Adaptive Mesh Refinement Technique Research Articles

Efficient Simulation of the Laser-Based Powder Bed Fusion Process Demonstrated on Open Lattice Materials Fabrication

Strut-based or open lattice materials are a category of advanced materials used in medical and aerospace applications due to their properties, such as high strength-to-weight ratio and energy absorption capability. The most prominent method for the fabrication of lattice materials is the Laser-based Powder Bed Fusion (L-PBF) additive manufacturing (AM) process, due to its ability to produce parts of complex geometries. The current work presents an efficient meso-scale finite element (FE) modeling methodology of the L-PBF process demonstrated in the fabrication of body-centered cubic (BCC) lattice materials. The modeling efficiency is gained through an adaptive mesh refinement technique, which results in accurate and efficient prediction of the temperature field during the process evolution. To examine the efficiency of the modeling method, the computational time is compared with that of a conventional FE simulation, based on the element and birth technique. The temperature history difference between the two approaches is minor but the adaptive mesh modeling requires only a small portion of the simulation time of the conventional model. In addition, the computational results present a good correlation with the available experimental measurements for various process parameters validating the presented efficient method.

DC3DPAFEM: An efficient and accurate 3-D direct current resistivity anisotropic forward modeling software for complex geological settings

Nowadays, there is a growing trend that direct current (DC) field surveys are shifting towards challenging areas characterized by mountainous topography and electrical anisotropy. Given these complex geological settings, there is an urgent need for 3-D DC forward modeling software capable of effectively addressing large-scale problems and delivering accurate modeling results to interpret field data. However, most open-source software packages face certain limitations, such as the high numerical cost to handle complex surface topography, the lack of consideration for anisotropic conductivity, the absence of mesh refinement techniques to guarantee accuracy in forward modeling, and the lack of parallel computing techniques to solve large-scale problems. In this study, we develop an efficient and highly accurate 3-D DC anisotropic forward modeling software, namely DC3DPAFEM, using the adaptive finite element algorithm based on the unstructured tetrahedral mesh. Firstly, we construct a strong compatible boundary value problem (BVP) for 3-D anisotropic DC problems by adopting a specialized secondary potential approach to handle the surface topography efficiently. Then, we develop a goal-oriented adaptive mesh refinement (AMR) technique to ensure accurate forward modeling results, even with a coarse initial mesh. To ensure time and memory efficiency, we employ a robust conjugate gradient (CG) algorithm preconditioned by the algebraic multigrid (AMG) solver to solve the large-scale linear system of equations resulting from complex geological structures. We aim to investigate the performance of the AMG scheme in anisotropic DC cases. Furthermore, we incorporate the domain decomposition technique into the iterative solution scheme for further efficiency gains. This technique significantly improves computing efficiency for large-scale problems in parallel clusters. Finally, we conduct comprehensive performance tests for DC3DPAFEM using a two-layer anisotropic model and a 3-D complex model with undulating terrain. The results of both examples validate the accuracy of DC3DPAFEM, as they closely align with the analytical solutions and the solutions obtained from the existing 3-D DC forward modeling code. Compared to traditional direct solver MUMPS and ILU-preconditioned iterative solvers, DC3DPAFEM exhibits highly scalable performance for large-scale problems, offering significant advantages in terms of memory and time consumption. Overall, DC3DPAFEM demonstrates substantial advances in efficiency, accuracy, and practicality through a series of numerical examples. This open-source code provides an efficient and available tool for developing a 3-D DC inversion method that can deal with large-scale problems involving intricate topography and anisotropic media.

Fragmentation of colliding liquid rims

We present direct numerical simulations of the splashing process between two cylindrical liquid rims. This belongs to a class of impact and collision problems with a wide range of applications in science and engineering, and motivated here by splashing of breaking ocean waves. Interfacial perturbations with a truncated white noise frequency profile are introduced to the rims before their collision, whose subsequent morphological development is simulated by solving the two-phase incompressible Navier–Stokes equation with the adaptive mesh refinement technique, within the Basilisk software environment. We first derive analytical solutions predicting the unsteady interfacial and velocity profiles of the expanding sheet forming between the two rims, and develop scaling laws for the evolution of the lamella rim under capillary deceleration. We then analyse the formation and growth of transverse ligaments ejected from the lamella rims, which we find to originate from the initial corrugated geometry of the perturbed rim surface. Novel scaling models are proposed for predicting the decay of the ligament number density due to the ongoing ligament merging phenomenon, and found to agree well with the numerical results presented here. The role of the mechanism in breaking waves is discussed further and necessary next steps in the problem are identified.

