On Solving the Poisson Equation with Discontinuities on Irregular Interfaces: GFM and VIM

Publisher's version (útgefin grein)We analyze the accuracy of two numerical methods for the variable coefficient Poisson equation with discontinuities at an irregular interface. Solving the Poisson equation with discontinuities at an irregular interface is an essential part of solving many physical phenomena such as multiphase flows with and without phase change, in heat transfer, in electrokinetics, and in the modeling of biomolecules’ electrostatics. The first method, considered for the problem, is the widely known Ghost-Fluid Method (GFM) and the second method is the recently introduced Voronoi Interface Method (VIM). The VIM method uses Voronoi partitions near the interface to construct local configurations that enable the use of the Ghost-Fluid philosophy in one dimension. Both methods lead to symmetric positive definite linear systems. The Ghost-Fluid Method is generally first-order accurate, except in the case of both a constant discontinuity in the solution and a constant diffusion coefficient, while the Voronoi Interface Method is second-order accurate in the -norm. Therefore, the Voronoi Interface Method generally outweighs the Ghost-Fluid Method except in special case of both a constant discontinuity in the solution and a constant diffusion coefficient, where the Ghost-Fluid Method performs better than the Voronoi Interface Method. The paper includes numerical examples displaying this fact clearly and its findings can be used to determine which approach to choose based on the properties of the real life problem in hand.The research of Á. Helgadóttir was supported by the University of Iceland Research Fund 2015 under HI14090070. The researches of A. Guittet and F. Gibou were supported in part by the NSF under DMS-1412695 and DMREF-1534264.Peer Reviewe

Mesh Twisting Technique for Swirl Induced Laminar Flow Used to Determine a Desired Blade Shape

Publisher's version (útgefin grein)Swirling flow has been shown to increase heat transfer in heat exchangers. However, producing swirl while not presenting a severe pressure drop can be a challenge. In this paper, a desired shape of guidance blades for laminar swirl flow is determined by numerical simulation in OpenFOAM. Emphasis is on the mesh technique, where a predefined blade shape is formed by mesh twisting, or morphing. The validity of numerical simulations on a twisted mesh is shown by comparing it to the theoretical solution of laminar flow in a pipe without swirl and guidance blades. A sensitivity study shows that a cell size ratio of 0.025 of diameter is sufficient and affects the solution minimally. To determine the desired shape of guidance blades previously found optimal swirl decay and velocity profile for laminar swirling flow are utilized. Three blade shapes are explored: (I) with a twist angle that varies with axial location only; (II) having a deviation angle matching the theoretical deviation angle for laminar swirling flow; (III) same as II but with a hollow center. Simulations are performed for Re=100 and swirl number S=0.2. Case II is able to sustain swirl longest while maintaining a low pressure drop and is therefore a desired swirler shape profile as predicted theoretically.Peer Reviewe

Imposing mixed Dirichlet–Neumann–Robin boundary conditions in a level-set framework

Pre-print (óritrýnt handrit)We consider the Poisson equation with mixed Dirichlet, Neumann and Robin boundary conditions on irregular domains. We describe a straightforward and efficient approach for imposing the mixed boundary conditions using a hybrid finite-volume/finite-difference approach, leveraging on the work of Gibou et al. (2002) [14], Ng et al. (2009) [30] and Papac et al. (2010) [33]. We utilize three different level set functions to represent the irregular boundary at which each of the three different boundary conditions must be imposed; as a consequence, this approach can be applied to moving boundaries. The method is straightforward to implement, produces a symmetric positive definite linear system and second-order accurate solutions in the L-infinity-norm in two and three spatial dimensions. Numerical examples illustrate the second-order accuracy and the robustness of the method. (C) 2015 Elsevier Ltd. All rights reserved.The research of Á. Helgadóttir, Y.T. Ng and F. Gibou were supported in part by ONR under grant agreement N00014-11-1-0027, by the National Science Foundation under grant agreement CHE 1027817 and by the W.M. Keck Foundation. The research of C. Min was supported in part by the Kyung Hee University Research Fund (KHU-20070608) in 2007 and by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2008-331-C00045)

Lagrangian Particle Tracking Data of a Straining Turbulent Flow Assessed Using Machine Learning and Parallel Computing

