arXiv subjects

Marcel Pfeiffer

Publications and source records attributed to Marcel Pfeiffer.

At least 19 recordsLinked to original sources

arXiv2026

Kinetic modeling of molecular beam formation in a cryogenic buffer-gas cell

Cryogenic buffer-gas cells are widely used to produce cold molecular beams, but the microscopic dynamics governing beam formation remain challenging to model. Here we present fully kinetic simulations of a cryogenic buffer-gas cell using the Direct Simulation Monte Carlo method implemented in the PICLas framework, treating the buffer gas and ablated molecules within a single unified model. We capture characteristic features of cryogenic buffer-gas sources, including plume cooling, directed transport toward the aperture, and the formation of a slow molecular beam, while also resolving energy transfer from the hot ablation plume to the helium buffer gas that is inaccessible to existing approaches relying on the background-gas approximation. Our results demonstrate that fully kinetic simulations can provide detailed insights into buffer-gas cell dynamics and open a route toward a systematic optimization of such sources.

physics.atom-ph↗

arXiv2026

A Multispecies ESBGK Model for Gas Mixtures with Variable Hard Sphere Transport: Theory and Verification

A multi-species Bhatnagar-Gross-Krook (BGK) model for gas mixtures is presented that achieves the correct species-wise relaxation of velocities, temperatures, and pressure tensors according to the Boltzmann collision integral, as well as the correct mixture Prandtl number, while retaining a single relaxation term per species. The model extends the ellipsoidal statistical BGK (ESBGK) model by introducing relative relaxation targets for each species, derived from the Variable Hard Sphere (VHS) production rates of the Grad 13 approximation. Three approaches for the species relaxation frequency are proposed and analyzed: a Grad 13-based per-species frequency, a mixture-averaged frequency, and an empirical harmonic mean of the two. The model is implemented in the particle-based code PICLas and verified against Direct Simulation Monte Carlo (DSMC) results for a range of test cases, including 0D reservoir relaxation, mass diffusion, supersonic Couette flow, and hypersonic flow around a 70{\deg} blunted cone for binary and ternary gas mixtures. Across all test cases, the proposed model reproduces the correct Prandtl number, species temperature, velocity relaxation rates and pressure tensor relaxation, with the empirical relaxation frequency consistently yielding the best agreement with DSMC.

physics.flu-dyn↗

arXiv2026

A harmonically-coupled-anharmonic-oscillator approach for polyatomic chemistry modeling in DSMC

Atmospheric entry processes are characterized by high-enthalpy gas flows in strong thermo-chemical non-equilibrium. Accurate simulations of such conditions remain challenging due to the extreme conditions and the complex influence of internal energy modes. In particular, the common assumption of uncoupled harmonic vibrations may break down, and excited internal energy states can directly influence reaction rates. Previously, an anharmonic oscillator model has been developed by Civrais et al. to improve the accuracy of the Direct Simulation Monte Carlo (DSMC) method under such conditions. However, this extension has so far been limited to diatomic molecules. To increase the accuracy of the DSMC method in the open-source code PICLas, the anharmonic oscillator model is extended to include polyatomic species. The proposed model explicitly considers anharmonic effects and intramolecular energy redistribution. Vibrational degrees of freedom are treated in a local mode basis, in which anharmonic stretching modes are harmonically coupled by harmonic bending modes. The coupling allows for the redistribution of localized vibrational excitation. Dissociation can occur by the strong excitation of a stretching mode, and specific modes can be coupled to the reaction coordinate of the transition state in bimolecular exchange reactions. The newly developed model is evaluated by the comparison to high-fidelity calculations for a set of representative processes. Investigated are different dissociation reactions, which exhibit a high degree of energy redistribution, and the hydrogen-exchange reaction between methane and a hydrogen radical, in which only selected modes contribute to the reactive process. In addition, the recombination-dissociation equilibrium system has been investigated for methane.

physics.chem-ph↗

arXiv2026

Conditional Normalizing Flow for Gas-Surface Scattering from Thermal to Hypersonic Velocities