Numerical investigation on the deformation and breakup of an elastoviscoplastic droplet in simple shear flow

In this paper, direct numerical simulations (DNSs) are performed to investigate the deformation and breakup of an elastoviscoplastic (EVP) droplet in a Newtonian matrix under simple shear flow. The two-phase interface is captured by the volume-of-fluid (VOF) method with adaptive mesh refinement technique. The Saramito model (Bingham model coupled exponential Phan-Thien–Tanner viscoelastic model) is used to characterize the rheological behavior of the droplet. The droplet deformation and conformational state are studied with different Capillary numbers Ca, Weissenberg numbers Wi, and Bingham numbers Bi, which represent the surface tension, elasticity, and yield stress of the droplet, respectively. Our results show that droplet deformation occurs at low Ca, while breakup occurs at high Ca. The droplet non-monotonically deforms with increasing Wi and Bi, while is elongated for higher Ca. In addition, three breakup modes (mid-point pinching, transitional breakup, and homogeneous breakup) are reported for EVP droplets, in which transitional breakup disappears due to the influence of high elasticity. The conformational state of the droplet intuitively demonstrates the change of breakup from horizontal shear to vertical breakup. In spite of the fact that the surface tension always inhibits the deformation of droplets, the present work indicates that Bi has little effect on the deformation with high Wi and high Ca, while the influence is obvious at low Wi and Ca. The observed elastic and plastic effects on droplet deformation and breakup are believed to have significant impacts, as yield stress fluids are widely encountered in industrial applications.

A study on the hydroacoustic characterisation of a cavitating propeller by dynamic adaptive mesh refinement technique

Underwater radiated noise (URN) of a marine propeller has received significant interest in recent decades due to its implications on marine fauna. Therefore, an accurate prediction of URN at an early stage of the propeller design is becoming imperative. This study presents a numerical investigation into the noise prediction of a marine propeller, including cavitation and a comparison with experimental test results obtained from the URN database from the King's College D (KCD) standard propeller series. Amongst the propellers tested in the series, the member KCD-193 was chosen to scrutinise in this study due to the significant variance of the cavitation types experienced by this propeller member and consequent characteristic variations observed in its URN spectral response. Numerical URN predictions of different flow conditions, represented by the advance coefficient and cavitation number, were conducted to investigate their effects on the noise spectrum. These predictions were compared with the experimental results to enable interpretation of the impact of various aspects of the simulation on URN prediction accuracy. In this investigation, one of the most prominent noise sources, tip-vortex cavitation (TVC), was identified as a critical aspect that needs to be captured by the numerical simulations for accurate URN predictions using CFD simulations. The influence of TVC on the spectrum was observed to be significant. The inception and stable presence of TVC dominated the frequency response of the broadband hump. In order to address this, a systematic adaptive mesh refinement strategy was implemented based on the vortex criterion to solve the flow characteristics in the propeller slipstream accurately. To further complement this task, a correlation between the cavitation bubble growth and collapse phenomenon by the sensitivity of the broadband hump on the spectrum was established based on the experimental results. The central frequency of the broadband hump was observed to vary with the advance coefficient and cavitation number. The reduction in the cavitation number resulted in a shift of this hump towards lower frequencies. The URN level of the hump decreased slightly in the high frequency by the reduction in the advance coefficient and the developing cavitation, demonstrating the cushioning effect on the spectrum. An accurate assessment of the noise spectrum, as far as numerical predictions are concerned, particularly on the broadband hump frequency bandwidth, was directly associated with the resolution of the TVC.

