Mesh Scheme Research Articles

PyPSA-Earth. A new global open energy system optimization model demonstrated in Africa

Macro-energy system modelling is used by decision-makers to steer the global energy transition towards an affordable, sustainable and reliable future. Closed-source models are the current standard for most policy and industry decisions. However, open models have proven to be competitive alternatives that promote science, robust technical analysis, collaboration and transparent policy decision-making. Yet, two issues slow the adoption: open models are often designed with particular geographic scope in mind, thus hindering synergies from collaborating, or are based on low spatially resolved data, limiting their use. Here we introduce PyPSA-Earth, an open-source global energy system model with data in high spatial and temporal resolution. It enables large-scale collaboration by providing a tool that can model the world’s energy system or any subset of it. The model is suitable for operational as well as combined generation, storage and transmission expansion studies. In this study, the novel power system capabilities of PyPSA-Earth are highlighted and demonstrated. The model provides two main features: (1) customizable data extraction and preparation with global coverage and (2) a PyPSA energy modelling framework integration. The data includes electricity demand, generation and medium to high-voltage networks from open sources, yet additional data can be further integrated. A broad range of clustering and grid meshing strategies help adapt the model to computational and practical needs. Data validation for the entire African continent is performed and the optimization features are tested with a 2060 net-zero planning study for Nigeria. The demonstration shows that the presented developments can build a highly detailed power system model for energy planning studies to support policy and technical decision-making. We anticipate that PyPSA-Earth can represent an open reference model for system planning, and we welcome joining forces to address the challenges of the energy transition together.

A Rational Approach to Meshing Cerebral Venous Geometries for High-Fidelity Computational Fluid Dynamics.

Computational fluid dynamics (CFD) of cerebral venous flows has become popular owing to the possibility of using local hemodynamics and hemoacoustics to help diagnose and plan treatments for venous diseases of the brain. Lumen geometries in low-pressure cerebral veins are different from those in cerebral arteries, often exhibiting fenestrations and flattened or triangular cross section, in addition to constrictions and expansions. These can challenge conventional size-based volume meshing strategies, and the ability to resolve nonlaminar flows. Here we present a novel strategy leveraging estimation of length scales that could be present if flow were to become transitional or turbulent. Starting from the lumen geometry and flow rate boundary conditions, centerlines are used to determine local hydraulic diameters and cross-sectional mean velocities, from which flow length scales are approximated using conventional definitions of local Kolmogorov and Taylor microscales. By inspection of these scales, a user specifies minimum and maximum mesh edge lengths, which are then distributed along the model in proportion to the approximated local Taylor length scales. We demonstrate in three representative cases that this strategy avoids some of the pitfalls of conventional size-based strategies. An exemplary CFD mesh-refinement study shows convergence of high-frequency flow instabilities even starting from relatively coarse edge lengths near the lower bounds of the approximated Taylor length scales. Rational consideration of the length scales in a possibly nonlaminar flow may thus provide a useful and replicable baseline for denovo meshing of complicated or unfamiliar venous lumen geometries.

OPS-ITO: Development of Isogeometric Analysis and Topology Optimization in OpenSEES for Free-Form Structural Design

Unlike the current design routine manually defining geometries for computational analyses, a future-oriented computer-aided design tool can generate a structural model through automated model optimization and iterative analyses. The topology optimization technique uses elemental density variables to formulate a computationally varying model based on analysis results, while an isogeometric analysis could facilitate the automatic iteration without adapting the mesh scheme at each step. This paper aims to bring these capabilities in the open-source simulation platform OpenSEES. The IGAQuad and IGABrick elements using NURBS based shape functions and geometric description are developed in this widely-used finite element modelling framework, which are then ported to a density-based topology optimization module. The modelling capabilities of the IGA elements have been verified using classic problems. The model optimization processes for loaded structural members are demonstrated using 2D and 3D cases, in which the eventually obtained geometric models are fundamentally different from the original boxy shapes but of less material cost and comparable structural performance. Although the development in this paper remains limited, the open-source and modular code infrastructure of OpenSees could facilitate continuous development on the basis of the topology optimization and isogeometric analysis in this paper, aiming for a computational tool to synergize the free form structural design and the advanced construction technologies.

