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Transmission system operators (TSOs) in recent years have faced challenges in order to ensure maximum transmission capacity of the system to satisfy market needs, while maintaining operational safety and permissible impact on the environment. A great help in the decision-making process was introduced with the Dynamic Thermal Rating (DTR) - an instrument to monitor and predict the maximal allowed ampacity of the power grid based on weather measurements and forecast. However, the introduction of DTR raises a number of questions related to the accuracy and uncertainty of the results of thermal assessment and the level of acceptable risk and its management. In this paper, we present a solution for estimating DTR uncertainty, appropriate for operational use at TSOs. With the help of conductor surface temperature measurements, weather measurements and predicted weather data, we also estimate the error of the weather forecast and the DTR itself. Following the results of the data analyses, we build an operative solution for estimating the ampacity uncertainty based on Monte Carlo random simulations and integrate it into the operational environment of ELES - the operator of the Slovenian electric power transmission network.

We present an algorithm for $hp$-adaptive collocation-based mesh-free numerical analysis of partial differential equations. Our solution procedure follows a well-established iterative solve-estimate-mark-refine paradigm. The solve phase relies on the Radial Basis Function-generated Finite Differences (RBF-FD) using point clouds generated by advancing front node positioning algorithm that supports variable node density. In the estimate phase, we introduce an Implicit-Explicit (IMEX) error indicator, which assumes that the error relates to the difference between the implicitly obtained solution (from the solve phase) and a local explicit re-evaluation of the PDE at hand using a higher order approximation. Based on the IMEX error indicator, the modified Texas Three Step marking strategy is used to mark the computational nodes for $h$-, $p$- or $hp$-(de-)refinement. Finally, in the refine phase, nodes are repositioned and the order of the method is locally redefined using the variable order of the augmenting monomials according to the instructions from the mark phase. The performance of the introduced $hp$-adaptive method is first investigated on a two-dimensional Peak problem and further applied to two- and three-dimensional contact problems. We show that the proposed IMEX error indicator adequately captures the global behaviour of the error in all cases considered and that the proposed $hp$-adaptive solution procedure significantly outperforms the non-adaptive approach. The proposed $hp$-adaptive method stands for another important step towards a fully autonomous numerical method capable of solving complex problems in realistic geometries without the user intervention., Preprint submitted to Computer Methods in Applied Mechanics and Engineering

Medusa, a novel library for implementation of non-particle strong form mesh-free methods, such as GFDM or RBF-FD, is described. We identify and present common parts and patterns among many such methods reported in the literature, such as node positioning, stencil selection, and stencil weight computation. Many different algorithms exist for each part and the possible combinations offer a plethora of possibilities for improvements of solution procedures that are far from fully understood. As a consequence there are still many unanswered questions in the mesh-free community resulting in vivid ongoing research in the field. Medusa implements the core mesh-free elements as independent blocks, which offers users great flexibility in experimenting with the method they are developing, as well as easily comparing it with other existing methods. The article describes the chosen abstractions and their usage, illustrates aspects of the philosophy and design, offers some executions time benchmarks and demonstrates the application of the library on cases from linear elasticity and fluid flow in irregular 2D and 3D domains.

With more than 50 variables, the Biogeochemical Flux Model (BFM) is one of the most advanced and complex marine biogeochemical models available. In addition to several phytoplankton and zooplankton groups, it also includes bacterioplankton, and its modular structure allows for the relatively straightforward addition of new plankton functional types (PFT). The BFM is used in the Copernicus Marine Service products for the Mediterranean Sea and these should provide ideal initial and boundary conditions for more detailed regional studies. Here we present the coupling of the BFM with the Coastal and Regional Ocean COmmunity model (CROCO; based on ROMS_AGRIF and SNH). The latter is a non-hydrostatic, terrain-following, free-surface ocean model with a highly efficient time-stepping algorithm, making it very suitable for high-resolution simulations and topographies with a wide range of depths. The models are directly coupled without an intermediate coupler and can be executed in parallel via Message Passing Interface (MPI). We present the results of an idealized case and these are in a good agreement with a similar configuration of a coupled MITgcm-BFM run (Cossarini et al., 2017). Not surprisingly, the coupled system CROCO-BFM proves to be computationally intensive given the large number of variables, and we explore different speed-up possibilities.

