arXiv subjects

Nikolaus A. Adams

Publications and source records attributed to Nikolaus A. Adams.

At least 19 recordsLinked to original sources

arXiv2026

A conservative Godunov-type mesh-free hydrodynamics scheme for weakly compressible multiphase flows

We present a Godunov-type mesh-free hydrodynamics scheme for the numerical simulation of weakly compressible single- and multiphase flows. The method employs a consistent second-order spatial reconstruction of the primitive variables at the inter-particle interface, applies slope limiting, and solves the moving Riemann problem using a subsonic HLLC approximate Riemann solver. Particles are advected with a quasi-Lagrangian material velocity incorporating an inherent self-relaxation mechanism that suppresses the formation of anisotropic particle distributions. Near material interfaces, one-sided renormalized gradients are used to handle density discontinuities and slope limiting is applied for each phase independently. The Lagrangian character of material interfaces is preserved by constraining the relaxation mechanism to act tangentially to the interface. For same-phase particle interactions, the Riemann problem is centered at the arithmetic mean of the two material velocities. For cross-phase interactions, it is centered at the contact-wave velocity. This choice naturally eliminates spurious mass fluxes across phase boundaries. The methodology is validated on a set of challenging benchmarks, including the inviscid Taylor-Green vortex, material interface advection, surface gravity waves near hydrostatic equilibrium, the Kelvin-Helmholtz instability, and the Rayleigh-Taylor instability under gravitational stratification.

physics.flu-dyn↗

arXiv2026

A Quantum-Classical Surrogate Model for the Collision Operator of the Lattice Boltzmann Method

We introduce a hybrid approach utilising a quantum machine learning surrogate model to approximate the non-linear collision dynamics of the LBM. It effectively offloads the non-unitary operations that challenge pure quantum solvers. The expressivity of the surrogate is built on the ability of parameterised quantum circuits to implement partial Fourier series, with data re-uploading extending the spectrum of representable frequencies. Unlike previous approaches with a fixed relaxation parameter, the surrogate recovers the complete Bhatnagar-Gross-Krook (BGK) collision dynamics across the full physically admissible range of relaxation without retraining. We reassess the relevance of standard variational quantum circuit (VQC) metrics, including expressibility, entanglement, and effective dimension, by relating them directly to task-specific surrogate performance and identifying the key architectural parameters that determine approximation accuracy. The proposed surrogate is validated against the classical BGK collision operator using established benchmark problems, including the Taylor-Green vortex for evaluating energy dissipation and the double shear layer for assessing shear-driven instabilities and nonlinear flow evolution. Our results demonstrate that the hybrid model achieves high accuracy and generalisability while closely replicating classical solutions. These findings suggest that hybrid quantum-classical strategies offer a practical path toward realising the potential of quantum computing in fluid engineering.

quant-ph↗

arXiv2026

A fully GPU-based workflow for building physics emulators of hypersonic flows

The ability to resolve complex physical phenomena with high fidelity and at low computational cost is central to addressing key challenges in modern engineering. A prime example lies in hypersonic flows, where the precise prediction of the full flowfield topology, in particular with respect to shock wave location and intensity, is critical. Yet supersonic and hypersonic flows continue to be a stumbling block for traditional reduced-order models and neural emulators that struggle to capture steep gradients in flow states with physical consistency in applications of industrial relevance. To that end, we introduce a fully GPU based workflow that integrates accelerated data generation with the training of neural emulators augmented by uncertainty quantification and physics-aware refinement. Our workflow is enabled by a differentiable high-fidelity solver (JAX-Fluids) which we employ for rapid dataset creation and residual-based improvement of the neural emulator to enhance physical consistency. Building on this framework, we first present a suite of model architectures and analyze their scaling behavior to expose their strengths and shortcomings. We then show that residual-based refinement enables training on cases where only mesh and input parameters are available, substantially reducing residuals and improving physical consistency. Together, differentiable simulation and residual-based refinement yield physics emulators that remain reliable beyond their training distribution, a key requirement for deploying surrogates in real-world engineering design loops.

