Computational Domain Research Articles

Numerical solution of the mixed boundary value problem for the heat equation in two-dimensional domains of complex shape

A finite-difference computational algorithm is proposed for solving a mixed boundary value problem for heat equation given in a two-dimensional domains of complex shape. To solve the problem, generalized curvilinear coordinates are used. The physical domain is mapped to the computational domain (unit square) in the space of generalized coordinates. The original problem is written in curvilinear coordinates and approximated on a uniform grid in the computational domain. The obtained results are mapped on a non-uniform boundary-fitted difference grid in the physical domain. The second-order approximations of mixed Neumann – Dirichlet boundary conditions are constructed. The results of computational experiments are presented. The second order of accuracy of the presented computational algorithm is confirmed.

Introduction of oblique plane waves through a forcing source term in Euler equations

The propagation of shock waves generated by a transonic flow at the tip of a propeller blade is numerically calculated in order to determine the pressure footprint on an aircraft fuselage. An academic case is first proposed to validate the methodology. An incoming signal is built up as oblique harmonic plane waves. The signal is introduced in the computational domain using a Gaussian volume forcing term in the conservation of mass and energy equations. The Euler equations are solved in two dimensions using finite-difference schemes with low dispersion and dissipation. Selective filtering has also been integrated in the algorithm to remove grid-to-grid oscillations. The numerical solution is compared to an analytical solution based on the tailored Green function. An illustration for a realistic open rotor is then considered. The pressure signal near the blade tip, determined from a preliminary RANS simulation, is introduced using a volume source in a solver of the Euler equations.

Modelling of courtyard acoustics using the nodal discontinuous Galerkin finite element method to validate a newly developed PML

Evaluating the acoustics of courtyards has gained increasing attention from a sustainable urban design perspective, which requires numerical predictions tools for estimation of noise pollution and assessment of the influence of acoustic conditions. Accurate modeling of the acoustics of a courtyard is scarce because of the variety of factors to include: meteorological effects, building material properties, and geometry of the inner façades. We consider the nodal Discontinuous Galerkin finite element method framework in a 3D static and uniform medium and use it to model the sound propagation in a courtyard. A new and efficient Perfectly Matched Layer formulation is implemented at the open boundary of the courtyard model to absorb outgoing acoustic waves and this way limiting the size of the computational domain. The numerical results are validated against experimental measurements carried out in a scaled model of a courtyard with an elementary design to implement an accurate corresponding numerical model. The experiments were conducted in an anechoic chamber where the meteorological effects are controlled, and the courtyard facades are modelled as flat surfaces with known material properties.

A Shifted Boundary Method for the compressible Euler equations

The Shifted Boundary Method (SBM) is applied to compressible Euler flows, with and without shock discontinuities. The SBM belongs to the class of unfitted (or immersed, or embedded) finite element methods and avoids integration over cut cells (and the associated implementation/stability issues) by reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. We specifically discuss the advantages the proposed method offers in avoiding spurious numerical artifacts in two scenarios: (a) when curved boundaries are represented by body-fitted polygonal approximations and (b) when the Kutta condition needs to be imposed in immersed simulations of airfoils. An extensive suite of numerical tests is included.

Assessment of the Influence of Input Parameters in CFD Simulation of Ventilation in an Experimental Chamber

Abstract The aim of this paper is to evaluate the impact of selected input parameters on the accuracy and usability of CFD simulations. This paper compares the achieved results of Computational Fluid Dynamics (hereinafter CFD) simulations of air age with the ventilation results of a specific experimental box. A total of 16 variants were simulated for different simulation settings, including various computational domains and meshes in OpenFOAM, Ansys Fluent, DesignBuilder, and BlueCFD-AIR software. The paper primarily focuses on the importance of meeting the suitability criterion for the yPlus parameter used in the wall function of turbulent models k-ε and k-ω SST, and the resulting air age. Simulation with the best yPlus parameter shows the best agreement in airflow velocity and air age with the experiment. Overall, this led to an improvement in accuracy by 41 % compared to original simulation and 56 % compared to the previous our best OpenFOAM simulation.

