Dynamic Mesh Adaptation Research Articles

Wake modeling and simulation of an experimental wind turbine using large eddy simulation coupled with immersed boundary method alongside a dynamic adaptive mesh refinement

Accurate numerical models of the flow around wind turbines is highly relevant for optimizing the energy efficiency of wind farms. The main goal of this work is to apply large eddy simulation (LES) along with an immersed boundary (IB) method to generate spatial and temporal information of the velocity field and forces acting on a fully-resolved NREL S809 airfoil and NREL Phase VI wind turbine. The numerical framework used in the simulations performs LES under a Cartesian block-structured mesh that is dynamically refined via adaptive mesh refinement (AMR) to increase accuracy and reduce computational costs. The mesh refinement criteria is based on Lagrangian points and vorticity. Solid surfaces of the wind turbine are captured using the Lagrangian formulation of the IB method. The simulations are based on the NREL Phase VI wind turbine, where blade analysis of lift and drag coefficients were performed, followed by time-averaged streamwise velocity and vorticity evaluations. For different angles of attack, the wake centerline velocity analysis demonstrates high energy extraction in the near wake of the wind turbine blade. In terms of validation, the drag coefficient of the NREL S809 airfoil achieves better agreement with the experimental data than the lift coefficient. Validation from the NREL Phase VI shows that the power performance difference between the simulation and experiment is lower than 6%. Wake analysis of the wind turbine scenario are based on downstream profiles of the time-averaged streamwise velocity. The numerical simulation shows a higher loss of kinetic energy in the near wake region, mainly in the centerline, compared to benchmark data, but achieves very similar results to literature in the far-wake region.

Multiresolution-Based Mesh Adaptation and Error Control for Lattice Boltzmann Methods with Applications to Hyperbolic Conservation Laws

Lattice Boltzmann methods (LBM) stand out for their simplicity and computational efficiency while offering the possibility of simulating complex phenomena. While they are optimal for Cartesian meshes, adapted meshes have traditionally been a stumbling block since it is difficult to predict the right physics through various levels of meshes. In this work, we design a class of fully adaptive LBM methods with dynamic mesh adaptation and error control relying on multiresolution analysis. This wavelet-based approach allows us to adapt the mesh based on the regularity of the solution and leads to a very efficient compression of the solution without loosing its quality and with the preservation of the properties of the original LBM method on the finest grid. This yields a general approach for a large spectrum of schemes and allows precise error bounds, without the need for deep modifications on the reference scheme. An error analysis is proposed. For the purpose of validating this error analysis, we conduct a series of test cases for various schemes and scalar and systems of conservation laws, where solutions with shocks are to be found and local mesh adaptation is especially relevant. Theoretical estimates are retrieved while a reduced memory footprint is observed. It paves the way to an implementation in a multidimensional framework and high computational efficiency of the method for both parabolic and hyperbolic equations, which is the subject of a companion paper.

Development and verification of a high-speed compressible reactive flow solver in OpenFOAM

This paper proposes a newly developed density-based compressible solver called DCRFoam on a basis of OpenFOAM platform for simulating detonation phenomena with detailed chemical kinetics. It employs AUSM+-up scheme to determine the convective fluxes and a four steps low storage Runge-Kutta time integration method for time integration. A total variation diminishing (TVD) and symmetrical flux limiter sgva is implemented for interpolation process. Also, the dynamic mesh adaptation method is applied to refine or coarsen the computational mesh dynamically since the resolution requirements of supersonic combustion are localized. The numerical solver has been validated systematically with many numerical and experimental results reported in the literature, including those from non-reacting cases (Sod’s shock tube problem, two-dimensional shock/cylinder interaction) to reacting flow cases (the ignition sequence in a shock tube, oblique detonation wave (ODW) initiating process and detonation propagating in a bifurcated channel). The results obtained by current schemes are compared with original central upwind Kurganov-Noelle-Petrova (KNP) scheme in official OpenFOAM. The corresponding result demonstrates the robustness and accuracy of the current solver.