Accurate aerodynamic modeling of satellites in very low Earth orbit (VLEO) requires gas-surface interaction (GSI) models that capture the full velocity spectrum from thermal to orbital speeds. Atmospheric particles initially strike spacecraft surfaces at hypersonic velocities of 6 000 - 10 000 m/s. Due to surface roughness and complex geometries, especially within air-breathing electric propulsion (ABEP) intake systems, multiple collisions occur, progressively reducing the particle velocities. A recent machine learning framework for deriving scattering kernels from molecular dynamics (MD) simulations has shown promise, but remains limited to high-velocity single impacts and possibly violates fundamental equilibrium principles such as detailed balance. This work extends this machine learning based scattering kernel to cover the complete velocity range using conditional normalizing flows trained with physics-informed constraints, enabling accurate modeling of multi-bounce scenarios in realistic VLEO applications. We train a conditional Real-valued Non-Volume Preserving (cRealNVP) model on expanded molecular dynamics simulations covering velocities from thermal to hypersonic speeds, incorporating a detailed balance loss term. The resulting model demonstrates improved accuracy compared to previous approaches even in the original high-velocity regime, while successfully capturing thermal-velocity scattering. Quantitative assessment shows that thermalization is approximated within acceptable tolerances. This framework provides essential capabilities for accurate ABEP intake optimization and VLEO mission planning while offering a general methodology applicable to broader rarefied gas dynamics problems requiring thermodynamic consistency.

physics.comp-ph↗

arXiv2026

Implementation and Extension of the Variance-Reduced BGK Method in PICLas

Traditional particle-based kinetic methods, such as DSMC, suffer from prohibitive computational cost in low-signal flows, where the deviation from thermodynamic equilibrium is small and statistical noise overwhelms the signal of interest. The Variance-Reduced BGK-DSMC scheme is further advanced and implemented to support this class of flows in the open-source gas-kinetics framework PICLas. Modified versions of flow estimators and collision operators enhancing stability are developed. The Shakhov and Ellipsoidal Statistical models for BGK are demonstrated, along with entirely new features such as adaptive equilibria, variable particle weights and domain axisymmetry. The implementation is validated using synthetic benchmarks, 1D, 2D and axisymmetric simulations. Comparison of VRBGK to BGK simulations shows exact agreement of the models. A further comparison with an analytical solution of thermal transpiration in a microchannel showcases the low-signal efficiency of the method as well as newly proposed features.

physics.flu-dyn↗

arXiv2026

A P-Adaptive Hybridizable Discontinuous Galerkin Spectral Element Method for Electrostatic Particle-in-Cell Simulations

This paper presents a p-adaptive high-order hybridizable discontinuous Galerkin spectral element method (HDG-SEM) for solving the Poisson equation in electrostatic plasma simulations using particle-in-cell (PIC) schemes. This approach enables element-local refinement of the polynomial degree, concentrating computational effort specifically in regions with strong gradients. Thus, the method significantly reduces the global number of degrees of freedom compared to uniform high-order methods. The proposed method is implemented in the open-source framework PICLas and validated through a series of benchmark test cases, including a dielectric sphere and a one-dimensional plasma sheath. Finally, a two-dimensional axisymmetric simulation of an ion optic demonstrates the method's capability to efficiently model complex plasma phenomena but also highlights current limitations.

physics.comp-ph↗

arXiv2026

A Shakhov-based Bhatnagar-Gross-Krook model for polyatomic molecules and for atomic as well as polyatomic mixtures

The implementation of the Shakhov Bhatnagar-Gross-Krook (SBGK) method in the open-source particle code PICLas is extended for modeling of polyatomic molecules, as well as mixtures including atoms and molecules, while accounting for non-equilibrium in the internal degrees of freedom. The conservation properties of the model are shown and the model parameter for the Prandtl number is derived. In order to determine the viscosity and thermal conductivity of gas mixtures, the first approximation of the transport properties using collision integrals is employed. The model is verified with simulation test cases of a supersonic Couette flow and a hypersonic flow around a 70{\deg} blunted cone with different flow parameters and gas compositions. The results are compared to the Direct Simulation Monte Carlo (DSMC) method as well as the Ellipsoidal Statistical BGK (ESBGK) method to assess the accuracy of the model, where overall good agreement is achieved. In particular, the proposed SBGK model captures the shock in front of the 70{\deg} blunted cone more precisely than the ESBGK model.