Since the advent of mesh-free methods as a tool for the numerical analysis of systems of Partial Differential Equations (PDEs), many variants of differential operator approximation have been proposed. In this work, we propose a local mesh-free strong-form method that combines the stability of Radial Basis Function-Generated Finite Differences (RBF-FD) with the computational effectiveness of Diffuse Approximation Method (DAM), forming a so-called hybrid method. To demonstrate the advantages of a hybrid method, we evaluate its computational complexity and accuracy of the obtained numerical solution by solving a two-dimensional Poisson problem with an exponentially strong source in the computational domain. Finally, we employ the hybrid method to solve a three-dimensional Boussinesq's problem on an isotropic half-space and show that the implementation overhead can be justified., Splitech 2022, Confernce paper

The actinomycete Amycolatopsis japonicum is the producer of the chelating compound [S,S]-ethylenediamine-disuccinc acid (EDDS). [S,S]-EDDS is an isomer of ethylenediamine-tetraacetic acid (EDTA), an economically important chelating compound that suffers from an extremely poor degradability. Frequent use of the persistent EDTA in various industrial and domestic applications has caused an accumulation of EDTA in soil as well as in aqueous environments. As a consequence, EDTA is the highest concentrated anthropogenic compound present in water reservoirs. The [S,S]-form of EDDS has chelating properties similar to EDTA, however, in contrast to EDTA it is readily biodegradable. In order to compete with the cost-effective chemical synthesis of EDTA, we aimed to optimize the biotechnological production of [S,S]-EDDS in A. japonicum by using metabolic engineering approaches. Firstly, we integrated several copies of the [S,S]-EDDS biosynthetic genes into the chromosome of A. japonicum and replaced the native zinc responsive promoter with the strong synthetic constitutive promoter SP44*. Secondly, we increased the supply of O-phospho-serine, the direct precursor of [S,S]-EDDS. The combination of these approaches together with the optimized fermentation process led to a significant improvement in [S,S]-EDDS up to 9.8 g/L with a production rate of 4.3 mg/h/g DCW.

The grain envelope model (GEM) describes the growth of envelopes of dendritic crystal grains during solidification. Numerically the growing envelopes are usually tracked using an interface capturing method employing a phase field equation on a fixed grid. Such an approach describes the envelope as a diffuse interface, which can lead to numerical artefacts that are possibly detrimental. In this work, we present a sharp-interface formulation of the GEM that eliminates such artefacts and can thus track the envelope with high accuracy. The new formulation uses an adaptive meshless discretization method to solve the diffusion in the liquid around the grains. We use the ability of the meshless method to operate on scattered nodes to accurately describe the interface, i.e., the envelope. The proposed algorithm combines parametric surface reconstruction, meshless discretization of parametric surfaces, global solution construction procedure and partial differential operator approximation using monomials as basis functions. The approach is demonstrated on a two-dimensional h-adaptive solution of diffusive growth of dendrites and assessed by comparison to a conventional diffuse-interface fixed-grid GEM., 6 pages, conference preprint

In this paper, we present a novel parallel dimension-independent node positioning algorithm that is capable of generating nodes with variable density, suitable for meshless numerical analysis. A very efficient sequential algorithm based on Poisson disc sampling is parallelized for use on shared-memory computers, such as modern workstations with multi-core processors. The parallel algorithm uses a global spatial indexing method with its data divided into two levels, which allows for an efficient multi-threaded implementation. The addition of bootstrapping enables the algorithm to use any number of parallel threads while remaining as general as its sequential variant. We demonstrate the algorithm performance on six complex 2- and 3-dimensional domains, which are either of non-rectangular shape or have varying nodal spacing or both. We perform a run-time analysis of the algorithm, to demonstrate its ability to reach high speedups regardless of the domain and to show how well it scales on the experimental hardware with 16 processor cores. We also analyse the algorithm in terms of the effects of domain shape, quality of point placement, and various parallelization overheads.

The development of Dynamic Thermal Rating (DTR) systems for transmission lines in recent years has led to a better and safer utilization of the existing transmission network, as it, for most cases, enables transmission capacity of lines to be increased above the traditionally used static thermal rating value, when weather conditions are favourable. Yet, on-site measurements in the Slovenian system have also shown that many sites are regularly subject to conditions of very limited or even no winds, causing the line rating to fall well below the static value. In those conditions, the natural convective cooling can surpass forced convective cooling and correctly assessing natural convective cooling becomes crucial for the Transmission System Operators (TSO). Different mathematical models deal with natural convective cooling in different ways. Moreover, references have emerged that claim that cooling due to the natural convection gives the same results as with forced convection at 0.6 m/s crossing wind. To clarify the thermal behaviour of power lines when no external wind is present, this paper employs thermo-fluid simulation of natural convection and compares it with laboratory measurements for two different conductors. The results are also compared with CIGRE, IEEE and IEC guidelines.