This study aimed to employ artificial intelligence capability and computing scalability to predict the velocity field of the straining turbulence flow. Rotating impellers in a box have generated the turbulence, subsequently subjected to an axisymmetric straining motion, with mean nominal strain rates of 4s^-1. Tracer particles are seeded in the flow, and their dynamics are investigated using high-speed Lagrangian Particle Tracking at 10,000 frames per second. The particle displacement, time, and velocities can be extracted using this technique. Particle displacement and time are used as input observables, and the velocity is employed as a response output. The experiment extracted data have been divided into training and test data to validate the models. Support vector polynomial regression (SVR) and Linear regression were employed to see how extrapolation for the velocity field can be extracted. These models can be done with low computing time. On the other hand, to create a dynamic prediction, Gated Recurrent Unit (GRU) is applied with a high-performance computing application. The results show that GRU presents satisfactory forecasting for the turbulence velocity field and the computing scale performed on the JUWELS and DEEP-EST and reported. GPUs have a significant effect on computing time. This work presents the capability of the GRU model for time series data related to turbulence flow prediction.This work was performed in the Center of Excellence (CoE) Research on AI and Simulation Based Engineering at Exascale (RAISE) and the EuroCC projects receiving funding from EU’s Horizon 2020 Research and Innovation Framework Programme under the grant agreement no.951733 and no. 951740 respectivelyPeer Reviewe

Implicit Equation for Photovoltaic Module Temperature and Efficiency via Heat Transfer Computational Model

This paper evaluates the photovoltaic (PV) module operating temperature’s relation to efficiency via a numerical heat transfer model. The literature reports that higher PV module operating temperatures impact PV module efficiency. There are dozens of explicit and implicit equations used to determine the PV module operating temperature. However, they are not universal, and for each application, it is necessary to insert a correction coefficient based on the environment and boundary conditions. Using a numerical method covering a more comprehensive range of PV module operation conditions to estimate a global equation, this study considers the solar radiation flux, Gt, solar ray direction with respect to the ground level, γ, convective heat transfer coefficient, h, tilt angle, β, ambient temperature, Ta, PV power output, Ppv, PV panel efficiency, η, and environmental properties. The results match the extant empirical work and related literature. PV module efficiency is found to have a linear relationship to the PV module operating temperature via a numerical heat transfer model corresponding to the well-known PV module. It specifies that heat transfer convection changes with PV module tilt angle, causing PV module operating temperature effects. It also represents the PV module operating temperature variations with ambient temperature and solar flux, like those reported in the literature.Center of Excellence (CoE) Research on AI and Simulation-Based Engineering at Exascale (RAISE).Peer Reviewe

A proposed hybrid two-stage DL-HPC method for wind speed forecasting: using the first average forecast output for long-term forecasting

Energy consumption is growing extensively, which is caused by new demanding technological applications and continuously changing lifestyles, also with respect to climate change. Climate change is a significant issue and scientific reports notice the temperature environment continuously increasing, particularly in the summer. To alleviate the heat, people in many countries tend to use air conditioning systems in residential and business buildings. This puts additional pressure on the electricity network and the energy producers must be able to predict such events. It is agreed worldwide that harvesting renewable energy is the best option for fighting climate change. For example, recently, the number of electric cars has increased and it becomes more and more attractive to utilize green energy, e.g., produced by wind turbines, for them. The advantages of wind energy have intensively been studied, and a wide range of methods to create very short-term, short-term, medium-term, and long-term predictions using wind energy models or wind speed profiles are in use [1,2]. However, some of the forecasting methods are highly complex and costly in computing [3,4]. This study uses a gated recurrent unit (GRU) model, a deep learning model, to efficiently perform medium-term predictions of wind energy production. There is effort to apply these medium-term predictions to create long-term forecasting models. The literature has reported that GRUs are faster than long short-term memory (LSTM) models, which have been used in recent studies, can deal with relatively fewer data, and are cheaper in computing. The study applies empirical wind speed data from 5 years, which the Iceland Metrological office has measured at 10 m height at the Búfrell location. The log law is used to scale the speed up to 55 m, which is the height of an Enercon E44 wind turbine hub. The predictions are performed on the DAM module of the DEEP cluster at the Jülich Supercomputing Centre. The parallel machine allows to speed up the model scaling. The results show that the proposed model can predict medium and long-term wind speeds as a function of the ratio of training data. This method conducts the forecasting cheaper in computing than LSTM but with equal performance