Coconut Libtool: Bridging Textual Analysis Gaps for Non‐Programmers

ABSTRACTIn the era of big and ubiquitous data, professionals and students alike are finding themselves needing to perform a number of textual analysis tasks. Historically, the general lack of statistical expertise and programming skills has stopped many with humanities or social sciences backgrounds from performing and fully benefiting from such analyses. Thus, we introduce Coconut Libtool (www.coconut-libtool.com/), an open‐source, web‐based application that utilizes state‐of‐the‐art natural language processing (NLP) technologies. Coconut Libtool analyzes text data from customized files and bibliographic databases such as Web of Science, Scopus, and Lens. Users can verify which functions can be performed with the data they have. Coconut Libtool deploys multiple algorithmic NLP techniques at the backend, including topic modeling (LDA, Biterm, and BERTopic algorithms), network graph visualization, keyword lemmatization, and sunburst visualization. Coconut Libtool is the people‐first web application designed to be used by professionals, researchers, and students in the information sciences, digital humanities, and computational social sciences domains to promote transparency, reproducibility, accessibility, reciprocity, and responsibility in research practices.

Physics simulation capabilities of LLMs

Large Language Models (LLMs) can solve some undergraduate-level to graduate-level physics textbook problems and are proficient at coding. Combining these two capabilities could one day enable AI systems to simulate and predict the physical world. We present an evaluation of state-of-the-art (SOTA) LLMs on PhD-level to research-level computational physics problems. We condition LLM generation on the use of well-documented and widely-used packages to elicit coding capabilities in the physics and astrophysics domains. We contribute ∼50 original and challenging problems in celestial mechanics (with REBOUND), stellar physics (with MESA), 1D fluid dynamics (with Dedalus) and non-linear dynamics (with SciPy). Since our problems do not admit unique solutions, we evaluate LLM performance on several soft metrics: counts of lines that contain different types of errors (coding, physics, necessity and sufficiency) as well as a more educational’ Pass-Fail metric focused on capturing the salient physical ingredients of the problem at hand. As expected, today's SOTA LLM (GPT4) zero-shot fails most of our problems, although about 40% of the solutions could plausibly get a passing grade. About 70%–90% of the code lines produced are necessary, sufficient and correct (coding & physics). Physics and coding errors are the most common, with some unnecessary or insufficient lines. We observe significant variations across problem class and difficulty. We identify several failure modes of GPT4 in the computational physics domain, such as poor physical units handling, poor code versioning, tendency to hallucinate plausible sub-modules, lack of physical justification for global run parameters (e.g., simulation time, or upper-lower bounds for parametric exploration) and inability to define steady-state or stopping conditions reliably. Our reconnaissance work provides a snapshot of current computational capabilities in classical physics and points to obvious improvement targets if AI systems are ever to reach a basic level of autonomy in physics simulation capabilities.

A Novel Approach Integrating the Method of Characteristics with Large Time-Step Scheme (MOC-LTS) for Efficient Transient Flow Simulation in Liquid Pipelines

Water hammer incidents pose a significant risk to the safety and stability of pipeline operations. Therefore, rapid and precise transient flow simulation is essential for efficiently developing scientific water hammer control strategies. Nevertheless, the prevailing transient flow simulation methods for liquid pipelines predominantly employ explicit schemes to solve transient flow control equations, necessitating adherence to the stability criterion of Courant-Friedrichs-Lewy (CFL) ≤ 1. This results in limited time step sizes, which in turn constrains computational efficiency, particularly when simulating hydraulic behavior in large-scale pipeline networks. In this paper, a novel approach integrating the method of characteristics (MOC) with a large time-step scheme (LTS) is proposed to enable rapid and accurate simulation of transient flow in liquid pipelines. The proposed approach discretizes the computational domain into contiguous control volumes, ategorizing them as either boundary or internal control volumes depending on whether they are affected by boundary conditions within a large time step. For internal control volumes, an LTS scheme based on the first-order Godunov format is employed to improve computational efficiency. For boundary control volumes, MOC is applied iteratively to accurately capture boundary dynamics until the simulated time matches that of the internal control volumes. Quantitative analysis is conducted to verify the performance of the proposed approach. The results confirm that the proposed approach outperforms the MOC in computational efficiency while maintaining minimal accuracy loss.