Coupled heat and water transfer in heterogeneous and deformable soils: Numerical model using mixed finite element method

We present a generic model framework for coupled heat and water transfer (CHWT) in deformable (non-rigid) soils with spatial variations of soil properties. The model backbone is a mixed finite element method (FEM), which solves the Philip and de Vries (1957) CHWT model and achieves conservation of mass and energy on both local and global scales. Spatial variations occur in soil hydraulic and thermal properties due to transient water content and temperature distributions. Based on the mixed FEM scheme, a gradient measure and a clustering model (“k-means”) are proposed to trace the regions with large spatial variations of soil properties, and an adaptive mesh refinement technique is developed to improve the spatial resolution and simulation accuracy. Deformation perturbates local soil topography and alters transient soil water and temperature regimes in the deformed regions. A quasi-static deformation model is presented, and the deformation effects are incorporated into the mixed FEM scheme. When external load exists, soil deformation is simulated with an updated Lagrangian formulation, and the local water content and temperature variations due to soil volume changes are also updated in the CHWT model. Numerical examples, including thermally induced soil water transfer and water infiltration, illustrate the model ability to provide plausible CHWT results, especially the refined solutions near the wetting fronts and the water content and temperature distributions when the soil is deformable. In conclusion, the proposed model framework provides an effective pipeline to incorporate and process the spatial variations of soil properties and soil deformation in CHWT simulations.

A new rapid deflagration-to-detonation transition in a short smooth tube

A new rapid deflagration-to-detonation transition in a short smooth tube

Polymeric droplet formation and flow pattern evolution in capillary microchannels: Effect of fluid elasticity

Polymeric droplets are widely employed in fields such as chemical, biomedical, and materials engineering. However, the study of polymeric droplet formation is still insufficient due to the complex elasticity. In this work, the effect of fluid elasticity on the flow patterns for polymeric droplet formation in cross-junction microchannels is investigated by means of finite-volume direct numerical simulations. The volume of fluid method with cell-based adaptive mesh refinement technique is used to capture the interface. Additionally, the rheological behavior of polymeric fluids is described using the exponential Phan-Thien–Tanner constitutive model. The simulated flow behaviors are highly consistent with the experimental observations. The results indicate that three typical flow patterns of dripping, jetting, and threading flows are obtained at different fluid elasticities (denoted by the Weissenberg number Wi) and viscosities (denoted by the Capillary number Ca). Meanwhile, the elastic effect is found to be greater in the dripping flow, significantly reducing the axial tensile stress. It is demonstrated that changes in the stretched state of polymer macromolecules with the same Wi at different Ca lead to variations in the strength of elastic action, which, in turn, affects the extension length and the pinch-off time of droplets. Finally, a relationship equation between the extension length and time of the polymer fluid is established. This present study aims to provide important insight into the preparation of polymeric droplets in microchannels.

Assessment of immersed boundary methods for hypersonic flows with gas-surface interactions

The efficacy of immersed boundary (IB) methods with adaptive mesh refinement (AMR) techniques is assessed in the context of atmospheric entry applications, including effects of chemical nonequilibrium (CNE) and gas-surface interactions (GSI). We scrutinize a conservative cut-cell IB method and two non-conservative ghost-cell IB methods, comparing their results with analytical solutions, data from the literature, and results obtained with a reference solver that operates on body-fitted grids. All solvers employ the same external thermochemistry library, ensuring that all observed differences can be attributed solely to differences in the underlying numerical methodologies. We present results for eight benchmark cases. Four verification cases verify the implementation of chemistry, transport properties, catalytic boundary conditions, and shock capturing. Four validation cases encompass blunt geometries with adiabatic and isothermal, as well as inert, catalytic and ablative boundary conditions. Overall, the results obtained with the IB solvers are in very good agreement with the reference data. Discrepancies arise in cases with large temperature or concentration gradients at the wall, and these are linked to conservation errors inherent to ghost-cell methods. Only a strictly conservative cut-cell IB method is on par with body-fitted grid methods.

