Mesh Resolution Research Articles

I-FENN with Temporal Convolutional Networks: Expediting the load-history analysis of non-local gradient damage propagation

In this paper, we demonstrate for the first time how the Integrated Finite Element Neural Network (I-FENN) framework, previously proposed by the authors [1,2], can efficiently simulate the entire loading history of non-local gradient damage propagation. To achieve this goal, we first adopt a Temporal Convolutional Network (TCN) as the neural network of choice to capture the history-dependent evolution of the non-local strain in a coarsely meshed domain. The quality of the network predictions governs the computational performance of I-FENN, and therefore we perform an extended investigation aimed at enhancing them. We explore a data-driven vs. physics-informed TCN setup to arrive at an optimum network training, evaluating the network based on a coherent set of relevant performance metrics. We address the crucial issue of training a physics-informed network with input data that span vastly different length scales by proposing a systematic way of input normalization and output un-normalization. We then integrate the trained TCN within the nonlinear iterative FEM solver and apply I-FENN to simulate the damage propagation analysis. I-FENN is always applied in mesh idealizations different from the one used for the TCN training, showcasing the framework’s ability to be used at progressively refined mesh resolutions. We illustrate several cases that I-FENN completes the simulation using either a modified or a full Newton–Raphson scheme, and we showcase its computational savings compared to both the classical monolithic and staggered FEM solvers. We underline that we satisfy very strict convergence criteria for every increment across the entire simulation, providing clear evidence of the robustness and accuracy of I-FENN. All the code and data used in this work will be made publicly available upon publication of the article.

Multiscale modelling of particulate composites with spherical inclusions

AbstractThis paper presents a novel and effective strategy for modelling three-dimensional periodic representative volume elements (RVE) of particulate composites. The proposed method aims to generate an RVE that can represent the microstructure of particulate composites with hollow spherical inclusions for homogenization (e.g., deriving the full-field effective elastic properties). The RVE features periodic and randomised geometry suitable for the application of periodic boundary conditions in finite element analysis. A robust algorithm is introduced following the combined theories of Monte Carlo and collision driven molecular dynamics to pack spherical particles in random spatial positions within the RVE. This novel technique can achieve a high particle-matrix volume ratio of up to 50% while still maintaining geometric periodicity across the domain and random distribution of inclusions within the RVE. Another algorithm is established to apply periodic boundary conditions (PBC) to precisely generate full field elastic properties of such microstructures. Furthermore, a user-friendly automatic ABAQUS CAE plug-in tool ‘Gen_PRVE’ is developed to generate three-dimensional RVE of any spherical particulate composite or porous material. Gen_PRVE provides users with a great deal of flexibility to generate Representative Volume Elements (RVEs) with varying side dimensions, sphere sizes, and periodic mesh resolutions. In addition, this tool can be effectively utilized to conduct a rapid mesh convergence study, an RVE size sensitivity study, and investigate the impact of inclusion/matrix volume fraction on the solution. Lastly, examples of these applications are presented.

Swift : a modern highly parallel gravity and smoothed particle hydrodynamics solver for astrophysical and cosmological applications

ABSTRACT Numerical simulations have become one of the key tools used by theorists in all the fields of astrophysics and cosmology. The development of modern tools that target the largest existing computing systems and exploit state-of-the-art numerical methods and algorithms is thus crucial. In this paper, we introduce the fully open-source highly-parallel, versatile, and modular coupled hydrodynamics, gravity, cosmology, and galaxy-formation code Swift. The software package exploits hybrid shared- and distributed-memory task-based parallelism, asynchronous communications, and domain-decomposition algorithms based on balancing the workload, rather than the data, to efficiently exploit modern high-performance computing cluster architectures. Gravity is solved for using a fast-multipole-method, optionally coupled to a particle mesh solver in Fourier space to handle periodic volumes. For gas evolution, multiple modern flavours of Smoothed Particle Hydrodynamics are implemented. Swift also evolves neutrinos using a state-of-the-art particle-based method. Two complementary networks of sub-grid models for galaxy formation as well as extensions to simulate planetary physics are also released as part of the code. An extensive set of output options, including snapshots, light-cones, power spectra, and a coupling to structure finders are also included. We describe the overall code architecture, summarize the consistency and accuracy tests that were performed, and demonstrate the excellent weak-scaling performance of the code using a representative cosmological hydrodynamical problem with ≈300 billion particles. The code is released to the community alongside extensive documentation for both users and developers, a large selection of example test problems, and a suite of tools to aid in the analysis of large simulations run with Swift.