Propagation of Free Infragravity Waves Generated at Distant Beaches

AbstractInfragravity (IG) waves are important drivers of extreme run‐up, morphological changes, and seiches. While locally forced IG waves have been extensively investigated, recent studies have revealed the significance of free IG waves generated on distant beaches. This study focuses on free IG waves generated at a coast facing southeast in Japan during the passage of a typhoon. The relationship between incident short waves and free IG waves as well as their contributions to nearshore IG waves, in particular to seiches in a small port, are analyzed using unique measurement data and numerical experiments. During the typhoon passage, more than 75% of the observed IG wave energy originates from free IG waves at an observatory located at a depth of 23 m, and their peak direction is alongshore. Six‐year measurement data demonstrate that peak directions of free IG waves strongly depend on the incident wave angles of short waves and that swells from the south generate alongshore propagating free IG waves. A numerical model can reproduce the alongshore propagating free IG waves accurately when using a large computational domain. Moreover, numerical experiments performed using the model demonstrate that the alongshore propagating free IG waves are IG waves reflected from distant beaches. The free IG waves from distant beaches are small outside the port, but seiches in the port are amplified by more than 10%. The relationship between seiches and incoming free IG waves is further discussed based on the numerical experiments.

Kinematics of Supernova Remnants Using Multiepoch Maximum Likelihood Estimation: Chandra Observation of Cassiopeia A as an Example

Decadal changes in a nearby supernova remnant (SNR) were analyzed using a multiepoch maximum likelihood estimation (MLE) approach. To achieve greater accuracy in capturing the dynamics of SNRs, kinematic features and point-spread function effects were integrated into the MLE framework. Using Cassiopeia A as a representative example, data obtained by the Chandra X-ray Observatory in 2000, 2009, and 2019 were utilized. The proposed multiepoch MLE was qualitatively and quantitatively demonstrated to provide accurate estimates of various motions, including shock waves and faint features, across all regions. To investigate asymmetric structures, such as singular components that deviate from the direction of expansion, the MLE method was extended to combine multiple computational domains and classify kinematic properties using the k-means algorithm. This approach allowed for the mapping of different physical states onto the image, and one classified component was suggested to interact with circumstellar material by comparison with infrared observations from the James Webb Space Telescope. Thus, this technique will help quantify the dynamics of SNRs and discover their unique evolution.

Shock wave interaction with a naturally generated vortex ring

The vortex ring is usually analytically modeled in computational studies involving vortex ring and shock wave interaction. However, incompressibility assumptions of the isolated vortex ring model mostly limits its applicability to the lower Mach number regime. To overcome this limitation, a compressible vortex ring is generated using a pulse jet exiting a circular nozzle, and its interaction with a shock wave is analyzed. The shock–vortex interaction and resulting sound wave generation is simulated by solving the compressible axisymmetric Navier–Stokes equations. A characteristics-based filter is used to isolate acoustic and hydrodynamic disturbances in the flow field. A reconfigured computational domain is used to negate the aftereffects of the nozzle on the flow field. The strong interaction of compressible vortex rings at higher Mach numbers with different shock wave Mach numbers in the flow field is studied including resultant acoustic wave generation.