A novel dynamic adaptive unstructured mesh algorithm for simulating multi‐object relative motion in incompressible fluid

AbstractA novel dynamic adaptive unstructured mesh (DAUM) algorithm is proposed to solve incompressible multi‐object relative motion (MORM). The DAUM algorithm, consisting of exponential function deformation, adaptive edge swapping, and area Laplace smoothing, can greatly improve dynamic mesh robustness and perfectly overcome mesh skewness. The core of DAUM is the adaptive edge swapping inspired by Delaunay triangulation, which is distinguished from traditional edge swapping. The adaptive edge swapping can fully consider the relationship of neighbor elements only using Delaunay triangulation. Meanwhile, the implementation and reliability of adaptive edge swapping are better than the traditional edge swapping method due to eliminating the interference of the non‐convex polygon, so more code remedies can be avoided. Using the DAUM, none of the vertices is inserted or deleted so that the manipulation of the dynamic mesh is easily implemented and maintains computational efficiency in the process of mesh motion. Three representative geometries are used to assess the performance of the DAUM in MORM. To systematically analyze the advantages of DAUM, two relatively moving cylinders have been numerically investigated in incompressible flow. The inline force and lift force profiles on two cylinders are obtained and analyzed by using the flow field information. Three interaction stages are divided based on the parameter G and the interactional intensity of two inner anticlockwise vortices is considered as the division criteria. At the running process of the DAUM algorithm, the dynamic mesh quality is well controlled and remains in the high‐quality range based on the aspect ratio (AR) criterion. The results indicate that the proposed DAUM algorithm can properly solve the difficulties caused by MORM, especially for period oscillation motion.

Three-dimensional features of the lateral thermal plume discharge in the deep cross-flow using dynamic adaptive mesh refinement

Three-dimensional features of the lateral thermal plume discharge in the deep cross-flow using dynamic adaptive mesh refinement

Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods

A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial discretization, which enables boundary and interface conditions to be enforced with high-order accuracy on curved embedded geometries. High-order accuracy is achieved via high-order quadrature rules for implicitly-defined domains and boundaries, whilst a cell-merging strategy addresses the presence of small cut cells. The framework is used to discretize the governing equations of elastodynamics, written using a first-order hyperbolic momentum-strain formulation, and an exact Riemann solver is employed to compute the numerical flux at the interface between dissimilar materials with general anisotropic properties. The space-discretized equations are then advanced in time using explicit high-order Runge–Kutta algorithms. Several two- and three-dimensional numerical tests including dynamic adaptive mesh refinement are presented to demonstrate the high-order accuracy and the capability of the method in the elastodynamic analysis of single- and bi-phases solids containing complex geometries.

A geometrical optimization and comparison study on the charging and discharging performance of shell-and-tube thermal energy storage systems

Shell-and-tube latent heat thermal energy storage (ST-LHTES) systems have been extensively studied due to their high thermal/cold storage capacity during the charging/discharging process and their wide range of applications. The thermal performance of these systems is heavily dependent on the shape and geometry of the shell part. This research aims to investigate the transient heat transfer of phase change material (PCM) in the vertical ST-LHTES systems during charging (melting) and discharging (solidification) and the impact of geometric design on the heat transfer characteristics and consequently the thermal performance of the system in both processes. For this purpose, phase change heat transfer in a conventional cylindrical shell is compared with conical configurations with arbitrary inclination angles. The different heat transfer characteristics, e.g., the rate of phase change fraction and the energy stored/released, are determined and compared for all systems to evaluate their thermal performance and find the optimal design. The phase change process is also numerically visualized to track the phase change interface during both charging and discharging processes. A dynamic adaptive mesh refinement technique is implemented to capture gradients and simulate phase change front accurately. Depending upon the inclination angle, a favorable result can be achieved for the charging process in conical shape compared with a cylindrical geometry, while inverse results are obtained for the discharging process. In other words, increasing the lateral slope of the shell from a vertical to tilted state enhances the melting process resulting in a faster energy storage rate during the charging process, whereas decreasing this slope leads to better thermal performance for discharging process. The optimum designs can improve the system performance by 52% and 56% for the charging and discharging processes, respectively. A comprehensive experimental setup is developed for the cylindrical case to visualize and compare the charging and discharging process experimentally as well. Results obtained from numerical simulations exhibit similar patterns to experimental visualizations.