An Unstructured Mesh Generation Tool for Efficient High‐Resolution Representation of Spatial Heterogeneity in Land Surface Models

AbstractThis study develops an unstructured mesh generation tool for land surface modeling using a multi‐scale hexagon discrete mesh. The tool can automatically determine the required mesh resolution for different regions based on multi‐objective criteria such as elevation, slope, land cover, and land use. The refined unstructured meshes demonstrate significant enhancement in the representation of spatial heterogeneity. The tool is coupled with the Common Land Model (CoLM) to enable land surface simulations using unstructured meshes. Evaluations focused on runoff, river discharge, and inundation indicate improved model performance compared to traditional structured mesh‐based CoLM simulations under the same computational cost constraints. This tool provides new capabilities for more efficiently capturing localized land surface processes and extreme events.

Locking-free isogeometric discretizations of linear plane Timoshenko rods: LAS elements

We make use of linear plane curved Timoshenko rods as a model problem to study how to overcome shear and membrane locking in NURBS-based discretizations. In this work, we propose lumped-assumed-strain (LAS) elements, a projection-based assumed-strain treatment that removes shear and membrane locking for a very broad range of slenderness ratios. For a NURBS patch with basis functions of degree p and Cp−1 continuity across element boundaries, the space of the assumed strains is defined on a B-spline patch with the same elements, but using basis functions of degree p−1 and Cp−2 continuity across element boundaries. The assumed strains are obtained by performing a L2 projection of the compatible strains at the patch level in which the consistent mass matrix is substituted with the lumped mass matrix. Our numerical investigations suggest that LAS elements need either the same or slightly finer mesh resolutions than B̄ elements in order for the relative errors in L2 norm of the unknowns and the stress resultants to be all below 1%. However, LAS elements are significantly more computationally efficient than B̄ elements for a given mesh. The use of C1-continuous quadratic LAS elements with 2 Gauss–Legendre quadrature points per element exhibit superconvergence of the stress resultants for most slenderness ratios, making it a particularly cost-effective choice of obtaining accurate results. When compared with linear Lagrange B̄ elements with 2 Gauss–Legendre quadrature points per element, C1-continuous quadratic LAS elements with 2 Gauss–Legendre quadrature points per element require far fewer elements in order to obtain relative errors in L2 norm of the unknowns and the stress resultants smaller than 1%.

Sensitivity analysis of wall-modeled large-eddy simulation for separated turbulent flow

In this study, we conduct a parametric analysis to evaluate the sensitivities of wall-modeled large-eddy simulation (LES) with respect to subgrid-scale (SGS) models, mesh resolution, wall boundary conditions and mesh anisotropy. While such investigations have been conducted for attached/flat-plate flow configurations, systematic studies specifically targeting turbulent flows with separation are notably sparse. To bridge this gap, our study focuses on the flow over a two-dimensional Gaussian-shaped bump at a moderately high Reynolds number, which involves smooth-body separation of a turbulent boundary layer under pressure-gradient and surface-curvature effects. In the simulations, the no-slip condition at the wall is replaced by three different forms of boundary condition based on the thin boundary layer equations and the mean wall-shear stress from high-fidelity numerical simulation to avoid the additional complexity of modeling the wall-shear stress. Various statistics, including the mean separation bubble size, mean velocity profile, and dissipation from SGS model, are compared and analyzed. The results reveal that capturing the separation bubble strongly depends on the choice of SGS model. While simulations approach grid convergence with resolutions nearing those of wall-resolved LES meshes, above this limit, the LES predictions exhibit intricate sensitivities to mesh resolution. Furthermore, both wall boundary conditions and the anisotropy of mesh cells exert discernible impacts on the turbulent flow predictions, yet the magnitudes of these impacts vary based on the specific SGS model chosen for the simulation.