A localized reduced basis approach for unfitted domain methods on parameterized geometries

This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient projection-based ROMs, which rely on techniques such as the reduced basis method and discrete empirical interpolation. The presence of geometrical parameters in unfitted domain discretizations entails challenges for the application of standard ROMs. Therefore, in this work we propose a methodology based on (i) extension of snapshots on the background mesh and (ii) localization strategies to decrease the number of reduced basis functions. The method we obtain is computationally efficient and accurate, while it is agnostic with respect to the underlying discretization choice. We test the applicability of the proposed framework with numerical experiments on two model problems, namely the Poisson and linear elasticity problems. In particular, we study several benchmarks formulated on two-dimensional, trimmed domains discretized with splines and we observe a significant reduction of the online computational cost compared to standard ROMs for the same level of accuracy. Moreover, we show the applicability of our methodology to a three-dimensional geometry of a linear elastic problem.

Effect of Graded Mesh Number on the Solution of Convection-Diffusion Flow Problem with Quadratic Source

Convection-diffusion phenomena are fundamentally modelled in a variety of engineering fields and physical sciences. A suitable meshing strategy is needed in computational fluid dynamics to solve model problems numerically. Unintentional implementation of the approach could lead to subpar solutions such as erroneous oscillations, over- or under-predictions, and excessive computing time. This paper highlights the significance of the influence of mesh structure on the solution of convection-diffusion flow problem with quadratic source for flow parameters of interest. Particularly, it presents the accuracy of the solution of the flow problem at low Peclet number with respect to graded mesh number, where the expansion factor used is based on an established linear logarithmic model involving Peclet number derived in previous works. The problem is solved by assigning several mesh intervals to graded mesh against each Peclet number of interest. Based on the values of the interval and Peclet number, 16 test cases are considered. Quantitative results lead to orders of accuracy of the solution of the flow problem. The effect of graded mesh number on the accuracy thus serves as a reference for a more structured decision-making and improves the heuristic process in choosing the computational domain mesh with expected order of accuracy for the numerical solution of the problem particularly in the calculation of scalar concentration. The orders of accuracy confirm the profiles of concentration.

The Study of the Lift Coefficient of NACA-0012 Airfoil Subjected to an Incompressible Media by Using the Cartesian Cut Cell Method

In order to shorten product design time, engineers need to create high quality meshes within a few days or hours. Newer automated techniques have been published to tackle this need, the Cartesian Cut Cell is one of them. This study is focused on the effect of different Cut Cell meshing strategies on the accuracy of aerodynamic performance predictions. The method can be described as a methodology in which Cut Cells are applied to the geometry utilizing a process involving rectangular/hexagonal cells on a regular lattice cutting through the geometry. The Cut Cell meshing is a general purpose designed for ANSYS FLUENT, making use of Workbench to construct the airfoil shape and the mesh. The results obtained for NACA-0012 are computed using two models available in ANSYS FLUENT, namely the Eq. 2 k-ω SST and the Eq. 3 k-kl-ω models. The three-dimensional numerical simulations were created for steady incompressible flow around NACA-0012 shape. Lift coefficient, Boundary layer thickness, mesh expansion ratio, and mesh density variation parameters were investigated. For this application both models produce good lift results. k-kl-ω produce better lift and the results are close to the measured data. The Cut Cell method showed a very good agreement between Computational Fluid Dynamics results and experimental data. This work illustrated that the Cartesian Cut Cell method has the ability to generate high quality mesh, which captures the details of the viscous boundary layer easily. The future work is to use more sophisticated turbulence models and mesh refinement for air craft wing with flap.