cs.LG↗

arXiv2026

Tensor Network Lattice Boltzmann Method for Data-Compressed Fluid Simulations

Resolving unsteady transport phenomena in geometrically complex domains is traditionally constrained by polynomial scaling of computational cost with spatial resolution. While methods based on tensor-network data representations or matrix-product states (MPS) data encodings have emerged as a technique to systematically reduce degrees of freedom, existing formulations do not extend to complex geometries and complex flow physics. Both capabilities are offered by lattice Boltzmann methods, for which we develop a generalized MPS formulation. This development marks a paradigm shift from classical methods that rely on explicit grid refinement for data reduction. Instead, our approach exploits non-local correlations in the MPS representation to systemically compress the global fluid state directly without modifying the underlying grid. We benchmark the proposed solver against classical LBM using three-dimensional flows through structured media and vascular geometries. The results confirm that the MPS formulation reproduces the reference solution with high fidelity while achieving compression ratios exceeding two orders of magnitude, positioning tensor networks or MPS encodings as a scalable paradigm for continuum mechanics on high-performance GPU hardware.

physics.flu-dyn↗

arXiv2026

Hybrid Fourier Neural Operator-Lattice Boltzmann Method

We propose an accelerated computational fluid dynamics framework based on a hybrid Fourier Neural Operator-Lattice Boltzmann Method (FNO-LBM) for steady and unsteady weakly compressible flows. FNO-based initialization significantly accelerates LBM in reaching steady-states of porous media flows across all macroscopic fields, achieving up to 70% speed-up in convergence of density and more than 40% of pressure-drop while preserving the final steady-state accuracy. Simulations of unsteady flows can be accelerated by hybrid coupling strategies that employ FNO rollouts embedded into LBM time advancement in a way of super-time-stepping. Global and time-resolved error metrics across 100 trajectories for generic 2D flows demonstrate that hybridization consistently improves accuracy and stabilizes long-horizon rollouts. Best efficiency is achieved for a lightweight 2.6M-parameter FNO, which diverges under pure autoregressive rollout but achieves 96-99.8% error reduction under hybrid coupling, matching the predictive capability of a much more expensive 11.2M-parameter model. The hybrid framework enhances predictive fidelity, suppresses error accumulation, and enables small and cheap surrogate models to operate effectively within the same error regime as larger surrogates. These results demonstrate that hybrid neural-operator coupling achieves robust and computationally efficient accelerated LBM while maintaining physically consistent flow evolution.

physics.flu-dyn↗

arXiv2026

Ray-tracing image simulations of transparent objects with complex shape and inhomogeneous refractive index

Optical images of transparent three-dimensional objects can be different from a replica of the object's cross section in the image plane due to refraction at the surface or in the body of the object. Simulations of the object's image are thus needed for the visualization and validation of physical models. We report ray-tracing image simulations that achieved high physical fidelity, reproducing optical behaviors and image features not rendered in previous studies. We replicated brightfield microscopy images of drops with complex shapes and images of pressure and shock waves traveling inside them. For high physical fidelity, the simulations must replicate the spatial and angular distribution of illumination rays, and both the experiment and the simulation must be designed for accurate optical modeling. The simulations are highly sensitive to the properties of the drops and can be used to diagnose and refine fluid dynamics models. The simulated images can also be optimized to extract multiple 3D properties from experimental images. Compared to specialized single-shot 3D imaging methods, this approach has the advantage that it preserves the experimental simplicity, the high resolution, and the visual interpretability characteristic to basic optical imaging. The techniques introduced here are directly applicable to optical microscopy, so they can be used in other fields, such as microfluidics and biology, to expand the type and the accuracy of three-dimensional information that can be extracted from basic optical images.

physics.optics↗

arXiv2026

Temperature transformation recovering the compressible law of the wall for turbulent channel flow

Velocity and temperature distributions are both crucial for modeling compressible wall-bounded turbulent flows. The compressible law of the wall for velocity has been extensively examined through velocity transformations. However, a well-established temperature transformation remains an open issue. We propose new Van Driest type (VD-type) and semi-local type (SL-type) temperature transformation for compressible turbulent channel flow. Our approach is based on an analysis of the momentum and energy balance equations in the overlap layer. It accounts for the influences of mixing length model, the work of the body force, and the turbulent kinetic energy (TKE) flux. The proposed transformations are evaluated using data from direct numerical simulations and wall-resolved large eddy simulations of compressible turbulent channel flow. The SL-type transformation provides better data collapse than the VD-type in the viscous sublayer and buffer layer. With a suitable mixing length model, the SL-type transformed temperature agrees well with the incompressible temperature profile or the extended law of the wall. For the isothermal wall, the integral mean error over the entire boundary layer remains below 2% for most cases, with root mean square value of about 1.7%. The results highlight the importance of mitigating the energy imbalance in the transformation. This work identifies the multi-layer structure of the turbulent TKE flux, which in turn enables approximate models and corresponding simplified yet effective temperature transformations. Applications of the proposed approach in near-wall modeling and inverse transformation, as well as its potential extension to more general configurations, are also discussed.