Doing more with less: Realistic stereoscopic three-dimensional anatomical modeling from smartphone photogrammetry.

Traditional teaching methods struggle to convey three-dimensional concepts effectively. While 3D virtual models and virtual reality platforms offer a promising approach to teaching anatomy, their cost and specialized equipment pose limitations, especially in disadvantaged areas. A simpler alternative is to use virtual 3D models displayed on regular screens, but they lack immersion, realism, and stereoscopic vision. To address these challenges, we developed an affordable method utilizing smartphone-based 360° photogrammetry, virtual camera recording, and stereoscopic display (anaglyph or side-by-side technique). In this study, we assessed the feasibility of this method by subjecting it to various specimen types: osteological, soft organ, neuroanatomical, regional dissection, and a dedicated 3D-printed testing phantom. The results demonstrate that the 3D models obtained feature a complete mesh with a high level of detail and a realistic texture. Mesh and texture resolutions were estimated to be approximately 1 and 0.2 mm, respectively. Additionally, stereoscopic animations were both feasible and effective in enhancing depth perception. The simplicity and affordability of this method position it as a technique of choice for creating easily photorealistic anatomical models combined with stereoscopic depth visualization.

Machine learning mesh-adaptation for laminar and turbulent flows: applications to high-order discontinuous Galerkin solvers

We present a machine learning-based mesh refinement technique for steady and unsteady incompressible flows. The clustering technique proposed by Otmani et al. (Phys Fluids 35(2):027112, 2023) is used to mark the viscous and turbulent regions for the flow past a cylinder at Re=40\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re=40$$\\end{document} (steady laminar flow), at Re=100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re=100$$\\end{document} (unsteady laminar flow), and at Re=3900\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re=3900$$\\end{document} (unsteady turbulent flow). Within this clustered region, we use high mesh resolution, while downgrading the resolution outside, to show that it is possible to obtain levels of accuracy similar to those obtained when using a uniformly refined mesh. The mesh adaptation is effective, as the clustering successfully identifies the two flow regions, a viscous/turbulent dominated region (including the boundary layer and wake) that requires high resolution and an inviscid/irrotational region, which only requires low resolution. The new clustering sensor is compared with traditional feature-based sensors (Q-criterion and vorticity based) commonly used for mesh adaptation. Unlike traditional sensors that rely on problem-dependent thresholds, our novel approach eliminates the need for such thresholds and locates the regions that require adaptation. After the initial validation using flows past cylinders, the clustering technique is applied in an engineering context to study the flow around a horizontal axis wind turbine configuration which has been tested experimentally at the Norwegian University of Science and Technology. The data used within this framework are generated using a high-order discontinuous Galerkin solver, allowing to locally refine the polynomial order (p-refinement) in each element of the clustered region. For the laminar test cases, we can reduce the computational cost by 32% (steady Re=40\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re=40$$\\end{document} case) and 20% (unsteady Re=100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re=100$$\\end{document} case), while we get a reduction of 33% for the Re=3900\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re=3900$$\\end{document} turbulent case. In the context of the wind turbine, a reduction of 43% in computational cost is observed, while maintaining the accuracy.