Analysis of Acoustic–Magnetic Fields Induced by Underwater Pressure Wave in a Finite-Depth Ocean

As underwater disturbances (natural or artificial) occur in the ocean, moving seawater crossing the geomagnetic fields will produce weak circular currents. These currents can induce measurable magnetic fields, which might be useful for monitoring ocean internal waves using aeromagnetic survey. In this research, a spectral-element method (SEM) based on Gauss–Lobatto–Legendre (GLL) polynomials is presented to characterize the magnetic field induced by the underwater pressure waves. A concise mathematical model is established through combining the acoustic wave equations and Maxwell’s equations. Specifically, the acoustic–magnetic coupling simulation adopts the nodal-based SEM for acoustic analysis and edge-based SEM for electromagnetic analysis. The proposed SEM has spectral accuracy, as the error exponentially decreases with the order of the basis functions. Additionally, by adopting an independent modeling and mesh scheme in two solvers, respectively, the waste of computing resources is avoided. The experimental analysis demonstrates that the induced magnetic fields mechanically propagate with the acoustic wave, producing the pseudo-radiation phenomenon. The signals of these magnetic fields may extend for tens of kilometers and exist for hours under certain circumstances, which provide a theoretical basis for underwater target identification via high-sensitivity atomic magnetometer.

Finite difference scheme for a non-linear subdiffusion problem with a fractional derivative along the trajectory of motion

Abstract The article is devoted to the construction and study of a finite-difference scheme for a one-dimensional diffusion–convection equation with a fractional derivative with respect to the characteristic of the convection operator. It develops the previous results of the authors from [5, 6] in the following ways: the differential equation contains a fractional derivative of variable order along the characteristics of the convection operator and a quasi-linear diffusion operator; a new accuracy estimate is proved, which singles out the dependence of the accuracy of mesh scheme on the curvature of the characteristics.

Direct embedment of RVE-based microscale into lab size coupons to research fracture process in unidirectional and bidirectional composites

The structural applicability of fibre-reinforced polymer (FRP) composites requires testing for their resilience against fracture. The paper presents a virtual tool to configure the microscale geometrical model constituting the representative volume element embedded in the homogeneous macroscale region, providing an alternative to the tedious experimental procedures. The conformal meshing strategies in the microregion are also elucidated in the paper. The microscale model is enriched with the constitutive material models exhibiting complex phenomena of individual constituents of the composite and cohesive damage properties. The elastoplastic and elastic–viscoplastic material models coupled with the energy-based and rate-dependent damage initiation criteria, respectively, are applied to the matrix. At the same time, the fibre-matrix interface is treated with the weak traction–separation law. Through the virtual tool, the microscale region allows to make an insightful study of the toughness mechanism and visualise the damage initiation and propagation in the FRP structure at different fracture modes.

Numerical investigation on solitary waves traveling over rigid vegetation by a 3D-MPS method

In this study, a three-dimensional wave-vegetation numerical model based on the moving particle semi-implicit (MPS) method is established to investigate the interaction between solitary waves and rigid vegetation. Different from traditional wave-vegetation models, the effect of vegetation in the present numerical model is considered in terms of the stress between fluid and solid particles. Several improvements are put forward to increase the simulation accuracy, including a higher-order pressure gradient discrete model, a multi-term source involving a background mesh scheme, and multi-condition free surface detection. Based on the improved 3D-MPS method, the propagation of solitary waves on a flat bed with and without vegetation is simulated. The results show improvement in resolving the issue of numerical energy dissipation. Because of the intrinsic advantage of the particle method, the attenuation and deformation of a wave on a vegetation area can be realistically reproduced, as can detailed velocity and curl fields. In addition, a parametric study of the effects of wave height, plant relative height, and stem density on the wave attenuation rate is conducted. The result indicates that the relationship between wave attenuation rate and plant height is nonlinear.