The decay of jellyfish blooms introduces a significant organic matter source to the local marine environment that has still an unknown impact on the ecosystem. In recent laboratory experiments, authors studied how the introduction of excess organic material affects the coastal pelagic microbiome by introducing Aurelia aurita detritus to jars of seawater. During these experiments they have monitored bacterial abundance, amino acids' concentrations, dissolved organic carbon, as well the build-up of some inorganic nutrients. They have found, that about half of the protein-rich organic matter in jellyfish detritus is almost instantly available to microbes as dissolved organic matter. Based on this experimental data we devised a mathematical model of the jellyfish proteins (amino acids) degradation caused by marine bacteria. The model is built on top of the Monod bacterial growth model and the Luedeking-Piret metabolite production model. In addition, we incorporated the bacterial populations' age to model the lag phase as well as bacterial decay. In this paper, we demonstrate that with the proposed model, we can sufficiently describe the laboratory measurements. Keywords-bacterial growth; Monod model; Luedeking-Piret model; jellyfish

We present numerical computation of stresses under fretting fatigue conditions derived from closed form expressions. The Navier-Cauchy equations, that govern the problem, are solved with strong and weak form meshless numerical methods. The results are compared to the solution obtained from well-established commercial package ABAQUS, which is based on finite element method (FEM). The results show that the weak form meshless solution exhibits similar behavior as the FEM solution, while, in this particular case, strong form meshless solution performs better in capturing the peak in the surface stress. This is of particular interest in fretting fatigue, since it directly influences crack initiation. The results are presented in terms of von Mises stress contour plots, surface stress profiles, and the convergence plots for all three methods involved in the study.

In this paper we investigate the impact of model and measurement uncertainties on the state-estimation results for different estimators, and different measurement configurations in a three-phase distribution network. To obtain all the sensitivities of interest, the approach with a perturbation of the Karush–Kuhn–Tucker conditions was implemented. We express the sensitivities obtained in terms of uncertainty intervals rather than just partial derivatives. We also propose an upper error bound on the interval analysis. The presented approach has been used in a real-world scenario within the SUNSEED FP7 project to design the measurement configuration for a targeted state-estimation system’s accuracy.

Domain discretization is an essential part of the solution procedure in numerical simulations. Meshless methods simplify the domain discretization to positioning of nodes in the interior and on the boundary of the domain. However, generally speaking, the shape of the boundary is often undefined and thus needs to be constructed before it can be discretized with a desired internodal spacing. Domain shape construction is far from trivial and is the main challenge of this paper. We tackle the simulation of moving boundary problems where the lack of domain shape information can introduce difficulties. We present a solution for 2D surface reconstruction from discretization points using cubic splines and thus providing a surface description anywhere in the domain. We also demonstrate the presented algorithm in a simulation of phase-change-like problem.

The Radial Basis Function-generated finite differences became a popular variant of local meshless strong form methods due to its robustness regarding the position of nodes and its controllable order of accuracy. In this paper, we present a GPU accelerated numerical solution of Poisson’s equation on scattered nodes in 2D for orders from 2 up to 6. We specifically study the effect of using different orders on GPU acceleration efficiency.

Local meshless methods obtain higher convergence rates when RBF approximations are augmented with monomials up to a given order. If the order of the approximation method is spatially variable, the numerical solution is said to be p-refined. In this work, we employ RBF-FD approximation method with polyharmonic splines augmented with monomials and study the numerical properties of p-refined solutions, such as convergence orders and execution time. To fully exploit the refinement advantages, the numerical performance is studied on a Poisson problem with a strong source within the domain.

Point sampling in interiors and on surfaces of 3D bodies has important applications in computer graphics, visualization and physical simulations. Some of those application require certain statistical properties of the generated sample, but many don’t and it is often only desired that the final points are distributed quasi regularly, with approximately equal distances to the neighboring points. We present a parallel version of an algorithm for point sampling that supports generation of locally regular point sets, but with globally variable point spacing. The behavior of the algorithm is show-cased on interiors and surfaces of 2D and 3D models. The speedups of the parallel execution are also reported.

In this chapter, the local sensitivities of the estimated state variables with respect to the uncertain line lengths and inaccurate (pseudo-) measurements in a three-phase distribution network for different measurement configurations and different estimators are investigated. The approach with a perturbation of the KKT conditions, which is agnostic to the choice of the estimator, is presented and implemented. The analysis was performed for a full three-phase branch-network model. The implemented estimators were the LAV, WLS, and SHGM. Based on the results and the selected optimization criterion, the optimal estimator is proposed.