On the Assessment of Wind Microclimate in a Complex Urban Environment Utilising Computational Fluid Dynamics

This paper presents an insight and key considerations for using Computation Fluid Dynamics (CFD) to simulate the Wind Microclimate in a Complex Urban Environment. The current study involved developing a local 10m height “reference” wind rose for the project site and then combining statistical meteorological data with aerodynamic information and wind comfort and wind safety criteria. Where wind speeds were found to be at undesirable wind levels at areas of interest (ground level, podium level, terraces, balconies, etc.), recommendations were made to reduce detrimental wind effects, e.g. using landscaping, porous windbreaks, canopies, etc. The criteria used in the evaluation of pedestrian-level winds surrounding the proposed development were based on the well-established “Lawson” criteria which couple the probability of exceeding winds at given statistical levels with wind speed magnitudes originally related to the Beaufort Land Scale. To take into account the influence of the immediate surrounding environment, all neighboring buildings and local topography within a diameter of almost 1,000 m around the site were included in the developed CFD model. Furthermore, all small canopies, balconies, and semi-open spaces were modeled in detail as per the provided architectural drawings. Based on a mesh sensitivity assessment, polyhedral elements were used for the entire computational domain. CFD analysis offers a comprehensive range of output including the velocity distribution in three directions and turbulence levels, allowing the identification of hot spot areas that have potentially unacceptable wind conditions for further assessment and mitigation treatments to reduce wind speed to acceptable levels. The baseline (no mitigation) scenario simulation results contributed to a better understanding of the environmental wind impact for the project at the site, enabling a targeted approach to the development of effective windbreak options This paper provides a comprehensive approach toward the establishment of a robust CFD assessment of human comfort to ensure that proposed building developments and their streetscapes create a comfortable wind environment to live and visit.

A stable decoupled perfectly matched layer for the 3D wave equation using the nodal discontinuous Galerkin method

In outdoor acoustics, the calculations of sound propagating in air can be computationally heavy if the domain is chosen large enough for the sound waves to decay. The computational cost is lowered by strategically truncating the computational domain with an efficient boundary treatment. One commonly used boundary treatment is the perfectly matched layer (PML), which dampens outgoing waves without polluting the computed solution in the inner domain. The purpose of this study is to propose and assess a new perfectly matched layer formulation for the 3D acoustic wave equation, using the nodal discontinuous Galerkin finite element method. The formulation is based on an efficient PML formulation that can be decoupled to further increase the computational efficiency and guarantee stability without sacrificing accuracy. This decoupled PML formulation is demonstrated to be long-time stable, and an optimization procedure for the damping functions is proposed to enhance the performance of the formulation.

Numerical Investigation of Bionic Axial Fan used in Split Air Conditioner

Abstract: Bionic axial fan is the main component in the outdoor unit split type room air-conditioner (AC) which impact the cooling and comfort. The present work aims to improve the aerodynamic performances of bionic axial fan by numerical technique. The detailed simulation has been carried out to investigate the aerodynamic performance of bionic axial fan with various design proposals for a detailed investigation and development of a prospective fan design prior to the manufacture and testing of costly prototypes. According to the biological fact that the serrations at the wing improve the acoustics as well the aerodynamic performances, various design modifications performed on the bionic axial fan blade. As the serrations at the trailing edge help to improve the aerodynamic performance, the fan blade design modified to investigate the change in mass flow rate. The flow field is simulated with the finite element Computational Fluid Dynamics (CFD) solver Altair-AcuSolve to analyse the influence of trailing edge serrations on the air flow rate of fan. The three-dimensional (3D) computational domain with SpalartAllmaras (SA) turbulence model is considered to predict the air flow rate. The present computation is carried out for the axial fan speed of 820 rpm. The flow rate is correlated with the test results to validate the CFD modeling approach. The result shows that the trailing edge serrations at the tip of the fan has predicted improvement in flow rate since it alter the length of separation bubble near the trailing edge which also helps to reduce the noise level.

Development and testing of hybrid (PNM–CFD) mathematical model and numerical algorithm for description of fluid flows in three-dimensional digital core models

Numerical simulation of fluid flow in porous and fractured rocks is an important task for many industrial applications. The most common approaches to constructing such models are direct (CFD or lattice Boltzmann) and porous network (PNM) modeling. Each approach has its own advantages and disadvantages. This paper presents a hybrid mathematical PNM–CFD model for describing fluid flows in three-dimensional digital core models, which has the high speed performance of PNM approaches and high accuracy of CFD models. Numerical technique has been developed for describing fluid flows in three-dimensional digital core models using a hybrid PNM–CFD model. The numerical technique links a one-dimensional pore network solver and a three-dimensional CFD solver into a combined model in original way by constructing a single pressure field for the entire computation domain. To validate the model, several tests were performed, including flow in straight channels and numerical simulation of fluid flow in a microfluidic chip. The test results have shown the adequacy of the hybrid model performance. The hybrid model for determining pressure drop in a branched network with three-dimensional chambers has an error of no more than 5 % when compared to experimental data. Similarly, the error in calculating velocity does not exceed 7 % when compared to the full three-dimensional calculation. The hybrid model has shown an almost twofold increase in calculation speed compared to the full three-dimensional model.