Role of water micro-explosion on fuel droplet size distribution, engine performance, and emissions in a water-diesel emulsified engine: A comprehensive numerical investigation

The global warming crisis and strict regulations have pushed the automotive industry into technological change, but it will take time, so finding quick solutions can be very helpful. Using water in diesel emulsion is one of the low-cost and fast solutions to reduce pollution and improve the performance of diesel engines. In this study, the effects of adding water to diesel fuel and the phenomena that occur when water enters the combustion chamber are investigated. For this purpose, a simulation of a four-cylinder diesel engine has been used with different content of water in diesel (0% or pure diesel, 5%, 10%, 15%, and 20%). The simulations are performed in Converge CFD using dynamic mesh and adaptive mesh refinement. The results showed that the use of water in diesel leads to an improvement of about 10% in engine indicated power and a simultaneous reduction in soot and NOx by 10 and 30%, respectively. The simulation results showed that water droplet micro-explosions accelerated the fuel droplet breakup process and reduced the combustion duration by 10%–30%.

An integrated FEA-CFD simulation of offshore wind turbines with vibration control systems

The vibration mitigation of a monopile Offshore Wind Turbine (OWT) under wind and sea wave excitation is investigated, incorporating dynamic Vibration Control systems (VCS). The application of VCS to the OWTs has the potential to significantly improve the damping of the structure and its overall dynamic responses. A novel passive vibration absorption configuration is proposed, namely the Extended KDamper (EKD). Contrary to the conventional tuned mass dampers, EKD can increase its vibration absorption capability by introducing negative stiffness elements, instead of increasing the additional mass at the top of the towers. Therefore, EKD provides better isolation properties. The EKD optimum design and its realization are based on engineering criteria and realistic manufacturing limitations. The turbulence wind load time histories are determined stochastically while the mean velocity value is produced using the Blade Element Momentum theory. The influence of the sea wave excitation is studied using an integrated Computational Fluid Dynamics (CFD) approach. For the sea wave simulation, both fluids (water and air) are discretized using a non-uniform grid on which the Navier–Stokes equations are solved using the Double Control Volume Finite Element Method (DCVFEM). In order to render the large-scale physical problem computationally feasible, the Dynamic Adaptive Mesh Optimisation (DMO) and High Performance Computing (HPC) schemes are incorporated. The OWT tower is modelled using variable cross section beam elements accounting for geometrical nonlinearity (second order phenomena). The monopile soil–structure interaction (SSI) is modelled using a prismatic beam on elastic foundation together with the corresponding springs and dashpots along the pile’s length. An extensive case study is carried out on a monopile OWT providing insight to the structural dynamics and illustrating the viability of the VCS on the offshore wind industry. It is shown that vibration control can extend the lifetime of the structure, increasing the OWTs’ reliability and sustainability.

Interaction between high-velocity gas and liquid in gas atomization revealed by a new coupled simulation model

Due to the high efficiency and low cost, gas atomization (GA) has been widely applied to produce metal powders. In this paper, the GA process is first modeled by combining the volume of fluid (VOF) model with dynamic adaptive mesh and the discrete phase model (DPM) to simulate the formation of the powders and the evolution of the defects. Simulation results show that the Kelvin-Helmholtz instability in the primary atomization and the membranous droplet breakup and closure in secondary atomization can form the hollow powder. While the presence of the satellite powder is caused by the collisions between the large and small droplets with different velocities. Moreover, the irregular powder is produced when the drag force is not enough to separate the droplets but deforms them. The estimated morphology and size distribution of the particles have a good agreement with the experimental ones. Finally, the possible measures to reduce the defects of the powders have been put forward based on the revealed mechanism of defect evolution. This work provides a deep simulation insight into the GA process, towards producing high-quality metal powders for additive manufacturing on a large scale.

