastic uncertainty, minimizing bias introduced by numerical diffusion, and preserving independence of particles. These requirements are analyzed for two limited cases of mixing between two particles and mixing between a large number of particles.

The problem of possible dependences between particles is most complicated. This problem is analyzed using a coupled chain of equations that has similarities with Bogolubov-Born-Green-Kirkwood-Yvon chain in statistical physics. Dependences between particles can be significant in close proximity of the particles resulting in a reduced rate of mixing.

This work develops further ideas introduced in the previously published letter [Phys. Fluids 19, ]. Fluids 19, ] where modeling of turbulent reacting flows by Lagrangian particles with localized mixing is specifically considered. Lagrangian particle method for compressible fluid dynamics. A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed.

While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order. The method is generalizable to coupled hyperbolic-elliptic systems. As a result, numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are a significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, b a second-order particle -based algorithm that reduces to the first-order upwind method at local extremal points, providing accuracy and long term stability, and c more accurate resolution of entropy discontinuities and states at free interfaces.

Numerical verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows. Matter Lagrangian of particles and fluids. We consider a model where particles are described as localized concentrations of energy, with fixed rest mass and structure, which are not significantly affected by their self-induced gravitational field. We show that the volume average of the on-shell matter Lagrangian Lm describing such particles , in the proper frame, is equal to the volume average of the trace T of the energy-momentum tensor in the same frame, independently of the particle 's structure and constitution.

Since both Lm and T are scalars, and thus independent of the reference frame, this result is also applicable to collections of moving particles and, in particular, to those which can be described by a perfect fluid.

Our results are expected to be particularly relevant in the case of modified theories of gravity with nonminimal coupling to matter where the matter Lagrangian appears explicitly in the equations of motion of the gravitational and matter fields, such as f R ,Lm and f R ,T gravity.

In particular, they indicate that, in this context, f R ,Lm theories may be regarded as a subclass of f R ,T gravity. Conventional cloud simulations are based on the Euler method and compute each microphysics process in a stochastic way assuming infinite numbers of particles within each numerical grid.

They therefore cannot provide the Lagrangian statistics of individual particles in cloud microphysics i. We here simulate the entire precipitation process of warm-rain, with tracking individual particles. In that framework, flow motion and scalar transportation are computed with the Euler method, and particle motion with the Lagrangian one.

The LCS tracks particle motions and collision events individually with considering the hydrodynamic interaction between approaching particles with a superposition method, that is, it can directly represent the collisional growth of cloud particles.

It is essential for trustworthy collision detection to take account of the hydrodynamic interaction. In this study, we newly developed a stochastic model based on the Twomey cloud condensation nuclei CCN activation for the Lagrangian tracking simulation and integrated it into the LCS.

Coupling with the Euler computation for water vapour and temperature fields, the initiation and condensational growth of water droplets were computed in the Lagrangian way. We applied the integrated LCS for a kinematic simulation of warm-rain processes in a vertically-elongated domain of, at largest, 0. Prescribed updraft at the early stage initiated development of a precipitating cloud. We have confirmed that the obtained bulk statistics fairly agree with those from a conventional spectral-bin scheme for a vertical column.

A Lagrangian stochastic model for aerial spray transport above an oak forest. An aerial spray droplets' transport model has been developed by applying recent advances in Lagrangian stochastic simulation of heavy particles. A two-dimensional Lagrangian stochastic model was adopted to simulate the spray droplet dispersion in atmospheric turbulence by adjusting the Lagrangian integral time scale along the drop trajectory. The other major physical processes affecting the transport of spray droplets above a forest canopy, the aircraft wingtip vortices and the droplet evaporation, were also included in each time step of the droplets' transport.

The model was evaluated using data from an aerial spray field experiment. In generally neutral stability conditions, the accuracy of the model predictions varied from run-to-run as expected. The average root-mean-square error was The model prediction was adequate in two-dimensional steady wind conditions, but was less accurate in variable wind condition. The results indicated that the model can simulate successfully the ensemble; average transport of aerial spray droplets under neutral, steady atmospheric wind conditions.

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## Algebra Anfossi 30

This dissertation presents the development and validation of the One Dimensional Turbulence ODT multiphase model in the Lagrangian reference frame. ODT is a stochastic model that captures the full range of length and time scales and provides statistical information on fine-scale turbulent- particle mixing and transport at low computational cost. The flow evolution is governed by a deterministic solution of the viscous processes and a stochastic representation of advection through stochastic domain mapping processes. The three algorithms for Lagrangian particle transport are presented within the context of the ODT approach. The Type-I and -C models consider the particle -eddy interaction as instantaneous and continuous change of the particle position and velocity, respectively. The models are applied to the multi-phase flows in the homogeneous decaying turbulence and turbulent round jet.

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## Algebra Maestro

An improved Lagrangian relaxation and dual ascent approach to facility location problems. Hence, an effective method for optimizing the Lagrangian dual function is of utmost importance for obtaining a computational advantage from the simplified Lagrangian dual function. In this paper, we suggest a new dual ascent Our computational results show that the method generally only requires a very few Lagrangian Differentiation, Integration and Eigenvalues Problems. Calogero recently proposed a new and very powerful method for the solution of Sturm-Liouville eigenvalue problems based on Lagrangian differentiation. In this paper, some results of a numerical investigation of Calogero's method for physical interesting problems are presented.

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## Anfossi, Agustín

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