Effects of combustor wall temperature on the outer recirculation zone combustion modes transition in lean premixed DME/air swirling flames

In this study, the effects of wall thermal boundary conditions on the outer recirculation zone (ORZ) combustion modes transition in the DME/air swirling flames were investigated using the Large Eddy Simulation (LES) and Flamelet Generated Manifold (FGM) method. The results show that the ORZ chemistry and temperature are highly sensitive to the wall thermal boundary condition. Based on the correlation between the temperature and species observed in the time-averaged numerical results, the relation between the combustion mode and temperature in the ORZ was discovered. Through temporal analysis of species and heat release rate in the ORZ, the stable Mode II and Mode IV as well as the unstable Mode III were identified. The chemical reaction pathway analysis for typical probe in the ORZ reveals that different combustion modes undergo distinct (low-temperature or high-temperature) chemical reaction pathways. Afterwards, the definition of ORZ combustion modes used in experiments was refined by utilizing the chemical reaction data from the simulations. And it was applied to identify the combustion mode across the entire computational domain. The results confirm the consistency between the combustion modes determined in experiments based on OH and CH2O and those determined in simulations using chemical reaction rates. Finally, this explains the mechanism of the flickering flame in Mode III is the competition between the low-temperature and high-temperature reaction in the ORZ. Whereas the unstable Mode III can be stabilized by changing the wall temperature to reach the stable Mode II or Mode IV.

Domain decomposition for physics-data combined neural network based parametric reduced order modelling

This paper proposes a novel domain decomposition (DD) method for the parametric reduced-order model based on the Physics-Data Combined Neural Network (DD-PDCNN). The computational domain is partitioned into a number of subdomains, and a Physics-Data Combined Neural Network (PDCNN) is constructed for each subdomain, which not only represents the dynamics within its region but also considers interactions with neighbouring subdomains. The interface conditions between subdomains are considered by averaging solutions at the neighbourhoods, incorporating averaged solutions, predicted solutions at current and next time levels into reduced governing equations. The implicit coupling among the subdomains ensures global continuity and establishes boundary conditions for each subdomain.The performance of this new DD-PDCNN is compared with that of PDCNN without domain decomposition, data-driven model and traditional Reduced Basis(RB) model. The capability of this model is tested using a number of parametric nonlinear problems, such as the Korteweg-de Vries (KdV) equation, the two-dimensional Kovasznay flow and the two-dimensional incompressible Navier–Stokes equation. The results indicate that the proposed method offers an effective way to construct an accurate reduced order model for parameterised PDEs through machine learning. In particular, in specific parameter ranges where distinct physical phenomenon regions are prominent, the method outperforms the model without domain decomposition, demonstrating excellent performance on several challenging problems.

Cascaded lattice Boltzmann simulation of Newtonian and non-Newtonian mixture nanofluids with variable thermophysical properties in a cavity with vertical heat radiator

