271 research outputs found
Lattice Boltzmann method for warm fluid simulations of plasma wakefield acceleration
A comprehensive characterization of lattice Boltzmann (LB) schemes to perform
warm fluid numerical simulations of particle wakefield acceleration (PWFA)
processes is discussed in this paper. The LB schemes we develop hinge on the
moment matching procedure, allowing the fluid description of a warm
relativistic plasma wake generated by a driver pulse propagating in a neutral
plasma. We focus on fluid models equations resulting from two popular closure
assumptions of the relativistic kinetic equations, i.e., the local equilibrium
and the warm plasma closure assumptions. The developed LB schemes can thus be
used to disclose insights on the quantitative differences between the two
closure approaches in the dynamics of PWFA processes. Comparisons between the
proposed schemes and available analytical results are extensively addressed.Comment: 8 figure
Molecular kinetic modelling of non-equilibrium transport of confined van der Waals fluids
A thermodynamically consistent kinetic model is proposed for the non-equilibrium transport of confined van der Waals fluids, where the long-range molecular attraction is considered by a mean-field term in the transport equation, and the transport coefficients are tuned to match the experimental data. The equation of state of the van der Waals fluids can be obtained from an appropriate choice of the pair correlation function. By contrast, the modified Enskog theory predicts non-physical negative transport coefficients near the critical temperature and may not be able to recover the Boltzmann equation in the dilute limit. In addition, the shear viscosity and thermal conductivity are predicted more accurately by taking gas molecular attraction into account, while the softened Enskog formula for hard-sphere molecules performs better in predicting the bulk viscosity. The present kinetic model agrees with the Boltzmann model in the dilute limit and with the Navier-Stokes equations in the continuum limit, indicating its capability in modelling dilute-to-dense and continuum-to-non-equilibrium flows. The new model is examined thoroughly and validated by comparing it with the molecular dynamics simulation results. In contrast to the previous studies, our simulation results reveal the importance of molecular attraction even for high temperatures, which holds the molecules to the bulk while the hard-sphere model significantly overestimates the density near the wall. Because the long-range molecular attraction is considered appropriately in the present model, the velocity slip and temperature jump at the surface for the more realistic van der Waals fluids can be predicted accurately
A kinetic Fokker-Planck algorithm for simulating multiscale gas flows
Numerical, aerodynamic analysis of spacecraft requires the modeling of rarefied hypersonic flows. Such flow regimes are usually dominated by broad shock waves and strong expansion flows. In such areas of the flow the gas is far from its equilibrium state and therefore conventional modeling approaches such as the Euler or Navier-Stokes equations cannot be used. Instead, non-equilibrium modeling approaches must be applied. While most non-equilibrium flow solvers are computationally expensive, a recently introduced kinetic Fokker-Planck (FP) method shows the potential of describing non-equilibrium flows with satisfactory accuracy and, at the same time, significantly reducing computational costs. However, the application of kinetic FP solvers was so far still limited to simple, single species gases.
The aim of this study is to extend the capabilities of the kinetic FP approach for describing complex gas flows. Particular attention is paid to the modeling of non-equilibrium aerodynamics, as it is relevant for describing spacecraft related gas flows.
Methods for describing polyatomic species as well as gas mixtures within the kinetic FP framework are constructed. All models are intensively validated by comparison to already established numerical methods, as well as in comparison to experimental studies.
Excited energy states are modeled by a stochastic jump process described by a master equation. This approach allows the description of both continuous and discrete energy levels. Gas mixtures are modeled based on the hard-sphere and variable hard-sphere collision potentials. For both cases, FP models are constructed for an arbitrary number of species. The efficiency of the described models is investigated and different strategies are proposed to use kinetic FP methods efficiently.