physics.flu-dyn↗

arXiv2025

Flux-controlled wall model for large eddy simulation integrating the compressible law of the wall

Recent advances in velocity and temperature transformations have enabled recovery of the law of the wall in compressible wall-bounded turbulent flows. Building on this foundation, a flux-controlled wall model (FCWM) for Large Eddy Simulation (LES) is proposed. Unlike conventional wall-stress models that solve the turbulent boundary layer equations, FCWM formulates the near-wall modeling as a control problem applied directly to the outer LES solution. It consists of three components: (1) the compressible law of the wall, (2) a feedback flux-control strategy, and (3) a shifted boundary condition. The model adjusts the wall shear stress and heat flux based on discrepancies between the computed and target transformed velocity and temperature, respectively, at the matching location. The proposed wall model is evaluated using LES of turbulent channel flows across a broad range of conditions, including quasi-incompressible cases with bulk Mach number \(M_b = 0.1\) and friction Reynolds number \(Re_τ= 180 \sim 10{,}000\), and compressible cases with \(M_b = 0.74 \sim 4.0\) and bulk Reynolds number \(Re_b = 7667 \sim 34{,}000\). The wall-modelled LES reproduce mean velocity and temperature profiles in agreement with direct numerical simulation data. For all tested cases with \(M_b \leq 3\), the wall model achieves relative errors of \(|ε_{C_f}| < 4.1\%\), \(|ε_{B_q}| < 2.7\%\), and \(|ε_{T_c}| < 2.7\%\) in friction coefficient, non-dimensional heat flux, and centerline temperature, respectively. In the quasi-incompressible regime, the wall model achieves \(|ε_{C_f}| < 1\%\). Compared to the conventional equilibrium wall model, the proposed FCWM achieves higher accuracy in compressible turbulent channel flows without solving the boundary layer equations, thereby reducing computational cost.

physics.flu-dyn↗

arXiv2025

Data-driven shape inference in three-dimensional steady state supersonic flows using ODIL and JAX-Fluids

We present a novel data- and first-principles-driven method for inferring the shape of a solid obstacle and its flow field in three-dimensional steady-state supersonic flows. The method combines the Optimizing a Discrete Loss (ODIL) technique with the automatically differentiable JAX-Fluids CFD solver to jointly reconstruct flow fields and obstacle shapes. ODIL minimizes the discrete residual of the governing PDE via gradient descent-based algorithms and inherits the consistency and stability of the chosen numerical discretization. Discrete residuals and their gradients are computed using JAX-Fluids, which features nonlinear shock-capturing schemes and level-set-based immersed solid boundaries. We validate our method on synthetic data for challenging inverse problems, including shape inference of solid obstacles in 3D steady-state supersonic flows. In particular, we study flow around a cylinder, sphere, and ellipse. Two shape representations are investigated: (1) parametric, where the shape is described by a small set of parameters (e.g., radius of the cylinder or sphere) optimized jointly with the flow field, and (2) free-form, where the level-set function is optimized pointwise over the mesh without predefined shapes. For the parametric case, we provide a detailed comparison with Physics-Informed Neural Networks. We demonstrate that the combination of nonlinear shock-capturing discretization and level-set-based interface representation enables accurate inference of obstacle shapes and flow fields via the ODIL method. This approach opens new avenues for solving complex inverse problems in supersonic aerodynamics.

physics.flu-dyn↗

arXiv2025

Dynamic Circuits for the Quantum Lattice-Boltzmann Method

We propose a quantum algorithm for the linear advection-diffusion equation (ADE) Lattice-Boltzmann method (LBM) that leverages dynamic circuits. Dynamic quantum circuits allow for an optimized collision-operator quantum algorithm, introducing partial measurements as an integral step. Efficient adaptation of the quantum circuit during execution based on digital information obtained through mid-circuit measurements is achieved. The proposed new collision algorithm is implemented as a fully unitary operator, which facilitates the computation of multiple time steps without state reinitialization. Unlike previous quantum collision operators that rely on linear combinations of unitaries, the proposed algorithm does not exhibit a probabilistic failure rate. Moreover, additional qubits no longer depend on the chosen velocity set, which reduces both qubit overhead and circuit complexity. Validation of the quantum collision algorithm is performed by comparing results with digital LBM in one and two dimensions, demonstrating excellent agreement. Performance analysis for multiple time steps highlights advantages compared to previous methods. As an additional variant, a hybrid quantum-digital approach is proposed, which reduces the number of mid-circuit measurements, therefore improving the efficiency of the quantum collision algorithm.