A 2.5D automatic FEM-SBM method for the evaluation of free-field vibrations induced by underground railway infrastructures

This paper presents an efficient method to predict underground railway-induced vibrations. The method uses the finite element method (FEM) to model the railway tunnel structure and the singular boundary method (SBM) to model the wave propagation in the surrounding soil. The FEM mesh and the distribution of SBM collocation points at the tunnel/soil interface are generated using an automatic meshing strategy. The presented method is one of the main components of VIBWAY, a user-friendly prediction tool to address railway-induced vibration problems. This paper presents three calculation examples in which the soil response due to forces applied on the tunnel structure are computed in terms of transfer functions. The results obtained for each one of the calculation examples are compared with those computed using a model based on a 2.5D FEM-BEM approach. The presented comparisons show that the proposed approach is a suitable strategy for predicting underground railway-induced vibrations, both in terms of accuracy and computational efficiency. Moreover, the use of an automatic meshing strategy and the SBM formulation not only eases the implementation of the approach but it also makes it easier to use, which is one of the key features of the VIBWAY tool.

Outcomes of Preprocedural Pulmonary Hypertension on All-Cause and Cardiac Mortality in Patients Undergoing Transcatheter Aortic Valve Implantation: A Systematic Review.

Patients with symptomatic aortic stenosis (AS) commonly have an associated finding of pulmonary hypertension (PH), and it has been previously shown to have increased morbidity and mortality following surgical aortic valve repair (SAVR) as well as transcatheter aortic valve implantation (TAVI). There are no guidelines stating the cut-off point for PH at which the patient can safely undergo TAVI with benefits outweighing the risks. This is partly due to the lack of uniformity in the PH definition used in various studies. This systematic review sought to study the effect of preprocedural pulmonary hypertension on early and late all-cause and cardiac mortality in patients undergoing TAVI.We performed a systematic review of studies comparing patients with AS undergoing TAVI having PH. The review was undertaken as per Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. Articles were identified from PubMed, Pubmed Central (PMC), Cochrane, and Medline on January 10, 2022, for literature published until January 10, 2022. MeSH strategy was used on PubMed to search the literature, and filters were applied to search only Observational Studies, randomized controlled trials(RCT), and meta-analysis.A total of 170 unique articles were identified and screened. Of the 33 full-text articles that were reviewed, 18 articles, including duplicates, were excluded. Fifteen articles fulfilled the selection criteria and were included in this review. The study design included two meta-analyses, one randomized control trial, one prospective cohort study, and 11 retrospective cohortstudies.The studies involved a total of approximately 30,000 patients. The observational studies in our review were of good to fair quality, the RCT had a low to moderate bias, and the meta-analysis was of moderate quality. Baseline PH and persistence of PH post-TAVI are strongly associated with all-cause and cardiac mortality. Few studies have shown that a decrease in post-TAVI PH carries mortality benefits. Therefore, efforts should be made to identify mechanisms of persistent PH post-TAVI and whether interventions to reduce PH pre-TAVI will have any clinical implications or not by conducting RCT.

The CFD simulation of E1619 propeller open-water tests validated by the EFD in the NCKU towing tank

Abstract This study established a Computational Fluid Dynamics (CFD) model based on a dynamic mesh strategy to conduct a comprehensive numerical investigation of the performance of the E1619 propeller in open-water tests. To capture the turbulence flows around the propeller, a large eddy simulation (LES) turbulence model was implemented. In order to validate the simulation results, a series of open-water tests were conducted in the towing tank at National Cheng Kung University, resulting in a successful achievement of total uncertainties of less than ∼6%. The approach of simultaneous grid and time refinement was utilized to perform the discretization analysis. Eventually, the simulation results were employed to analyze the hydrodynamic performance and flow structure around the propeller, resulting in a conclusion based on the attained level of accuracy. The results indicate that the cases for a propeller with a strut exhibit favorable predictions compared to those of a single propeller, with error values for the thrust coefficients and propeller efficiencies falling below 6%. On the other hand, the torque coefficient was more accurately estimated for the cases of a single propeller than for those of a propeller with a strut, with error values below 2%.