Methods for the numerical solution of different state estimators are reviewed in this chapter. The MLE and WLS estimators can be solved directly using the Gauss–Newton or Newton–Raphson method, while the SHGM can be solved using the IRLS, which also leverages the Gauss–Newton method. We show that with the Gauss–Newton or Newton–Raphson method, the least squares problem with the normal equations can be successfully solved. Since the normal equations have a significant effect on the conditioning of the system, Hachtel’s augmented-matrix method that mitigates the intrinsic ill-conditioning of the normal equations was reviewed. In addition, in this chapter the implementation and performance evaluation of different state estimation methods on the proposed unified three-phase branch model is also presented. In order to apply the numerical solution to our problem, first, the partial derivatives with respect to the state variables were calculated. Numerical simulations were performed for all estimators, with different measurement configurations on the IEEE test feeder networks with 13 and 123 buses.

Domain discretization is considered a dominant part of solution procedures for solving partial differential equations. It is widely accepted that mesh generation is among the most cumbersome parts of the FEM analysis and often requires human assistance, especially in complex 3D geometries. When using alternative mesh-free approaches, the problem of mesh generation is simplified to the problem of positioning nodes, a much simpler task, though still not trivial. In this paper we present an algorithm for generation of nodes on arbitrary $d$-dimensional surfaces. This algorithm complements a recently published algorithm for generation of nodes in domain interiors, and represents another step towards a fully automated dimension-independent solution procedure for solving partial differential equations. The proposed algorithm generates nodes with variable density on surfaces parameterized over arbitrary parametric domains in a dimension-independent way in $O(N\log N)$ time. It is also compared with existing algorithms for generation of surface nodes for mesh-free methods in terms of quality and execution time.

This paper deals with a numerical solution of an incompressible Navier-Stokes flow on non-uniform domains. The numerical solution procedure comprises the Meshless Local Strong Form Method for spatial discretization, explicit time stepping, local pressure-velocity coupling and an algorithm for positioning of computational nodes inspired by Smoothed Particles Hydrodynamics method. The presented numerical approach is demonstrated by solving a lid driven cavity flow and backward facing step problems, first on regular nodal distributions up to 315,844 (562 × 562) nodes and then on domain filled with randomly generated obstacles. It is demonstrated that the presented solution procedure is accurate, stable, convergent, and it can effectively solve the fluid flow problem on complex geometries. The results are presented in terms of velocity profiles, convergence plots, and stability analyses.

The transfer capabilities of overhead power lines are often limited by the critical power line temperature that depends on the magnitude of the transferred current and the ambient conditions, i.e. ambient temperature, wind, precipitation, etc. To utilize existing power lines more effectively and more safely concerning the critical power line temperatures and to enforce safety measures during potentially dangerous events, dynamic assessment of the thermal rating is required. In this paper, a Dynamic Thermal Rating model that covers the most important weather phenomena, with special emphasis on rain, is presented. The model considers a dynamic heat generation due to the Joule losses within the conductor and heat exchange with the surrounding in terms of convection, radiation, evaporation, rain impinging and solar heating. The model is validated by comparison of the skin and core temperature of the power line with measurements under realistic environmental conditions.

While pseudospectral (PS) methods can feature very high accuracy, they tend to be severely limited in terms of geometric flexibility. Application of global radial basis functions overcomes this, however at the expense of problematic conditioning (1) in their most accurate flat basis function regime, and (2) when problem sizes are scaled up to become of practical interest. The present study considers a strategy to improve on these two issues by means of using hybrid radial basis functions that combine cubic splines with Gaussian kernels. The parameters, controlling Gaussian and cubic kernels in the hybrid RBF, are selected using global particle swarm optimization. The proposed approach has been tested with radial basis-pseudospectral method for numerical approximation of Poisson, Helmholtz, and Transport equation. It was observed that the proposed approach significantly reduces the ill-conditioning problem in the RBF-PS method, at the same time, it preserves the stability and accuracy for very small shape parameters. The eigenvalue spectra of the coefficient matrices in the improved algorithm were found to be stable even at large degrees of freedom, which mimic those obtained in pseudospectral approach. Also, numerical experiments suggest that the hybrid kernel performs significantly better than both pure Gaussian and pure cubic kernels., Accepted in Engineering Analysis With Boundary Elements (2017). For better understanding of this work, see also arXiv:1512.07584