Applying Convolutional Neural Networks to data on unstructured meshes with space-filling curves

This paper presents the first classical Convolutional Neural Network (CNN) that can be applied directly to data from unstructured finite element meshes or control volume grids. CNNs have been hugely influential in the areas of image classification and image compression, both of which typically deal with data on structured grids. Unstructured meshes are frequently used to solve partial differential equations and are particularly suitable for problems that require the mesh to conform to complex geometries or for problems that require variable mesh resolution. Central to our approach are space-filling curves, which traverse the nodes or cells of a mesh tracing out a path that is as short as possible (in terms of numbers of edges) and that visits each node or cell exactly once. The space-filling curves (SFCs) are used to find an ordering of the nodes or cells that can transform multi-dimensional solutions on unstructured meshes into a one-dimensional (1D) representation, to which 1D convolutional layers can then be applied. Although developed in two dimensions, the approach is applicable to higher dimensional problems. To demonstrate the approach, the network we choose is a convolutional autoencoder (CAE), although other types of CNN could be used. The approach is tested by applying CAEs to data sets that have been reordered with a space-filling curve. Sparse layers are used at the input and output of the autoencoder, and the use of multiple SFCs is explored. We compare the accuracy of the SFC-based CAE with that of a classical CAE applied to two idealised problems on structured meshes, and then apply the approach to solutions of flow past a cylinder obtained using the finite-element method and an unstructured mesh.

Flow2Mesh: A flow-guided data-driven mesh adaptation framework

Mesh adaptation is crucial in numerical simulation, providing optimal resource allocation for accurately capturing physical phenomena. However, when applied to Computational Fluid Dynamics (CFD) problems with complex multi-scale properties, existing adaptation methods face huge challenges due to the high computational cost of solving auxiliary partial differential equations (PDEs) and the difficulty in aligning the flow features with mesh geometric features. In this work, an end-to-end data-driven mesh adaptation framework, Flow2Mesh, is proposed to address these challenges by adopting a hybrid modeling strategy to construct the mapping from pixelated flow-fields to graph-based meshes. It achieves a rapid and accurate one-step mesh adaptation via a perceptual feature network (PFN) and a mesh movement network (MMN). PFN extracts the global perceptual features from flow-fields to enhance flow feature representation and mesh resolution independence. In MMN, these features are utilized to deform the initial mesh to a topology-invariant adaptive mesh by a proposed physically driven mesh convolutional network. It considers the inherent mesh geometric information for efficient node feature aggregation and alignment of mesh density with a flow-field structure. To generate high-quality adaptive meshes, various mesh-related losses are designed to regularize the mesh movement and alleviate the mesh tangling. Experiments in CFD scenarios demonstrate the generalization of our model to different design parameters and mesh configurations. It takes three orders of magnitude less time to generate similar meshes than the PDE-based method. The results exhibit the potential of Flow2Mesh to be a flexible and reliable tool for rapid mesh adaptation in scientific and industrial fields.

Iterative dynamics-based mesh discretisation for multi-scale coastal ocean modelling

Flow in coastal waters contains multi-scale flow features that are generated by flow separation, shear-layer instabilities, bottom roughness and topographic form. Depending on the target application, the mesh design used for coastal ocean modelling needs to adequately resolve flow features pertinent to the study objectives. We investigate an iterative mesh design strategy, inspired by hydrokinetic resource assessment, that uses modelled dynamics to refine the mesh across key flow features, and a target number of elements to constrain mesh density. The method is solver-agnostic. Any quantity derived from the model output can be used to set the mesh density constraint. To illustrate and assess the method, we consider the cases of steady and transient flow past the same idealised headland, providing dynamic responses that are pertinent to multi-scale ocean modelling. This study demonstrates the capability of an iterative approach to define a mesh density that concentrates mesh resolution across areas of interest dependent on model forcing, leading to improved predictive skill. Multiple design quantities can be combined to construct the mesh density, refinement can be applied to multiple regions across the model domain, and convergence can be managed through the number of degrees of freedom set by the target number of mesh elements. To apply the method optimally, an understanding of the processes being model is required when selecting and combining the design quantities. We discuss opportunities and challenges for robustly establishing model resolution in multi-scale coastal ocean models.