The expansion of synthetic air from an axially symmetric orifice is numerically reproduced using the developed models and results are compared with experimental measurements. Although the numerical simulations capture several magnitudes of Knudsen numbers, from the continuum flow in the reservoir up to the free-molecular far field, good agreement between simulation and experiment is seen
The Effective Mean-Free-Path of the Solar Wind
The high temperature and rarefied ionised gas (plasma) that constitutes the corona of the sun escapes the gravitational bound and flows out into interplanetary space. This plasma is called the solar wind. It is characterised by a long collision mean-free-path (i.e., weakly collisional); it is not in thermodynamic equilibrium. While the plasma is ultimately governed by a kinetic equation, it does appear that the solar wind is described by fluid equations, where it is assumed to be at equilibrium. This is in stark contradiction to the long collision mean-free-path. The suggestion is that collisionless relaxation processes are playing a strong role in dictating the dynamics of the solar wind. These processes are wave-particle interactions that cause the plasma to relax towards equilibrium, i.e., they are effective collision processes. This thesis takes a novel route to measure the effective mean-free-path of the solar wind, by modelling compressive fluctuations of arbitrary effective mean-free-path, and making a robust comparison to solar wind observations. The effective mean-free-path is measured to be approximately 10 times shorter than the collisional mean-free-path. It is shown to be consistent with and justify decades of past solar wind research that use fluid equations. The theory for the numerical model is derived from first principles and is shown to coincide with previous results, and draw together many concepts about compressive plasma waves. The solar wind dataset used in this thesis was not previously used for scientific analysis, so verification of the data quality is demonstrated. In addition, data analysis tools are constructed to measure some of the potential effective collision mechanisms. The analysis is tested on simulation data, to verify the accuracy, by measuring key quantities in identifying the relevant role of various effective collision mechanisms. The analysis of the numerical simulation data is shown to be satisfactory and can be employed on spacecraft data. This measurement resolves a long-standing debate on the utility and accuracy of fluid equations in studying the solar wind. The direct measurement of the effective mean-free-path is important for the field of plasma physics because it dictates the transport and thermodynamics of weakly collisional plasmas
Kinetic modelling of non-equilibrium flow of hard-sphere dense gases
A kinetic model is proposed for the nonequilibrium flow of dense gases composed of hard sphere molecules, which significantly simplifies the collision integral of the Enskog equation using the relaxation time approach. The model preserves the most important physical properties of high density gas systems, including the Maxwellian at rest as the equilibrium solution and the equation of state for hard sphere fluids; all the correct transport coefficients, namely, the shear viscosity, thermal conductivity, and bulk viscosity; and inhomogeneous density distribution in the presence of a solid boundary. The collision operator of the model contains a Shakhov model like relaxation part and an excess part in low order spatial derivatives of the macroscopic flow properties; this latter contribution is used to account for the effect arising from the finite size of gas molecules. The density inhomogeneity in the vicinity of a solid boundary in a confined flow is captured by a method based on the density functional theory. Extensive benchmark tests are performed, including the normal shock structure and the Couette, Fourier, and Poiseuille flow at different reduced densities and Knudsen numbers, where the results are compared with the solutions from the Enskog equation and molecular dynamics simulations. It is shown that the proposed kinetic model provides a fairly accurate description of all these nonequilibrium dense gas flows. Finally, we apply our model to simulate forced wave propagation in a dense gas confined between two plates. The inhomogeneous density near the solid wall is found to enhance the oscillation amplitude, while the presence of bulk viscosity causes stronger attenuation of the sound wave. This shows the importance of a kinetic model to reproduce density inhomogeneity and correct transport coefficients, including bulk viscosity
Synergies between Numerical Methods for Kinetic Equations and Neural Networks
The overarching theme of this work is the efficient computation of large-scale systems. Here we deal with two types of mathematical challenges, which are quite different at first glance but offer similar opportunities and challenges upon closer examination.
Physical descriptions of phenomena and their mathematical modeling are performed on diverse scales, ranging from nano-scale interactions of single atoms to the macroscopic dynamics of the earth\u27s atmosphere. We consider such systems of interacting particles and explore methods to simulate them efficiently and accurately, with a focus on the kinetic and macroscopic description of interacting particle systems.
Macroscopic governing equations describe the time evolution of a system in time and space, whereas the more fine-grained kinetic description additionally takes the particle velocity into account.
The study of discretizing kinetic equations that depend on space, time, and velocity variables is a challenge due to the need to preserve physical solution bounds, e.g. positivity, avoiding spurious artifacts and computational efficiency.
In the pursuit of overcoming the challenge of computability in both kinetic and multi-scale modeling, a wide variety of approximative methods have been established in the realm of reduced order and surrogate modeling, and model compression. For kinetic models, this may manifest in hybrid numerical solvers, that switch between macroscopic and mesoscopic simulation, asymptotic preserving schemes, that bridge the gap between both physical resolution levels, or surrogate models that operate on a kinetic level but replace computationally heavy operations of the simulation by fast approximations.
Thus, for the simulation of kinetic and multi-scale systems with a high spatial resolution and long temporal horizon, the quote by Paul Dirac is as relevant as it was almost a century ago.
The first goal of the dissertation is therefore the development of acceleration strategies for kinetic discretization methods, that preserve the structure of their governing equations. Particularly, we investigate the use of convex neural networks, to accelerate the minimal entropy closure method. Further, we develop a neural network-based hybrid solver for multi-scale systems, where kinetic and macroscopic methods are chosen based on local flow conditions.
Furthermore, we deal with the compression and efficient computation of neural networks. In the meantime, neural networks are successfully used in different forms in countless scientific works and technical systems, with well-known applications in image recognition, and computer-aided language translation, but also as surrogate models for numerical mathematics.