A macroscale thermal simulation strategy with track-scale resolution for laser powder bed fusion

Numerical modelling is an effective tool to investigate the rapid temperature cycling in laser powder bed fusion. However, the high computational cost limits the modelling of part-scale components due to the significantly different scales between the highly local energy input region and the global field response region. This study presents a macroscale finite element thermal simulation strategy with a track-scale resolution by combining the recently developed characteristic time-based heat input (CTI) model with a currently proposed adaptive mesh re-mapping method. Due to the uniformly distributed power density along the scan direction in the CTI model, the optimized mesh strategy allows one element to capture the temperature solutions over the majority of a scan track except at the two ends. The adaptive mesh re-mapping method is used to map simulated results from a previous scan track model to a current scan track model with a new mesh configuration. This strategy has been implemented for a Ti-6Al-4V part with the dimensions of 20×40×3mm3. The predicted temperature histories agree well with the in-situ measurements at the points in both the printed part and powder bed. Three case studies demonstrate that our strategy can improve computational efficiency between 6 and 30 times.

ALE-ANCF modeling of the lowering process of a J-lay pipeline coupled with dynamic positioning

A novel structural dynamics model for the lowering process of a J-lay pipeline is established by combining the absolute nodal coordinate formula with the arbitrary Lagrangian–Eulerian description. The constraint on the top of the pipeline is introduced into the dynamic equation in the form of generalized coordinates by using a material transport boundary to simulate the lowering process of the top end of the pipeline. A mesh scheme is adopted to control the element length and prevent numerical disturbances. The accuracy of the material transport boundary and mesh scheme is verified for the case of a pendulum with a time-varying length. Then, a coupled analysis program is developed to investigate J-lay deployment by a vessel using dynamic positioning. The tensioner is modeled as a damper to adjust the pay-out speed of the upper end of the pipeline. The numerical analysis is carried out on an explanatory example of a 16-inch pipeline being laid at a 1000-m water depth. The results show that the lowering process strongly affects the dynamic characteristics of the touch-down zone.

A single–region Finite Volume framework for modeling discontinuous magnetic field distributions

In this paper we present a novel method to model discontinuous distributions of magnetic fields. The method is based on a finite volume discretization of a divergence form of the magnetostatic equations. The theoretical framework is written in terms of the vector potential, therefore, the computational implementation is capable of predicting the magnetic field distribution in permeable, permanently magnetized, and current-carrying media. The use of a single-region meshing scheme simplifies the simulation set-up due to the fact that it avoids the use of interface boundary conditions. This renders it computationally more effective than the multi-region counterpart. In order to test the performance of the present approach we execute several numerical experiments and compare the results against a multi-region discontinuous method and a single-region boundary layerless method. The experiments demonstrate that provided the boundary layer complies with certain topological rules, the method gives accurate results of the magnitude and direction of the magnetic field, both near and far from the interfaces. We show that, for orthogonal meshes, the results obtained with a single-region approach using boundary layers are comparable to the results obtained with a multi-region framework that imposes the magnetic field gradient discontinuity as a boundary condition.

Parabolic transport measurement of hydrodynamic forces for flow around circular/triangular distance dependent obstructions: Finite element analysis

<abstract><p>The present effort is the low Reynolds finite element hybrid meshed solution to apprehend the flow field properties in a convergent-divergent (CD) domain having engineering standpoints applications. To be more specific, we have considered the CD domain rooted with two types of obstructions in three various arrangements namely triangular/triangular, circular/triangular, and triangular/circular in CD throat. The viscous fluid is introduced from the inlet and interacts with installed obstacles. The moving stream in the channel is modelled mathematically in terms of the two-dimensional time-independent equations. The finite element approach is used to disclose numerical solutions by means of a hybrid meshing scheme. Optimized drag and lift force values encountered by an obstruction are offered through line integration across the external obstruction surfaces. In comparison to obstruction in left vicinity, the lift force faced by the triangle obstacle on the right side of the CD throat is larger. Furthermore, as compared to the drag force faced by the triangular obstruction in the same proximity, the circular obstacle experienced greater values as a drag. The lifting force sensed by the triangular cylinder is larger than circular cylinders. The assessment of marine hydrodynamic forces and stability individualities for fully or partially submerged objects in ocean engineering will benefit from the results of this study.</p></abstract>