The flow around a stepped cylinder with turbulent wake and stable shear layer

The turbulent external flow around a three-dimensional stepped cylinder is studied by means of direct numerical simulations with the adaptive mesh refinement technique. We give a broad perspective of the flow regimes from laminar to turbulent wake at $Re_D=5000$ , which is the highest ever considered for this flow case. In particular, we focus on the intermediate Reynolds number $Re_D=1000$ that reveals a turbulent wake coupled with a stable cylinder shear layer (subcritical regime). This flow shows a junction dynamics similar to the laminar $Re_D=150$ , where no hairpin vortex appears around the edges, and just two horseshoe vortices are visible. A new stable vortex in the form of a ring, which coils around the rear area, is also identified. In the turbulent wake, the presence of three wake cells is pointed out: the large and small cylinder cells together with the modulation region. However, the modulation dynamics varies between the subcritical and turbulent regimes. A time-averaged, three-dimensional set of statistics is computed, and spatially coherent structures are extracted via proper orthogonal decomposition (POD). The POD identifies the (long-debated) connection between the N-cell and the downwash behind the junction. Furthermore, as the Reynolds number increases, the downwash phenomenon becomes less prominent. Eventually, a reduced-order reconstruction with the most energetically relevant modes is defined to explain the wake vortex interactions. This also serves as a valuable starting point for simulating the stepped cylinder wake behaviour within complex frameworks, e.g. fluid–structure interaction.

The influence of aspect ratios of two elliptical cylinders on the solid-liquid phase change flow

Nowadays, phase change materials are widespread in different engineering applications including cooling of electronics, thermal performance in building elements, heat exchangers, and many more. It is critical to gain thorough comprehension on phase change material behavior. The present research aims to numerically simulate phase change material in a heat storage unit having two isothermal elliptical elements. The formulated partial differential equations have been solved by the finite element technique taking into account the enthalpy-porosity approach and adaptive mesh refinement technique. The developed computational code has been validated using numerical and experimental data from the literature. The influence of the aspect ratios of the two elliptical cylinders on the melting phenomenon has been scrutinized, and the most efficient shapes have been identified. It has been found that more intensive melting occurs when the aspect ratios of the upper and lower cylinders are ARu = 0.25 and ARl = 4.0, with a reduction of 18.45 % in the melting time compared to the case with ARu = ARl = 1.0. Furthermore, the case with ARu = 1.0 and ARl = 0.5 shows the longest melting time, with an increase of 0.6 % in the melting time compared to the case with ARu = ARl = 1.0.

Study of mixed-mode fracture in functionally graded material using an adaptive phase-field fracture model

This work systematically investigates the mixed-mode fracture propagation in functionally graded materials. The crack trajectory and load–displacement responses were effectively simulated using the mixed-mode phase field approach in combination with an adaptive mesh refinement technique. The mesh refinement is carried out using quadtree decompositions, and the elements with hanging nodes are handled as n−sided polygons. The adaptive implementation is validated by solving benchmark problems from the literature. The adaptive technique demonstrates greater computational efficiency by significantly reducing the number of elements without compromising the accuracy of the solution. This study provides insight into how fracture propagation behavior is influenced by gradient profile, material gradation, crack location, energy release rate, and displacement configuration in uni-directional and bi-directional functionally graded material. Remarkably, it is found that the peak load on the load–displacement graph changes noticeably, and the fracture path remains constant despite variations in the critical energy release rate. Notably, the results show that materials with lower fracture toughness have an early failure when studying a center fractured plate. This thorough examination deepens our understanding of the propagation of mixed-mode cracks and provides insight into improving the analysis and design methodologies for functionally graded materials.

A finite-volume implementation of the phase-field model for brittle fracture with adaptive mesh refinement

The phase-field method (PFM) has advantages in modeling crack propagation in rock-like materials by treating the crack surface as a continuous function, therefore avoiding dealing with the sharp discontinuous displacement field. This study presents an implementation of PFM using the finite volume method (FVM) to discretize the governing equations for the conservation of linear momentum and the evolution of phase field. The coupled equations are solved by an iterative staggered scheme. The adaptive mesh refinement (AMR) technique is further employed to improve computational efficiency, which is relatively easy to achieve in FVM as the method can naturally handle unstructured meshes with hanging nodes in both two- and three-dimensional problems, as opposed to the finite element method (FEM). Several classical crack propagation problems, including the single-edge notched tension and shear tests, the L-shaped panel test, and the test on a notched plate with a hole, are simulated and compared with available experimental and FEM results, which demonstrate that the FVM-based PFM can model crack propagation accurately and effectively and could be more efficient than the FEM-based PFM.