Although the first neural networks were already presented in the 1950s, the scientific discipline has enjoyed increasing popularity mainly during the last 15 years, since only now sufficient computing capacity is available. Remarkably, the increasing availability of computing resources is accompanied by a hunger for larger models, fueled by the common conception of machine learning practitioners and researchers that more trainable parameters equal higher performance and better generalization capabilities. The increase in model size exceeds the
growth of available computing resources by orders of magnitude. Since , the computational resources used in the largest neural network models doubled every months\footnote{\url{https://openai.com/blog/ai-and-compute/}}, opposed to Moore\u27s Law that proposes a -year doubling period in available computing power.
To some extent, Dirac\u27s statement also applies to the recent computational challenges in the machine-learning community. The desire to evaluate and train on resource-limited devices sparked interest in model compression, where neural networks are sparsified or factorized, typically after training. The second goal of this dissertation is thus a low-rank method, originating from numerical methods for kinetic equations, to compress neural networks already during training by low-rank factorization.
This dissertation thus considers synergies between kinetic models, neural networks, and numerical methods in both disciplines to develop time-, memory- and energy-efficient computational methods for both research areas
Lattice Boltzmann Methods for Partial Differential Equations
Lattice Boltzmann methods provide a robust and highly scalable numerical technique in modern computational fluid dynamics. Besides the discretization procedure, the relaxation principles form the basis of any lattice Boltzmann scheme and render the method a bottom-up approach, which obstructs its development for approximating broad classes of partial differential equations. This work introduces a novel coherent mathematical path to jointly approach the topics of constructability, stability, and limit consistency for lattice Boltzmann methods. A new constructive ansatz for lattice Boltzmann equations is introduced, which highlights the concept of relaxation in a top-down procedure starting at the targeted partial differential equation. Modular convergence proofs are used at each step to identify the key ingredients of relaxation frequencies, equilibria, and moment bases in the ansatz, which determine linear and nonlinear stability as well as consistency orders of relaxation and space-time discretization. For the latter, conventional techniques are employed and extended to determine the impact of the kinetic limit at the very foundation of lattice Boltzmann methods. To computationally analyze nonlinear stability, extensive numerical tests are enabled by combining the intrinsic parallelizability of lattice Boltzmann methods with the platform-agnostic and scalable open-source framework OpenLB. Through upscaling the number and quality of computations, large variations in the parameter spaces of classical benchmark problems are considered for the exploratory indication of methodological insights. Finally, the introduced mathematical and computational techniques are applied for the proposal and analysis of new lattice Boltzmann methods. Based on stabilized relaxation, limit consistent discretizations, and consistent temporal filters, novel numerical schemes are developed for approximating initial value problems and initial boundary value problems as well as coupled systems thereof. In particular, lattice Boltzmann methods are proposed and analyzed for temporal large eddy simulation, for simulating homogenized nonstationary fluid flow through porous media, for binary fluid flow simulations with higher order free energy models, and for the combination with Monte Carlo sampling to approximate statistical solutions of the incompressible Euler equations in three dimensions
Explore the Nature of Dark Matter in the Context of Galaxy Formation
The nature of dark matter (DM) is a fundamental question in modern cosmology. Despite its significant role in various physical processes throughout the Universe, the particle nature of DM remains elusive. With the non-detection of classical candidates (e.g. WIMPs), the theoretical space for DM is becoming increasingly open. This thesis revolves around studying the nature of DM in the context of structure formation and we will focus on a category of DM with self-interactions (SIDM), which can be constrained only through astrophysical probes if DM has no coupling with the standard model particles. Utilizing advanced cosmological hydrodynamical simulations, we examine the effects of DM elastic and dissipative self-interactions on galaxy structure and their interplay with baryonic physics processes. Our numerical studies encompass a range of systems, such as Local dwarf galaxies, massive galaxy clusters in the Local Universe, and rare massive quasar-host galaxies at high redshift (z ≳ 6). In Local dwarf galaxies, we analyze the unique signatures of dissipative self-interacting DM (dSIDM) with typical self-interaction cross-section σ/m ~ 0.1-10 cm² g⁻¹ and dissipation factor ~ 0.5. We find a universal cuspy central density profile and systematic changes in halo morphology in dSIDM. By comparing our results with observations, we derive constraints for effective parameters of dSIDM and identify the parameter space where it remains viable and exhibits interesting observational implications. For a similar type of dSIDM with fairly low σ/m ≾ 0.05 cm² g⁻¹, we also explore the possibility that the direct collapse of dSIDM halos at high redshift can seed supermassive black holes and serve as progenitors for massive bright quasars observed at high redshift. This scenario predicts a large population of quiescent supermassive black holes (SMBHs) at high redshift, which could be tested by future LISA observations. Lastly, in Local massive galaxy clusters, we compare the X-ray morphology of hot gas in observed clusters with simulations of elastic SIDM. Although SIDM models with large interaction cross-sections (σ/m ≳ 0.5 cm² g⁻¹) are favored, uncertainties from cooling and feedback physics in galaxy clusters must be taken into account. This thesis summarizes the findings and constraints on DM properties, with a particular emphasis on its potential self-interactions, as derived from a combination of research projects
Layered double hydroxide-derived oxygen carriers for chemical looping processes
In chemical looping combustion, the combustion reaction is split into two sub-reactions linked by metal oxide oxygen carriers to transfer oxygen from the air to the fuel. The oxygen carriers play a crucial role in chemical looping processes and must maintain high performance during extended redox cycling at high temperatures. The preparation of mixed metal oxides (MMOs) via the calcination of layered double hydroxide (LDH) precursors has been shown to achieve a high degree of dispersion of active metal oxide within the support due to the high degree of mixing of metals in the LDH structure. In this thesis, CuO-based oxygen carriers derived from LDHs for chemical looping processes were evaluated.