Modelling principal stress orientations in the Arabian Plate using plate velocities

Abstract We model maximum principal horizontal stress orientations in the Arabian Plate using a 3D finite element approach in conjunction with plate velocities. To capture the impact of geometry and tectonics, the model considers an accurate plate boundary shape and associated deformations. Three primary geological units represent plate architecture: sedimentary cover, crust and upper mantle. The mesh resolution varies to capture important geometrical features. Subsequently, we calculate the stress field using the force balance equation. Displacement boundary conditions are evaluated as accumulative deformation. NE–SW maximum principal horizontal stress (S Hmax ) azimuths dominate in northeastern Saudi Arabia and Kuwait, whilst NW–SE to NNW–SSE define the Dead Sea area. The Red Sea Basin and Saudi Arabia's interior is characterized by north–south S Hmax azimuths. Iraq's western area shows azimuths from NNW–SSE to NW–SE due to the collision at the Zagros Mountain Range, but changes to NE–SW in the east at the Zagros fold-and-thrust belt. An extensive literature review reveals publicly available S Hmax azimuth data which augment the sparse records compiled in the World Stress Map database. Our simulated S Hmax azimuths are consistent with these data. The results further corroborate ongoing tectonic processes, deepen our understanding of in situ stress variation drivers and inform current elastic deformation mechanisms in the Arabian Plate.

Thermal energy management using supersonically sprayed copper pyramids decorated with zinc oxide nanowires for surface cooling

Miniaturized microelectronics or small modular reactors (SMRs) simultaneously undergo an increase in heat flux and a decrease in size with the enhancement of device functionalities. Therefore, efficient convection cooling is required to prevent the malfunctioning of electronic devices or small nuclear reactors. Herein, mesh-patterned copper pyramids were fabricated via supersonic spraying for surface cooling applications. Zinc oxide nanowires (ZnO NWs) were patterned on top of the copper pyramids to produce a highly efficient cooling system for a high-heat-flux surface by increasing the overall surface area of the pyramids. In addition, ZnO NW decoration imparted superhydrophilicity to the surface with firm anchoring and spreading of impacting spray liquid drops until complete evaporation. The effects of macroscale pyramid mesh resolution and introduction of ZnO NWs on the spray cooling efficiency were quantified and compared. Herein, the pyramids with coarse resolution and ZnO NWs yielded the highest heat flux during the drop impact heat transfer process and the lowest surface temperature under air and spray cooling conditions owing to the maximized surface area. The use of the pyramids and introduction of ZnO NWs increased the Leidenfrost temperature from 140 to 190 °C, thereby expanding the range of the evaporation cooling regime.

Modeling fluid flow in fractured porous media: a comparative analysis between Darcy–Darcy model and Stokes–Brinkman model

AbstractThere are limited comparative studies on modeling fluid transport in fractured porous media. Hence, this paper systematically compares the steady-state creeping flow Stokes–Brinkman and Darcy–Darcy models for computational efficiency and accuracy. Sensitivity analyses were also conducted on the effect of fracture orientations, fracture sizes, mesh resolution, and fractures with Local Grid Refinement (LGR) under the FEniCS computational framework. Both models were validated numerically, and the accuracy of their solution is compared using the R-squared metric and L2 norm estimates. Key results showed that both models have similar pressure and velocity field solutions for a given fracture orientation. The computational time required for solving the Stokes–Brinkman models for a single fracture case was unusually lower than that of the Darcy–Darcy model when the pressure and velocity terms in the Darcy–Darcy model were solved simultaneously using two equations, contrary to where only one equation solves for the pressure and the velocity is obtained by projecting the gradient of pressure onto a vector space. The Stokes–Brinkman model is more sensitive to mesh resolution, and as a result, the Darcy–Darcy model tends to be more accurate than the Stokes–Brinkman model at low resolutions. Local Grid Refinement (LGR) can improve the Stokes–Brinkman model's accuracy at low mesh resolution. Furthermore, both models showed similar results when compared for complex fracture systems such as multiple fracture cases: interconnecting and isolated fractured porous media systems under low-velocity and steady-state creeping flow conditions. The FEniCS code in this paper is shared for future researchers to reproduce results or extend the research work.