Adaptive fail-safe topology optimization using a hierarchical parallelization scheme

This work presents an efficient, flexible, and scalable strategy to implement density-based topology optimization formulation for fail-safe structural design. Such optimized designs can operate after faults modeled as loss of stiffness. However, the need for assessing the physical behavior in all the fault cases can make this problem unfeasible computationally. We combine many ingredients to exploit the different levels of parallelism of the formulation to deal successfully with this problem. We use a non-overlapping domain decomposition method to solve the failure cases using multi-core computing with distributed memory computation. These subdomains use adaptive mesh refinement (AMR) techniques to focus computing efforts on the regions of interest. A key point to evaluate the fault cases is the organization of the computing threads, especially in clusters of computers. We group the computing threads by physical computing nodes to reduce the inter-node communications, maximizing intra-node communications to mitigate bandwidth problems. Another ingredient of paramount importance is the use of computing buffers to adapt the evaluation of the fault cases to the computing resources. We test the scalability of the computational framework using a large cluster of computers.

An Adaptive Mesh Refinement–Rotated Lattice Boltzmann Flux Solver for Numerical Simulation of Two and Three-Dimensional Compressible Flows with Complex Shock Structures

An adaptive mesh refinement–rotated lattice Boltzmann flux solver (AMR-RLBFS) is presented to simulate two and three-dimensional compressible flows with complex shock structures. In the method, the RLBFS, which has a strong shock-capturing capability and can effectively eliminate the shock instability phenomenon, is applied to solve the flow filed by reconstructing the fluxes at each cell interface adaptively with the mesoscopic lattice Boltzmann model. To locally and dynamically improve the resolution of intricate shock structures and optimize the required computational resources, a block-structured adaptive mesh refinement (AMR) technique is introduced. The validity and effectiveness of the proposed method are confirmed through a range of two and three-dimensional numerical cases, including the shock tube problem, the four-wave Riemann problem, explosion within a rectangular box, and the vorticity induced by a shock. The results obtained using the AMR-RLBFS exhibit excellent agreement with published data and demonstrate high accuracy in capturing complex shock structures. The computational efficiency of the AMR-RLBFS can be also improved significantly compared to the RLBFS on uniform grids. Furthermore, the numerical outcomes underscore the capability of the AMR-RLBFS to eliminate shock instability effects while efficiently capturing a broader spectrum of small-scale vertical structures. These findings highlight the ability of AMR-RLBFS to improve the computational efficiency and capture intricate shock structures effectively, making it a valuable tool for studying a wide range of compressible flows from aerodynamics to astrophysics.

Analysis of high-speed drop impact onto deep liquid pool

The present work is devoted to the analysis of drop impact on a deep liquid pool, focusing on the high-energy splashing regimes caused by large raindrops at high velocities. Such cases are characterized by short time scales and complex mechanisms, thus they have received very little attention until now. The BASILISK open-source solver is used to perform three-dimensional direct numerical simulations. The capabilities of octree adaptive mesh refinement techniques enable capturing of the small-scale features of the flow, while the volume of fluid approach combined with a balanced-force surface-tension calculation is applied to advect the volume fraction of the liquids and reconstruct the interfaces. The numerical results compare well with experimental visualizations: both the evolution of crown and cavity, the emanation of ligaments, the formation of bubble canopy and the growth of a downward-moving spiral jet that pierces through the cavity bottom, are correctly reproduced. Reliable quantitative agreements are also obtained regarding the time evolution of rim positions, cavity dimensions and droplet distributions through an observation window. Furthermore, simulation gives access to various aspects of the internal flows, which allows us to better explain the observed physical phenomena. Details of the early-time dynamics of bubble ring entrapment and splashing performance, the formation/collapse of bubble canopy and the spreading of drop liquid are discussed. The statistics of droplet size show the bimodal distribution in time, corroborating distinct primary mechanisms of droplet production at different stages.

Dynamic and adaptive mesh-based graph neural network framework for simulating displacement and crack fields in phase field models

Fracture is one of the main causes of failure in engineering structures. Phase field methods coupled with adaptive mesh refinement (AMR) techniques have been widely used to model crack propagation due to their ease of implementation and scalability. However, phase field methods can still be computationally demanding making them unfeasible for high-throughput design applications. Machine learning (ML) models such as Graph Neural Networks (GNNs) have shown their ability to emulate complex dynamic problems with speed-ups orders of magnitude faster compared to high-fidelity simulators. In this work, we present a dynamic mesh-based GNN framework for emulating phase field simulations of single-edge crack propagation with AMR for different crack configurations. The developed framework – ADAPTive mesh-based graph neural network (ADAPT-GNN) – exploits the benefits of both ML methods and AMR by describing the graph representation at each time step as the refined mesh itself. Using ADAPT-GNN, we predict the evolution of displacement fields and scalar damage field (or phase field) with good accuracy compared to the conventional phase-field fracture model. We also compute crack stress fields with good accuracy using the predicted displacements and phase field parameter.