Novel CuO-based oxygen carriers supported on Al2O3 and MgAl2O4 were developed by tuning the synthetic chemistry of the LDHs prepared via co-precipitation at constant pH. The choice of co-precipitating agent was found to significantly affect the morphology of the LDHs and the dispersion of active CuO in the aluminate support phase in the MMOs. The oxygen carriers supported on MgAl2O4 showed much higher rates of oxygen release and re-oxidation and higher chemical stability than those supported on Al2O3. The co-precipitation pH was determined to be an important parameter for tuning the mechanical properties of the MMOs. An increase in co-precipitation pH from 9.5 to 11 was found to decrease the porosity and increase the crushing strength of the MMOs. The higher-strength MMOs demonstrated near-constant conversion over extended redox cycling in a fluidised bed reactor.
For design, accurate knowledge of the intrinsic kinetics of the oxygen release reaction of the oxygen carriers is needed to scale up chemical looping reactors. The oxygen release kinetics were determined using an adapted effectiveness factor-based kinetic model. An activation energy of 51 ± 3 kJ mol−1 was calculated using an Arrhenius expression, which agreed well with values reported in the literature.
The formation mechanism of the Cu-Mg-Al LDHs was investigated by varying the co-precipitation pH value. The diameter and height of the LDH platelets and porosity of the bulk material were observed to generally decrease with increasing pH, except for LDHs synthesised at pH 10. The large LDH platelet diameters synthesised at pH 10 were attributed to an interplay of supersaturation, thermodynamic and electrostatic factors. The more porous MMOs synthesised at pH 9, 9.5 and 10 showed much higher rates of oxygen release than the less porous materials synthesised at pH 10.5, 11 and 11.5.
In this thesis, the LDH-MMO design strategy was shown to be effective for the development of CuO-based oxygen carriers with extremely high chemical stability and tuneable mechanical properties. The structural diversity of LDHs enables versatile combinations of metal ions to be highly dispersed in their structure, which could inspire the development of highly stable oxygen carriers for many emerging chemical looping processes.Open Acces
Heat equations beyond Fourier: from heat waves to thermal metamaterials
In the past decades, numerous heat conduction models beyond Fourier have been
developed to account for the large gradients, fast phenomena, wave propagation,
or heterogeneous material structure, such as being typical for biological
systems, superlattices, or thermal metamaterials. It became a challenge to
orient among the models, mainly due to their various thermodynamic backgrounds
and possible compatibility issues. Additionally, in light of the recent
findings on the field of non-Fourier heat conduction, it is not even
straightforward how to interpret and utilize a non-Fourier heat equation,
primarily when one aims to thermally design the material structure to construct
the new generation of thermal metamaterials. Adding that numerous modeling
strategies can be found in the literature accompanying different
interpretations even for the same heat equation makes it even more difficult to
orient ourselves and find a comprehensive picture of this field of research.
Therefore, this review aims to ease the orientation among advanced heat
equations beyond Fourier by discussing properties concerning their possible
practical applications in light of experiments. We start from the simplest
model with basic principles and notions, then proceed toward the more complex
models related to coupled phenomena such as ballistic heat conduction. We do
not enter the often complicated technical details of each thermodynamic
framework but do not aim to compare each approach. However, we still briefly
present their background to highlight their origin and the limitations acting
on the models. Additionally, the field of non-Fourier heat conduction has
become quite segmented, and that paper also aims to provide a common ground, a
comprehensive mutual understanding of the basics of each model, together with
what phenomenon they can be applied to
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