Numerical investigation of dam break flow over erodible beds with diverse substrate level variations

Abstract This study aimed to comprehensively investigate the influence of substrate level difference and material composition on dam break wave evolution over two different erodible beds. Utilizing the Volume of Fluid (VOF) method, we tracked free surface advection and reproduced wave evolution using experimental data from the literature. For model validation, a comprehensive sensitivity analysis encompassed mesh resolution, turbulence simulation methods, and bed load transport equations. The implementation of Large Eddy Simulation (LES), non-equilibrium sediment flux, and van Rijn’s (1984) bed load formula yielded higher accuracy compared to alternative approaches. The findings emphasize the significant effect of substrate level difference and material composition on dam break morphodynamic characteristics. Decreasing substrate level disparity led to reduced flow velocity, wavefront progression, free surface height, substrate erosion, and other pertinent parameters. Initial air entrapment proved substantial at the wavefront, illustrating pronounced air-water interaction along the bottom interface. The Shields parameter experienced a one-third reduction as substrate level difference quadrupled, with the highest near-bed concentration observed at the wavefront. This research provides fresh insights into the complex interplay of factors governing dam break wave propagation and morphological changes, advancing our comprehension of this intricate phenomenon.

Three-component volume of fluid method coupling with interface compression method and Eulerian–Lagrangian spray atomization surface density model for prediction of cavitating sprays

In this work, a new three phase cavitation model with Eulerian–Lagrangian Spray Atomization (ELSA) and Interface Capturing Method (ICM) coupling is presented to allow for, in a unified approach, physical insight of the surface evolution of cavitating sprays at the Sub-Grid Scale (SGS). Phase change is accounted for in the framework via mass transfer across a liquid and corresponding vapor phase. The surface density model was validated against direct numerical simulation data of an atomizing jet with a systematic variation of mesh resolutions. The sensitivity of the adjustable parameters such as the critical Weber number was also demonstrated. Then, experimental comparisons were made with a more realistic orthogonal spray geometry within a cavitating and turbulent non-cavitating system. These comparisons include both large scale visualizations and small scale SGS quantities such as the Sauter mean diameter. To our knowledge, this is the first study that presents the performance of a three phase cavitating framework with SGS ELSA-ICM coupling.

Hybrid Rocket Engine Burnback Simulations Using Implicit Geometry Descriptions

The performance of hybrid rocket engines is significantly influenced by the fuel geometry. Burnback simulations, to determine the fuel surface and fluid volume, are therefore an important tool for preliminary design. This work presents a method for the simulation of spatially constant burn-ups on arbitrary geometries. An implicit surface definition by means of a signed distance function is used to represent the fluid volume and the fuel block on tetrahedral meshes. Two methods each are used to determine the fluid volume and the burning surface. The first method is based on a direct integration of the signed distance function with the Heaviside function or the Dirac delta distribution, respectively. The second method linearly interpolates the position of an isosurface and thus reconstructs the fuel surface. Both methods are compared and validated with analytical results of four example geometries. Both calculations of the fluid volume and the calculation of the surface content with the interpolation method are characterized as first-order methods. With practicable mesh resolutions of one million computational cells, errors below two percent can be achieved. With the interpolation method, numerical meshes can also be exported for any time points of the burn. Finally, the application of the program to the fuel geometry of the Viserion hybrid rocket engine is demonstrated.