physics.flu-dyn↗

arXiv2025

A Multi-Species Enskog-Vlasov Solver to Determine Evaporation Coefficients of Fluids in High Pressure Environments

This paper introduces a novel multi-species Enskog-Vlasov solver. It is used to determine evaporation coefficients of fluids under high-pressure conditions, a critical factor for efficient fuel mixing in internal combustion engines. The solver handles collisions for different fluid species separately, thereby accurately capturing species-specific interactions essential for realistic evaporation modeling. A new pair correlation function based on the BMCSL equation of state is employed to enhance modeling accuracy, though compliance with Onsager relations remains to be explored. Validation through various numerical simulations demonstrates the solver's capability. Results from binary fluid relaxation simulations closely match molecular dynamics (MD) data, highlighting accurate collision frequency modeling. Comparative studies against state-of-the-art models verify the solver's precision in predicting liquid-vapor equilibria and evaporation coefficients across diverse pressure scenarios. Detailed simulations of argon-neon mixtures with realistic particle diameters and masses underscore the significant improvements achieved by employing this multi-species approach over traditional single-species methods. Comparisons with the SAFT-VRQ Mie and classical density functional theory confirm the solver's reliability in predicting liquid and vapor compositions and detailed density profiles at interfaces over a wide range of pressures and temperatures. Further analyses illustrate complex dependencies of evaporation and condensation coefficients on temperature and pressure, consistent with existing research findings. Overall, this work advances computational modeling of multi-species evaporation processes in high-pressure environments at different temperatures, providing essential data for improved combustion modeling and broader applications in multi-phase fluid dynamics.

physics.flu-dyn↗

arXiv2025

A Machine Learning Framework for Scattering Kernel Derivation Using Molecular Dynamics Data in Very Low Earth Orbit

The free molecular flow regime in VLEO makes gas-surface interactions (GSIs) crucial for satellite aerodynamic modeling. The Direct Simulation Monte Carlo (DSMC) method is required to estimate aerodynamic forces due to the breakdown of the continuum assumption. In DSMC, the Maxwell model is the most widely used approach for GSI. It simplifies the process by treating it as a superposition of diffuse and specular reflections while assuming a constant accommodation coefficient. In reality, this coefficient is influenced by multiple factors, such as the angle and magnitude of the incident velocity. A high-precision GSI model could significantly improve satellite aerodynamics optimization and the design of efficient intakes for atmospheric breathing propulsion systems. This advancement would greatly refine mission planning and fuel requirement calculations, ultimately extending operational lifetimes and lowering costs. To gain a deep understanding of the GSI at the microscopic level, molecular dynamics (MD) simulations provide valuable insights into the physical processes involved. However, due to computational limitations, simulating an entire satellite is impractical. Instead, we use MD to analyze the impact of selected velocity vectors on a amorphous $\text{Al}_2\text{O}_3$ surface. The obtained scattering kernels for the respective velocity vectors are then used to train a conditional Variational Autoencoder (cVAE). This model is able to generate scattering kernels for any incident velocity vector and can be integrated into DSMC simulations, significantly enhancing their accuracy. Applications of this model on a flat plate have shown that the cVAE is able to predict the shift from diffuse to quasi-specular reflection with increasing polar angle. Additionally, the aerodynamic coefficients and molecular fluxes are considerably different from those obtained with the Maxwell model.

physics.comp-ph↗

arXiv2025

Comparison of stochastic BGK and FP methods for the simulation of non-equilibrium multi-species molecular gas flows

Due to limited possibilities of experimental investigations for non-equilibrium gas flows, numerical results are of highest interest. Although the well-established Direct Simulation Monte Carlo (DSMC) method achieves highly accurate solutions, the computational requirements increase excessively for lower Knudsen regimes. Computationally more efficient simulations can be achieved with stochastic continuum-based methods using either the Bhatnagar-Gross-Krook (BGK) or the Fokker-Planck (FP) approximations where, instead of particle collisions, particle relaxation processes are considered. This paper explains the implementation of different stochastic BGK and FP methods in the open-source particle code PICLas for multi-species molecular gas flows. For verification, the results of different test cases are compared.

