arXiv subjects

Jörg Kuhnert

Publications and source records attributed to Jörg Kuhnert.

6 recordsLinked to original sources

arXiv2026

Meshfree Snow Modelling using a Modified Cam-Clay Approach

Snow is a complex geomaterial whose macroscopic response is governed by density, temperature, and the topology of its evolving microstructure. Its mechanical behavior spans elastic, plastic, viscous, and failure dominated regimes, imposing significant challenges for numerical methods, which intends to simulate large deformations, evolving free surfaces, and complex boundary interactions. This work presents the first integration of a Modified Cam-Clay constitutive formulation for snow into a purely meshfree strong-form collocation framework based on the Generalized Finite Difference Method. The main methodological contribution is a numerical coupling that combines a global implicit mixed formulation for pressure and velocity with a constitutive return-mapping algorithm. The hydrostatic pressure contribution is obtained from a Poisson equation and subsequently corrected through the Modified Cam-Clay return-mapping procedure, while the deviatoric response is treated semi-implicitly using a numerical viscosity formulation. This partitioned treatment of the volumetric and deviatoric stress contributions enables stable simulations with comparatively large time steps while producing smooth spatial pressure fields. As a result, forces on complex boundary geometries can be evaluated accurately. Numerical results of this coupling illustrate the algorithmic stability of the framework, the effective imposition of boundary conditions, and the suitability of local spatial refinement. The feasibility of applying the framework to vehicle-snow interaction through rigid-body coupling is also illustrated. The presented formulation provides a robust basis for future simulations of dynamic snow loading on vehicle structures.

math.NA↗

arXiv2026

Boundary treatment algorithms for meshfree RANS turbulence modeling

In this paper, we propose improved wall-treatment strategies for meshfree methods applied to turbulent flows. The goal is to enhance wall-function handling in simulations of high-Reynolds-number turbulent flows and to understand the performance of turbulence models within these frameworks. While wall-function techniques are well established for mesh-based methods, their implementation in meshfree methods faces unique challenges. The main difficulties arise from scattered point distributions and dynamic point movement in Lagrangian frameworks. To address these issues, we evaluate a baseline closest-neighbor approach alongside two novel techniques: the nearest-band neighbor (NBN) method and the shifted boundary (SB) method. The NBN method enforces wall functions on a band of interior points, helping to maintain uniform point selection. On the other hand, the SB method virtually moves boundary points to a fixed wall-normal distance, eliminating the spatial noise associated with point movement. We evaluate these methods using turbulence closures: Spalart--Allmaras, $k-\varepsilon$, and $k-ω$ turbulence models. These methods are validated on 1D Couette flow, a turbulent flat plate, and a 3D NACA 0012 airfoil at high Reynolds numbers. Results demonstrate that both novel methods outperform the standard closest-neighbor approach on flat geometries. For flat plates, the SB method provides stability and perfectly smooth $y^+$ distributions. However, when applied to a curved NACA 0012 profile, the NBN method proves to be robust and flexible. In contrast, the SB method exhibits setbacks in numerical diffusion and premature flow separation on curved geometries. This is due to uncorrected normal-vector shifting and adverse pressure gradients. This work establishes the NBN method as a reliable, robust foundation for simulating turbulent flows over practical geometries using meshfree methods.

physics.flu-dyn↗

arXiv2024

Higher-Order Generalized Finite Differences for Variable Coefficient Diffusion Operators

We present a novel approach of discretizing variable coefficient diffusion operators in the context of meshfree generalized finite difference methods. Our ansatz uses properties of derived operators and combines the discrete Laplace operator with reconstruction functions approximating the diffusion coefficient. Provided that the reconstructions are of a sufficiently high order, we prove that the order of accuracy of the discrete Laplace operator transfers to the derived diffusion operator. We show that the new discrete diffusion operator inherits the diagonal dominance property of the discrete Laplace operator. Finally, we present the possibility of discretizing anisotropic diffusion operators with the help of derived operators. Our numerical results for Poisson's equation and the heat equation show that even low-order reconstructions preserve the order of the underlying discrete Laplace operator for sufficiently smooth diffusion coefficients. In experiments, we demonstrate the applicability of the new discrete diffusion operator to interface problems with point clouds not aligning to the interface and numerically show first-order convergence.

math.NA↗

arXiv2023

Parameter Identification by Deep Learning of a Material Model for Granular Media

Classical physical modelling with associated numerical simulation (model-based), and prognostic methods based on the analysis of large amounts of data (data-driven) are the two most common methods used for the mapping of complex physical processes. In recent years, the efficient combination of these approaches has become increasingly important. Continuum mechanics in the core consists of conservation equations that -- in addition to the always necessary specification of the process conditions -- can be supplemented by phenomenological material models. The latter are an idealized image of the specific material behavior that can be determined experimentally, empirically, and based on a wealth of expert knowledge. The more complex the material, the more difficult the calibration is. This situation forms the starting point for this work's hybrid data-driven and model-based approach for mapping a complex physical process in continuum mechanics. Specifically, we use data generated from a classical physical model by the MESHFREE software to train a Principal Component Analysis-based neural network (PCA-NN) for the task of parameter identification of the material model parameters. The obtained results highlight the potential of deep-learning-based hybrid models for determining parameters, which are the key to characterizing materials occurring naturally, and their use in industrial applications (e.g. the interaction of vehicles with sand).

cs.CE↗

arXiv2023

Volume and Mass Conservation in Lagrangian Meshfree Methods

Meshfree Lagrangian frameworks for free surface flow simulations do not conserve fluid volume. Meshfree particle methods like SPH are not mimetic, in the sense that discrete mass conservation does not imply discrete volume conservation. On the other hand, meshfree collocation methods typically do not use any notion of mass. As a result, they are neither mass conservative nor volume conservative at the discrete level. In this paper, we give an overview of various sources of conservation errors across different meshfree methods. The present work focuses on one specific issue: unreliable volume and mass definitions. We introduce the concept of representative masses and densities, which are essential for accurate post-processing especially in meshfree collocation methods. Using these, we introduce an artificial compression or expansion in the fluid to rectify errors in volume conservation. Numerical experiments show that the introduced frameworks significantly improve volume conservation behaviour, even for complex industrial test cases such as automotive water crossing.

physics.flu-dyn↗

arXiv2022

A Meshfree Point Collocation Method for Elliptic Interface Problems

We present a meshfree generalized finite difference method for solving Poisson's equation with a diffusion coefficient that contains jump discontinuities up to several orders of magnitude. To discretize the diffusion operator, we formulate a strong form method that uses a smearing of the discontinuity; and a conservative formulation based on locally computed Voronoi cells. Additionally, we propose a novel conservative formulation for enforcing Neumann boundary conditions that is compatible with the conservative formulation of the diffusion operator. Finally, we introduce a way to switch from the strong form to the conservative formulation to obtain a locally conservative and positivity preserving scheme. The presented numerical methods are benchmarked against four test cases of varying complexity and jump magnitude on point clouds with nodes that are not aligned to the discontinuity. Our results show that the new hybrid method that switches between the two formulations produces better results than the classical generalized finite difference approach for high jumps in diffusivity.

math.NA↗