On the simulation of a wing with detached end-plates using an actuator line based on an anisotropic Gaussian kernel

The results of an actuator line method (ALM) using an anisotropic Gaussian kernel for both, velocity sampling and force projection, are compared to the wall-resolved results of a NACA 0015 rectangular wing at an angle of attack of 10°. The rectangular wing is simulated both, with and without, detached end-plates to show that the ALM is capable of accounting for the presence of a narrow gap of 0.01 c between the tip of the wing and the end-plate. The anisotropic kernel shape is varied in the chordwise, thickness-wise, and spanwise directions for different grid sizes and number of actuating points. The body forces are truncated and regularized to enforce proper spacing between the actuating line and the end-plate. ALM and wall-resolved results are compared on the basis of the integrated lift and drag coefficients, the sectional lift and drag coefficients, as well as the tip vortex core size, position, and circulation. Recommendations are made regarding the optimal kernel shape for a given number of actuating points and mesh resolution.

Modeling liquid transport in the Earth's mantle as two-phase flow: effect of an enforced positive porosity on liquid flow and mass conservation

Abstract. Fluid and melt transport in the solid mantle can be modeled as a two-phase flow in which the liquid flow is resisted by the compaction of the viscously deforming solid mantle. Given the wide impact of liquid transport on the geodynamical and geochemical evolution of the Earth, the so-called “compaction equations” are increasingly being incorporated into geodynamical modeling studies. When implementing these equations, it is common to use a regularization technique to handle the porosity singularity in the dry mantle. Moreover, it is also common to enforce a positive porosity (liquid fraction) to avoid unphysical negative values of porosity. However, the effects of this “capped” porosity on the liquid flow and mass conservation have not been quantitatively evaluated. Here, we investigate these effects using a series of 1- and 2-dimensional numerical models implemented using the commercial finite-element package COMSOL Multiphysics®. The results of benchmarking experiments against a semi-analytical solution for 1- and 2-D solitary waves illustrate the successful implementation of the compaction equations. We show that the solutions are accurate when the element size is smaller than half of the compaction length. Furthermore, in time-evolving experiments where the solid is stationary (immobile), we show that the mass balance errors are similarly low for both the capped and uncapped (i.e., allowing negative porosity) experiments. When Couette flow, convective flow, or subduction corner flow of the solid mantle is assumed, the capped porosity leads to overestimations of the mass of liquid in the model domain and the mass flux of liquid across the model boundaries, resulting in intrinsic errors in mass conservation even if a high mesh resolution is used. Despite the errors in mass balance, however, the distributions of the positive porosity and peaks (largest positive liquid fractions) in both the uncapped and capped experiments are similar. Hence, the capping of porosity in the compaction equations can be reasonably used to assess the main pathways and first-order distribution of fluids and melts in the mantle.

Large eddy simulations fire modeling of JIS A 1310 façade calibration test with respect to sidewall

AbstractThe full‐scale façade standard test is widely employed as a comprehensive method to assess the façade fire spread. Within this approach, the calibration test without combustible façade decouples the intricate interaction between gas‐phase combustion and material pyrolysis, which simplifies diagnostics and provides an ideal scenario for model validation. This paper presents large eddy simulations (LES) accompanied by comparisons of calibration tests in accordance with JIS A 1310. The calibration tests were conducted to obtain the flame morphologies, gas‐phase temperature, and heat flux of over‐ventilated façade fires, and the LES modeling is complemented by the modified eddy dissipation model for combustion, the one‐equation model for the sub‐grid scale turbulence, and the discrete ordinate method with the gray mean absorption‐emission approach for thermal radiation. The accuracy of LES data is discussed by comparing with measurements, and the mesh resolution is optimized as 2.5 cm for achieving mesh independency with good qualitative agreement. Furthermore, simulations are conducted to investigate the impact of sidewall distances on façade flame spread. The results highlight that the enhancement of sidewall in façade flame spread occurs under external heat release rate, and the 0.2 m sidewall distance for the designated JIS test is identified as a critical threshold increasing façade thermal load.