A finite-volume method for simulating contact lines on unstructured meshes in a conservative level-set framework

Accurate numerical simulation of moving contact lines on complex boundaries with surface wettability effect remains a challenging problem. In this paper, we introduce a robust and accurate method to perform 3D contact line simulations on unstructured meshes with an imposed contact angle. The contact angle is imposed through a sub-grid scale curvature term and the contact line motion is enabled thanks to partial slip on the wall. Moreover, an original strategy has been designed to improve normal and curvature computation at contact line from the level-set field. The whole method is validated on 2D and 3D test cases and shows good mass conservation properties. The drop detachment from a horizontal fiber due to gravity or surface tension is then investigated. For this purpose, dynamic mesh adaptation is used to keep high resolution around the interface with moderate number of cells. These realistic cases demonstrate the ability of the numerical method to handle surface wettability effects on resolved complex geometries.

The Utrecht Finite Volume Ice-Sheet Model: UFEMISM (version 1.0)

Abstract. Improving our confidence in future projections of sea-level rise requires models that can simulate ice-sheet evolution both in the future and in the geological past. A physically accurate treatment of large changes in ice-sheet geometry requires a proper treatment of processes near the margin, like grounding line dynamics, which in turn requires a high spatial resolution in that specific region, so that small-scale topographical features are resolved. This leads to a demand for computationally efficient models, where such a high resolution can be feasibly applied in simulations of 105–107 years in duration. Here, we present and evaluate a new ice-sheet model that solves the hybrid SIA–SSA approximation of the stress balance, including a heuristic rule for the grounding-line flux. This is done on a dynamic adaptive mesh which is adapted to the modelled ice-sheet geometry during a simulation. Mesh resolution can be configured to be fine only at specified areas, such as the calving front or the grounding line, as well as specified point locations such as ice-core drill sites. This strongly reduces the number of grid points where the equations need to be solved, increasing the computational efficiency. A high resolution allows the model to resolve small geometrical features, such as outlet glaciers and sub-shelf pinning points, which can significantly affect large-scale ice-sheet dynamics. We show that the model reproduces the analytical solutions or model intercomparison benchmarks for a number of schematic ice-sheet configurations, indicating that the numerical approach is valid. Because of the unstructured triangular mesh, the number of vertices increases less rapidly with resolution than in a square-grid model, greatly reducing the required computation time for high resolutions. A simulation of all four continental ice sheets during an entire 120 kyr glacial cycle, with a 4 km resolution near the grounding line, is expected to take 100–200 wall clock hours on a 16-core system (1600–3200 core hours), implying that this model can be feasibly used for high-resolution palaeo-ice-sheet simulations.

Implementation of a hybrid Lagrangian filtered density function–large eddy simulation methodology in a dynamic adaptive mesh refinement environment

Multispecies mixing processes play an important role in many engineering, biological, and environmental applications. Since simulating mixing flows can be useful to understand its physics and to study industrial issues, this work aims to develop the basis of a methodology able to simulate the physics of multiple-species mixing flows, using a hybrid large eddy simulation/Lagrangian filtered density function (FDF) method on an adaptive, block-structured mesh. A computational model of notional particles transport on a distributed processing environment is built using a parallel Lagrangian map. This map connects the Lagrangian information with the Eulerian framework of the in-house code MFSim, in which transport equations are solved. The Lagrangian composition FDF method, through the Monte Carlo technique, performs algebraic calculations over an ensemble of notional particles and provides composition fields statistically equivalent to those obtained by finite volume numerical solution of partial differential equations. Finally, to maintain high accuracy in the system of stochastic differential equations solver when an adaptive mesh refinement environment is used, a methodology for ensuring mass conservation is developed to preserve at least the statistical moments up to order two, even in the case of annihilation or cloning of a large number of notional particles in one time step, ensuring the applicability of Lagrangian FDF methods in dynamically adaptive grid refinement.