quant-ph↗

arXiv2024

Rational-WENO: A lightweight, physically-consistent three-point weighted essentially non-oscillatory scheme

Conventional WENO3 methods are known to be highly dissipative at lower resolutions, introducing significant errors in the pre-asymptotic regime. In this paper, we employ a rational neural network to accurately estimate the local smoothness of the solution, dynamically adapting the stencil weights based on local solution features. As rational neural networks can represent fast transitions between smooth and sharp regimes, this approach achieves a granular reconstruction with significantly reduced dissipation, improving the accuracy of the simulation. The network is trained offline on a carefully chosen dataset of analytical functions, bypassing the need for differentiable solvers. We also propose a robust model selection criterion based on estimates of the interpolation's convergence order on a set of test functions, which correlates better with the model performance in downstream tasks. We demonstrate the effectiveness of our approach on several one-, two-, and three-dimensional fluid flow problems: our scheme generalizes across grid resolutions while handling smooth and discontinuous solutions. In most cases, our rational network-based scheme achieves higher accuracy than conventional WENO3 with the same stencil size, and in a few of them, it achieves accuracy comparable to WENO5, which uses a larger stencil.

math.NA↗

arXiv2024

Neural SPH: Improved Neural Modeling of Lagrangian Fluid Dynamics

Smoothed particle hydrodynamics (SPH) is omnipresent in modern engineering and scientific disciplines. SPH is a class of Lagrangian schemes that discretize fluid dynamics via finite material points that are tracked through the evolving velocity field. Due to the particle-like nature of the simulation, graph neural networks (GNNs) have emerged as appealing and successful surrogates. However, the practical utility of such GNN-based simulators relies on their ability to faithfully model physics, providing accurate and stable predictions over long time horizons - which is a notoriously hard problem. In this work, we identify particle clustering originating from tensile instabilities as one of the primary pitfalls. Based on these insights, we enhance both training and rollout inference of state-of-the-art GNN-based simulators with varying components from standard SPH solvers, including pressure, viscous, and external force components. All Neural SPH-enhanced simulators achieve better performance than the baseline GNNs, often by orders of magnitude in terms of rollout error, allowing for significantly longer rollouts and significantly better physics modeling. Code available at https://github.com/tumaer/neuralsph.

physics.flu-dyn↗

arXiv2024

JAX-SPH: A Differentiable Smoothed Particle Hydrodynamics Framework

Particle-based fluid simulations have emerged as a powerful tool for solving the Navier-Stokes equations, especially in cases that include intricate physics and free surfaces. The recent addition of machine learning methods to the toolbox for solving such problems is pushing the boundary of the quality vs. speed tradeoff of such numerical simulations. In this work, we lead the way to Lagrangian fluid simulators compatible with deep learning frameworks, and propose JAX-SPH - a Smoothed Particle Hydrodynamics (SPH) framework implemented in JAX. JAX-SPH builds on the code for dataset generation from the LagrangeBench project (Toshev et al., 2023) and extends this code in multiple ways: (a) integration of further key SPH algorithms, (b) restructuring the code toward a Python package, (c) verification of the gradients through the solver, and (d) demonstration of the utility of the gradients for solving inverse problems as well as a Solver-in-the-Loop application. Our code is available at https://github.com/tumaer/jax-sph.

physics.flu-dyn↗

arXiv2024

Unitary Quantum Algorithm for the Lattice-Boltzmann Method

We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium within a single time step. Our quantum algorithm enables the computation of multiple time steps in the linearized case, specifically for solving the advection-diffusion equation, before necessitating a full state measurement. Moreover, our formulation can be extended to compute the non-linear equilibrium distribution function for a single time step prior to measurement, utilizing the measurement as an essential algorithmic step. However, in the non-linear case, a classical postprocessing step is necessary for computing the moments of the distribution function. We validate our algorithm by solving the one dimensional advection-diffusion of a Gaussian hill. Our results demonstrate that our quantum algorithm captures non-linearity.