Simulation of dendritic grain structures with a Cellular Automaton – Parabolic Thick Needle model

A multiscale numerical model, coupling the Cellular Automaton (CA) method to the Parabolic Thick Needle (PTN) method, is developed to compute dendritic microstructures. It is applied to directional solidification of bi-crystals under a frozen temperature approximation with fixed temperature gradient and fixed cooling rate. A dendritic branch is modeled as a cylinder headed by a parabolic tip. Its kinetics is computed using the PTN method from the composition field in the liquid in the vicinity of the parabola. This dendritic branch takes part in the definition of a grain envelope by its integration in a CA growth algorithm. The so-called Cellular Automaton – Parabolic Thick Needle (CAPTN) model can simulate the growth of dendritic grains while accounting for non-steady diffusion fields. The PTN method is implemented using Finite Element (FE) method on a heterogeneous mesh. An adaptive FE mesh strategy is developed to optimize computational time. The grain boundary orientation angle of a diverging bi-crystal configuration is investigated at steady state and compared to the Phase-Field (PF) method and the classical CA method. It is shown that contrary to the CA method, the CAPTN model is in good agreement with data deduced from PF simulations, demonstrating the interest of this coupling in the modeling of dendritic growth.

Nonlinear programming reformulation of dynamic flux balance analysis models

Dynamic flux balance analysis (dFBA) models are very popular in systems biology because of the many possible applications. dFBA consists of dynamic mass balance equations that describe the concentration of external metabolites and an optimization model to compute the internal flux distribution of the cell. Here, we applied a nonlinear programming formulation for solving dFBA models. The ODE system is discretized using the orthogonal collocation technique and the optimization problem is replaced by its first-order optimality conditions. In addition, an adaptive mesh scheme is applied to improve performance by efficiently handling changes in the active set of constraints. This formulation ensures total differentiability of the model, which can be solved by large-scale solvers and take advantage of automatic differentiation packages. The new approach presents results equivalent to state-of-the-art methods and outperforms them in dynamic optimization problems by avoiding calling an external solver to handle the embedded optimization model.

Wear modelling and sealing performance prediction of C/C composite finger seal

Due to the high speed and high pressure operating conditions, wear between the finger seal and the rotor is inevitable, and this leads to an increase of leakage clearance and becomes an important factor affecting the seal life. The theory of anisotropic elasticity was employed to describe the mechanical characteristics of the seal material. An improved Archard wear model was proposed to calculate the nodal wear rate, and the local wear direction was also determined. The wear simulation model and procedure were established based on the Arbitrary Lagrangian Eulerian adaptive mesh strategy. The effects of material density, fabric orientation, pressure differential and rotor speed on the wear characteristics of finger seal and the change of leakage clearance caused by wear loss were studied. The results show that the wear first occurs at the heel area of the finger foot bottom and gradually extends to the toe area. C/C (carbon fibre reinforced carbon matrix) composite finger seal with higher material density has smaller leakage clearance and wear depth. With the increase of fabric orientation angle, the wear depth in the heel area of finger foot is smaller, and the circumferential wear area is narrower. The average wear depth of finger seal decreases with the orientation angle. When the orientation angle is 0, the seal leakage clearance is smaller. The increase of pressure differential not only aggravates the seal wear, but also expands the wear area, and also increases the average contact pressure and leakage clearance. Increasing the rotor speed make the wear depth of the heel area of finger foot gradually increase, but the wear area becomes narrower. The average contact pressure decreases and the average leakage clearance increases. This study provides a theoretical method and basis for the prediction and evaluation of the wear life and performance of C/C composite finger seal.