The central moments-based cascaded lattice Boltzmann method (CLBM) for then Newtonian and non-Newtonian Buongiorno’s model mixture nanofluids (CuO, ZnO, Al2O3-water) has been implemented and applied in a square chamber with a vertical heat radiator using accelerated graphics processing unit (GPU) computing through compute unified device architecture (CUDA) C/C++ platform. Due to the higher numerical stability, the CLBM is a superior numerical tool to the raw moments-based MRT-LBM (multiple-relaxation-time lattice Boltzmann method). Three different models for the viscosity and thermal conductivity of the nanofluids: (i) the Binkmann model for the constant viscosity and the Maxwell model for the constant thermal conductivity (ii) Binkmann and Maxwell model with temperature dependent Brownian motion and (iii) Corcione model with non-Newtonian fluid where the temperature and strain rate determine the nanofluid effective thermal conductivity and viscosity, have been used. The enclosure’s upper and bottom walls are thermally adiabatic, but the left and right walls are uniformly cold. A vertical heater is immersed in the middle position of the cavity. The benchmark results for non-Newtonian, Newtonian, and nanofluids for the various computational domains are used to validate the current code adequately. The Bingham number (Bn), the Rayleigh number (Ra), and The volume fraction of the nanoparticles (ϕ) are the three key parameters that are varied in this investigation to demonstrate the effects of natural convection on the isotherms, streamlines, isolines of nanoparticle volume fractionation, yielded and unyeilded zone, and average Nusselt number (Nu¯). The Brownian motion effects of the nanoparticles augmented the average rate of heat transfer and the use of the Bingham nanofluids reduced the heat transfer enhancement. For the CuO-water nanofluid, the augmentation of the rate of heat transfer is 15.42% from ϕ=0 to 4% while Ra=106 and the corresponding heat transfer enhancement for the ZnO-water nanofluid is 11.11%. For the Bingham fluid, the rate of heat transfer increases 7% from Ra=105 to Ra=106 while ϕ=2% and Bn=0.3. The findings can be applied to optimize automotive radiator systems, which are crucial for maintaining engine temperature.

Enhanced water management in PEMFC cathode using streamlined baffles

This research investigates the impact of baffle configurations on water management within Polymer Electrolyte Membrane Fuel Cells (PEMFCs) using novel flow fields in configurations featuring staggered and parallel streamlined baffles. Utilizing the Volume of Fluid method, the two-phase flow is modeled within computational domains that encompass the flow field above the porous Catalyst and Gas Diffusion Layers. A key feature is the use of Dynamic Contact Angle model, accounting for surface tension and wall adhesion over time, which provides detailed insights into liquid water movement and pressure changes. Streamlined baffles significantly enhance water removal and reactant transport by creating circulations and increasing flow velocities. The parallel-baffle configuration demonstrated the highest water removal capability, reducing water content in flow channels by 20.08 % compared to straight channels and offering a more uniform distribution of reactants. Both baffled configurations improve performance by promoting reactant infiltration and water expulsion, but they also increase pressure drops. The parallel configuration experiences the highest pressure drop, about 4.5 times greater than the conventional straight channel, illustrating a trade-off between better water management and energy efficiency. This study provides important insights into how baffled flow field designs in PEMFCs influence flooding behavior and potentially overall performance.

Implementation of PMDL and DRM in OpenSees for Soil-Structure Interaction Analysis

It is widely acknowledged that the effects of soil-structure interaction (SSI) can have substantial implications during periods of intense seismic activity; therefore, accurate quantification of these effects is of paramount importance in the design of earthquake-resistant structures. The analysis of SSI is typically conducted using either direct or substructure methods. Both of these approaches involve the use of numerical models with truncated or reduced-order computational domains. To ensure effective truncation, it is crucial to employ boundary representations that are capable of perfectly absorbing outgoing waves and allowing for the consistent application of input motions. At present, such capabilities are not widely available to researchers and practicing engineers. In order to address this issue, this study implemented the Domain Reduction Method (DRM) and Perfectly Matched Discrete Layers (PMDLs) in OpenSees. The accuracy and stability of these implementations were verified through the use of vertical and inclined incident SV waves in a two-dimensional problem. In terms of computational efficiency, PMDLs require a shorter analysis time (e.g., with PMDLs, the analysis concluded in 35 min as compared to 250 min with extended domain method) and less computational power (one processor for PMDLs against 20 processors for the extended domain method) thus offering a balance between accuracy and efficiency. Furthermore, illustrative examples of the aforementioned implemented features are presented, namely the response analysis of single-cell and double-cell tunnels exposed to plane waves inclined at an angle.