quant-ph↗

arXiv2024

A generalized hybrid method for surfactant dynamics

In this paper, we develop a generalized hybrid method for both two-dimensional (2-D) and three-dimensional (3-D) surfactant dynamics. While the Navier-Stokes equations are solved by the Eulerian method, the surfactant transport is tracked by a Lagrangian particle method, in which the remeshing technique is employed to prevent particle clustering. For the mass redistribution during remeshing, the redistribution weight is selected with weighted least squares, which shares the theoretical basis of the moving least squares method (MLS) and enables the present hybrid method to work in both 2-D and 3-D cases. This optimized mass redistribution effectively strengthens the robustness of the present hybrid method, as validated by 2-D topological changes of the dumbbell. The conservation, accuracy, and convergence of the present hybrid method have also been validated with both 2-D and 3-D test cases, including a translation circle/sphere, a deformed circle/sphere in the shear flow, and droplet deformation.

physics.comp-ph↗

arXiv2024

Analysis of the particle relaxation method for generating uniform particle distributions in smoothed particle hydrodynamics

We establish a theoretical framework of the particle relaxation method for uniform particle generation of Smoothed Particle Hydrodynamics. We achieve this by reformulating the particle relaxation as an optimization problem. The objective function is an integral difference between discrete particle-based and smoothed-analytical volume fractions. The analysis demonstrates that the particle relaxation method in the domain interior is essentially equivalent to employing a gradient descent approach to solve this optimization problem, and we can extend such an equivalence to the bounded domain by introducing a proper boundary term. Additionally, each periodic particle distribution has a spatially uniform particle volume, denoted as characteristic volume. The relaxed particle distribution has the largest characteristic volume, and the kernel cut-off radius determines this volume. This insight enables us to control the relaxed particle distribution by selecting the target kernel cut-off radius for a given kernel function.

math.NA↗

arXiv2024

JAX-Fluids 2.0: Towards HPC for Differentiable CFD of Compressible Two-phase Flows

In our effort to facilitate machine learning-assisted computational fluid dynamics (CFD), we introduce the second iteration of JAX-Fluids. JAX-Fluids is a Python-based fully-differentiable CFD solver designed for compressible single- and two-phase flows. In this work, the first version is extended to incorporate high-performance computing (HPC) capabilities. We introduce a parallelization strategy utilizing JAX primitive operations that scales efficiently on GPU (up to 512 NVIDIA A100 graphics cards) and TPU (up to 1024 TPU v3 cores) HPC systems. We further demonstrate the stable parallel computation of automatic differentiation gradients across extended integration trajectories. The new code version offers enhanced two-phase flow modeling capabilities. In particular, a five-equation diffuse-interface model is incorporated which complements the level-set sharp-interface model. Additional algorithmic improvements include positivity-preserving limiters for increased robustness, support for stretched Cartesian meshes, refactored I/O handling, comprehensive post-processing routines, and an updated list of state-of-the-art high-order numerical discretization schemes. We verify newly added numerical models by showcasing simulation results for single- and two-phase flows, including turbulent boundary layer and channel flows, air-helium shock bubble interactions, and air-water shock drop interactions.

physics.flu-dyn↗

arXiv2023

LagrangeBench: A Lagrangian Fluid Mechanics Benchmarking Suite

Machine learning has been successfully applied to grid-based PDE modeling in various scientific applications. However, learned PDE solvers based on Lagrangian particle discretizations, which are the preferred approach to problems with free surfaces or complex physics, remain largely unexplored. We present LagrangeBench, the first benchmarking suite for Lagrangian particle problems, focusing on temporal coarse-graining. In particular, our contribution is: (a) seven new fluid mechanics datasets (four in 2D and three in 3D) generated with the Smoothed Particle Hydrodynamics (SPH) method including the Taylor-Green vortex, lid-driven cavity, reverse Poiseuille flow, and dam break, each of which includes different physics like solid wall interactions or free surface, (b) efficient JAX-based API with various recent training strategies and three neighbor search routines, and (c) JAX implementation of established Graph Neural Networks (GNNs) like GNS and SEGNN with baseline results. Finally, to measure the performance of learned surrogates we go beyond established position errors and introduce physical metrics like kinetic energy MSE and Sinkhorn distance for the particle distribution. Our codebase is available at https://github.com/tumaer/lagrangebench .

cs.LG↗