physics.comp-ph↗

arXiv2024

Crank-Nicolson BGK Integrator for Multi-Scale Particle-Based Kinetic Simulations

Solving the Bhatnagar-Gross-Krook (BGK) equation with a stochastic particle approach enables efficient and flexible simulations of flows in the transition regime, between continuum and free molecular flow. However, the usual first-order operator splitting between particle movement and relaxation imposes restrictions on the time step, causing the computational cost to increase with the gas density. The Crank-Nicolson stochastic particle BGK (CN-SPBGK) method is introduced here as an advanced particle-based kinetic solver designed for multi-scale gas flow simulations. This method integrates the BGK equation with second-order accuracy across all Knudsen number regimes without requiring additional parameters, while asymptotically preserving the Navier-Stokes flux in the continuum regime. Comparisons with pre-existing particle BGK methods are conducted on several test cases, with CN-SPBGK demonstrating more consistent convergence and accuracy.

physics.flu-dyn↗

arXiv2024

Generalized Treatment of Energy Accommodation in Gas-Surface Interactions for Satellite Aerodynamics Applications

In the context of satellite aerodynamics in the Very-Low-Earth-Orbit (VLEO) regime, accurate modeling of gas-surface interactions (GSI) is crucial for determining aerodynamic forces and torques. Common models such as Sentman's assume that gas particles are reflected diffusely from a surface, which leads to the incorporation of energy accommodation into the model. This technical note discusses the limitations of existing approaches for handling energy accommodation and provides a generalized treatment thereof that is valid for any molecular speed ratio. A new general expression for the temperature ratio of reflected to impinging particles is derived, which, when used in a GSI model, retains its validity even in hypothermal flows. Additionally, a simplified hyperthermal approximation is presented, proven to be an asymptote of the general expression, and shown to be an improvement upon existing approximations by comparison for a realistic VLEO scenario. The results contribute to a better understanding and modeling of GSI, potentially benefiting scientific investigations and operational applications in satellite aerodynamics.

physics.flu-dyn↗

arXiv2023

Multi-species modeling in the particle-based ellipsoidal statistical Bhatnagar-Gross-Krook method including internal degrees of freedom

The implementation of the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) method in the open-source particle code PICLas is extended for multi-species modeling of polyatomic molecules, including internal energies with multiple vibrational degrees of freedom. For this, the models of Mathiaud, Mieussens, Pfeiffer, and Brull are combined. In order to determine the transport coefficients of the gas mixture, Wilke's mixing rules and collision integrals are compared. The implementation is verified with simulation test cases of a supersonic Couette flow as well as a hypersonic flow around a 70{\deg} blunted cone. The solutions of the ESBGK method are compared to the Direct Simulation Monte Carlo (DSMC) method to assess the accuracy, where overall good agreement is achieved. In general, collision integrals should be preferred for the determination of the transport coefficients, since the results using Wilke's mixing rules show larger deviations in particular for large mass ratios. Considering the computational efficiency of the methods, a considerable reduction in computational time is possible with the ESBGK model.

physics.flu-dyn↗

arXiv2023

Fokker-Planck-Poisson kinetics: Multi-phase flow beyond equilibrium

Multi-phase phenomena remain at the heart of many challenging fluid dynamics problems. Molecular fluxes at the interface determine the fate of neighboring phases, yet their closure far from the continuum needs to be modeled. Along the hierarchy of kinetic approaches, a multi-phase particle method is devised in this study. This approach is built closely upon the previous studies on the kinetic method development for dense gasses [Phys. Fluids, 29 (12), 2017] and long-range interactions [J. Comput. Phys, 378, 2019]. It is on this background that the current work on Fokker-Planck-Poisson modeling of multi-phase phenomena is initiated. Molecular interactions are expressed via stochastic forces driven by the white noise, coupled with long-range attractions. The former is local and pursues diffusive approximation of molecular collisions, whereas the latter takes a global feature owing to mean-field forces. The obtained Fokker-Planck-Poisson combination provides an efficient workflow for physics-driven simulations suitable for multi-phase phenomena far from the equilibrium. Besides highlighting the computational efficiency of the method, various archetypical and complex problems ranging from inverted-temperature-gradient between droplets to spinodal decomposition are explored. Detailed discussions are provided on different characteristics of the droplets dispersed in low/high density background gases; including the departure of heat fluxes from Fourier's law as well as droplets growth in spinodal phases.

