Higher-Order GFDM for Linear Elliptic Operators

We present a novel approach of discretizing diffusion operators of the form $\nabla\cdot(\lambda\nabla u)$ 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 $\lambda$. 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 and fulfills enrichment properties. Our numerical results for elliptic and parabolic partial differential equations 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 prove first-order convergence

Modeling Intra‐ and Interannual Variability of BVOC Emissions From Maize, Oil‐Seed Rape, and Ryegrass

Air chemistry is affected by the emission of biogenic volatile organic compounds (BVOCs), which originate from almost all plants in varying qualities and quantities. They also vary widely among different crops, an aspect that has been largely neglected in emission inventories. In particular, bioenergy-related species can emit mixtures of highly reactive compounds that have received little attention so far. For such species, long-term field observations of BVOC exchange from relevant crops covering different phenological phases are scarcely available. Therefore, we measured and modeled the emission of three prominent European bioenergy crops (maize, ryegrass, and oil-seed rape) for full rotations in north-eastern Germany. Using a proton transfer reaction–mass spectrometer combined with automatically moving large canopy chambers, we were able to quantify the characteristic seasonal BVOC flux dynamics of each crop species. The measured BVOC fluxes were used to parameterize and evaluate the BVOC emission module (JJv) of the physiology-oriented LandscapeDNDC model, which was enhanced to cover de novo emissions as well as those from plant storage pools. Parameters are defined for each compound individually. The model is used for simulating total compound-specific reactivity over several years and also to evaluate the importance of these emissions for air chemistry. We can demonstrate substantial differences between the investigated crops with oil-seed rape having 37-fold higher total annual emissions than maize. However, due to a higher chemical reactivity of the emitted blend in maize, potential impacts on atmospheric OH-chemistry are only 6-fold higher

Elliptic operators with discontinuous coefficients in meshfree GFDM

peer reviewedIn phase change simulations, material properties such as density, viscosity, or thermal conductivity may exhibit jump discontinuities, possibly of several orders of magnitude. These jump discontinuities represent interfaces between the phases, and they emerge naturally during the simulation; thus, their exact location is generally unknown a priori. Our goal is to simulate phase change processes with a meshfree generalized finite difference method in a monolithic model without distinguishing between the different phases. There, the material properties mentioned above appear as coefficients inside elliptic operators in divergence form and the jumps must be treated adequately by the numerical method. We present a numerical method for discretizing elliptic operators with discontinuous coefficients without the need for a domain decomposition or tracking of interfaces. Our method facilitates the construction of diagonally dominant diffusion operators that lead to M‐matrices for the discrete Poisson's equation, and thus, satisfy the discrete maximum principle. We demonstrate the applicability of the new method for the case of smooth diffusivity and discontinuous diffusivity. We show that the method is first‐order accurate for discontinuous diffusion problems and provides second‐order and fourth‐order convergence for continuous diffusion coefficients

Meshfree one-fluid modeling of liquid–vapor phase transitions

peer reviewedWe introduce a meshfree collocation framework to model the phase change from liquid to vapor at or above the boiling point. While typical vaporization or boiling simulations focus on the vaporization from the bulk of the fluid, here we include the possibility of vaporization from the free surface, when a moving fluid comes into contact with a superheated surface. We present a continuum, one-fluid approach in which the liquid and vapor phases are modeled with the same constitutive equations, with different material properties. The novelty here is a monolithic approach without explicit modeling of the interface between the phases, neither in a sharp nor diffuse sense. Furthermore, no interface boundary conditions or source terms are needed between the liquid and vapor phases. Instead, the phase transition is modeled only using material properties varying with temperature. Towards this end, we also present an enrichment of strong form meshfree generalized finite difference methods (GFDM) to accurately capture derivatives in the presence of jumps in density, viscosity, and other physical properties. The numerical results show a good agreement with experimental results, and highlight the ability of our proposed framework to model phase changes with large jumps

Astrocyte mediated modulation of blood-brain barrier permeability does not correlate with a loss of tight junction proteins from the cellular contacts

In the central nervous system (CNS) complex endothelial tight junctions (TJs) form a restrictive paracellular diffusion barrier, the blood-brain barrier (BBB). Pathogenic changes within the CNS are frequently accompanied by the loss of BBB properties, resulting in brain edema. In order to investigate whether BBB leakiness can be monitored by a loss of TJ proteins from cellular borders, we used an in vitro BBB model where brain endothelial cells in co-culture with astrocytes form a tight permeability barrier for 3H-inulin and 14C-sucrose. Removal of astrocytes from the co-culture resulted in an increased permeability to small tracers across the brain endothelial cell monolayer and an opening of the TJs to horseradish peroxidase as detected by electron microscopy. Strikingly, opening of the endothelial TJs was not accompanied by any visible change in the molecular composition of endothelial TJs as junctional localization of the TJ-associated proteins claudin-3, claudin-5, occludin, ZO-1 or ZO-2 or the adherens junction-associated proteins β-catenin or p120cas did not change. Thus, opening of BBB TJs is not readily accompanied by the complete loss of the junctional localization of TJ protein