Efficient GPU parallelization of adaptive mesh refinement technique for high-order compressible solver with immersed boundary

A new, highly parallelized, adaptive mesh refinement (AMR) library, equipped with an accurate immersed boundary (IB) method for solving the compressible Navier–Stokes system is presented. The library, named ADAM, is designed to efficiently exploit modern exascale GPU-accelerated supercomputers and it is implemented with a highly modular structure in order to make easy to leverage it for a wide range of CFD applications. The structured Cartesian grids at the basis of (octree) AMR approach allows to implement very high order accurate models retaining a low computational cost and high level of parallelization. The accurate IB method coupled with efficient AMR technique enables the simulation flows with complex (possibly moving and deforming) geometries. The library is applied to the simulation of a strong shock diffraction over a solid sphere and a detailed discussion concerning the physical results and the parallel performance obtained is presented.

DetonationFoam: An open-source solver for simulation of gaseous detonation based on OpenFOAM

Detonation has promising applications in advanced propulsion systems, and numerical simulation is widely used to gain insights into the complex interaction between the hydrodynamic flow and chemical reactions involved in detonation. In this work, detonationFoam, an open-source solver for accurate and efficient simulation of compressible reactive flow and detonation are developed based on OpenFOAM. detonationFoam can simulate compressible, multi-component, reactive flow and it can accurately evaluate the detailed transport coefficients using the mixture-averaged transport model. Compared to rhoCentralFoam, the improved HLLC-P approximate Riemann solver is used in detonationFoam and it helps to accurately resolve shock waves appearing in detonation. Besides, the adaptive mesh refinement and dynamic load balancing algorithms are used in detonationFoam, which greatly improves the computational efficiency. Validation tests including homogenous ignition, unsteady diffusion, shock tube problem, premixed flame, planar detonation, double Mach reflection, detonation cellular structure and oblique detonation wave are conducted. These tests demonstrate that detonationFoam can be used to accurately and efficiently to simulate the compressible, multi-component reactive flow and detonation processes. Program summaryProgram Title: detonationFoamCPC Library link to program files:https://doi.org/10.17632/x45zh4nz28.1Developer's repository link:https://github.com/JieSun-pku/detonationFoamLicensing provisions: GPLv3Programming language: C++Nature of problem: Gaseous detonation involves different length scales and complicated chemistry. To accurately and efficiently simulate the gaseous detonation, adaptive mesh refinement needs to be conducted and detailed chemistry should be considered. Besides, the severe load imbalance caused by the chemical source term evaluation may greatly reduce the computation efficiency.Solution method: An open-source solver, detonationFoam is developed based on OpenFOAM. The species equations considering detailed chemistry are solved in detonationFoam and thereby detonation in a compressible, multi-component, reactive flow can be simulated. The adaptive mesh refinement technique and the dynamic load balancing algorithm are incorporated into detonationFoam. It is demonstrated that detonationFoam can accurately and efficiently simulate gaseous detonation.

An adaptive lattice boltzmann method based on nodal linked-list data structure

An adaptive mesh refinement (AMR) technique based on nodal linked-list data structure for lattice Boltzmann method (LBM) is proposed in this paper. It makes connections between nodal linked-list data structure which is hierarchical and LBM calculation to retain the simplicity of LBM. Based on uniform meshes, the adaptive algorithm refines the meshes by constructing the linked-list of nodes and levels for mesh levels refined. In the nodal linked-list data structure, the relationships for nodal neighbors and upper and lower level indexes of nodes are appointed to help implement the LBM process in the different mesh levels. To guarantee precise transmission of flow field information and numerical stability in the different mesh levels, the average interpolation for temporal and spatial space is used, which chimes in with the accuracy of LBM itself. To verify the present method, flows over square cylinder at Re=30 and circle cylinder at Re=200 are carried out.