physics.flu-dyn↗

arXiv2023

Implementation of Asymptotic Preserving Discrete Velocity Methods into the Simulation Code PICLas

The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation allows for efficient flow simulations, especially in the transition regime between continuum and high rarefaction. However, ensuring efficient performances for multiscale flows, in which the Knudsen number varies by several orders of magnitude, is never straightforward. Discrete velocity methods as well as particle-based solvers can each reveal advantageous in different conditions, but not without compromises in specific regimes. This article presents a second-order asymptotic preserving discrete velocity method to solve the BGK equation, with the particularity of maintaining positivity when operations are conducted with the cell-local distribution function. With this procedure based on exponential differencing, it is therefore also possible to construct an adapted version of this second-order method using the stochastic particle approach, as previously presented. The deterministic variant and its implementation are detailed here and its performances are evaluated on several test cases. Combined to the probabilistic solver and with the possibility of a future coupling, our exponential differencing discrete velocity method provides a robust toolbox, useful for efficiently simulating multiscale gas phenomena.

physics.flu-dyn↗

arXiv2022

Hybrid Parallelization of Euler-Lagrange Simulations Based on MPI-3 Shared Memory

The use of Euler-Lagrange methods on unstructured grids extends their application area to more versatile setups. However, the lack of a regular topology limits the scalability of distributed parallel methods, especially for routines that perform a physical search in space. One of the most prominent slowdowns is the search for halo elements in physical space for the purpose of runtime communication avoidance. In this work, we present a new communication-free halo element search algorithm utilizing the MPI-3 shared memory model. This novel method eliminates the severe performance bottleneck of many-to-many communication during initialization compared to the distributed parallelization approach and extends the possible applications beyond those achievable with the previous approach. Building on these data structures, we then present methods for efficient particle emission, scalable deposition schemes for particle-field coupling, and latency hiding approaches. The scaling performance of the proposed algorithms is validated through plasma dynamics simulations of an open-source framework on a massively parallel system, demonstrating an efficiency of up to 80% on 131000 cores.

physics.comp-ph↗

arXiv2022

Optimisation of VLEO Satellite Geometries for Drag Minimisation and Lifetime Extension

The utilisation of the Very Low Earth Orbit (VLEO) region offers significant application specific, technological, operational, and cost benefits. However, attaining sustained and economically viable VLEO flight is challenging, primarily due to the significant, barely predictable and dynamically changing drag caused by the residual atmosphere, which leads to a rapid deterioration of any spacecraft's orbit unless mitigated by a combination of active and passive techniques. This article addresses one passive method by optimising satellite shapes in order to achieve a minimisation of the atmospheric drag force and thus extension of operational lifetime. Contrary to previous investigations in the field, a constant internal volume is maintained to account for the placement of satellite instruments and payload inside the structure. Moreover, the satellite geometry is not varied heuristically but optimised via a numerical 2D profile optimisation specifically developed for this purpose. From the resulting optimal satellite profiles, 3D satellite bodies are derived, which are then verified via the Direct Simulation Monte Carlo method within the open-source particle code PICLas. In addition, rather unconventional designs, i.e. ring geometries, which are based on the assumption of fully specular particle reflections, are proposed and assessed. The optimised satellite geometries offer pure passive lifetime extensions of up to 46 $\%$ compared to a GOCE like reference body, while the above-mentioned ring geometries achieve passive lifetime extensions of more than 3000 $\%$. Finally, the article presents design recommendations for VLEO satellites in dependence of different surface properties.

physics.flu-dyn↗

arXiv2022

An ES-BGK model for diatomic gases with correct relaxation rates for internal energies

We propose a new ES-BGK model for diatomic gases which allows for translational-rotational and translational-vibrational energy exchanges, as given by Landau-Teller and Jeans relaxation equations. This model is consistent with the general definition of the vibrational and rotational collision numbers that are also commonly used in DSMC solvers. It is proved to satisfy the H-theorem and to give the correct transport coefficients, up to the volume viscosity.

physics.flu-dyn↗