Numerical Simulation of Energy Distribution of Turbulent Vortices in Atmosphere Effects on Aircraft Wake Vortices

The effect of energy distribution of turbulent vortices in atmosphere on the evolution of wake vortices is studied using the numerical simulation approach. Solution-Based Dynamic adaptive mesh method is applied to compute the wake vortex evolution using FLUENT. Two series of cases are designed to study the role of larger and small-scale vortices in the decay of wake vortex, respectively. The results show that energy distribution of different scale vortices has a significant effect on the onset time of vortex linking and the decay rate of wake vortices at the turbulent diffusion phase and fast decay phase.

Технология адаптивного уточнения сетки для задач механики сплошных сред

Adaptive Mesh Refinement (AMR) is widely used today as a way to solve problems in the mechanics of continuous media, which makes it possible to increase the accuracy of the solution at an economical cost of computational resources. The paper presents new structures for storing and processing data for octree mesh adaptation in the leaf model paradigm. The current version of the technique implements a set of algorithms focused on applications to cluster-type parallel computing systems: dynamic mesh adaptation, data structure synchronization, and load balancing of the computing complex. The developed toolkit supports the functionality required for the implementation of various numerical models of continuum mechanics. As an example of possible applications, a difference schemes for heat conduction and gas dynamics using the developed AMR technique are discussed. The results of numerical experiments with model problems are presented.

The Aggregated Unfitted Finite Element Method on Parallel Tree-Based Adaptive Meshes

In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting scheme on locally adapted Cartesian forest-of-trees meshes. We propose a two-step algorithm to construct the finite element space at hand by means of a discrete extension operator that carefully mixes aggregation constraints of problematic degrees of freedom, which get rid of the small cut cell problem, and standard hanging degree of freedom constraints, which ensure trace continuity on nonconforming meshes. Following this approach, we derive a finite element space that can be expressed as the original one plus well-defined linear constraints. Moreover, it requires minimum parallelization effort, using standard functionality available in existing large-scale finite element codes. Numerical experiments demonstrate its optimal mesh adaptation capability, robustness to cut location, and parallel efficiency, on classical Poisson hp-adaptivity benchmarks. Our work opens the path to functional and geometrical error-driven dynamic mesh adaptation with the aggregated finite element method in large-scale realistic scenarios. Likewise, it can offer guidance for bridging other scalable unfitted methods and parallel adaptive mesh refinement.

Hydrodynamic and heat transfer characteristics of droplet train spreading-splashing transition on heated surface

Heat transfer and hydrodynamic characteristics of droplet-induced spreading-splashing transition have been investigated experimentally and numerically. Specifically, the study involved the characterization of a train of monodispersed micron-sized droplets impinging on a heated surface covered by a thin liquid film at different droplet Weber number values. A single stream of mono-dispersed droplets was generated using a piezo-electric droplet generator with the ability to adjust parameters such as droplet impingement frequency, droplet diameter and droplet impingement velocity. A thin layer of Indium Tin Oxide was coated on a translucent sapphire substrate, which was used as a heating element. High-speed optical imaging and infrared thermal imaging techniques were used to characterize the hydrodynamics and heat transfer of droplet train impingement, respectively. It was observed that at low Weber number (We = 280), droplet impingements resulted in smooth spreading of the droplet-induced crown while splashing was observed at high Weber number (We > 489) cases. The effect of spreading-splashing transition on surface heat transfer has also been investigated at fixed flow rate conditions. Time-averaged temperature measurements indicate that the heat flux-surface temperature curves are linear at low surface temperature and before the onset of dry-out. However, a sharp increase in surface temperature was observed when dry-out appeared on the heater surface due to phase change. It was also found that strong splashing is unfavorable for heat transfer at high surface temperatures due to the instabilities seen in the liquid film, which leads to the onset of dry-out. Numerically, the Coupled Level Set-Volume of Fluid approach was used successfully to capture the hydrodynamic and thermal aspects of droplet train impingement on a heated surface. Furthermore, the dynamic mesh adaption technique was used in all simulations, which is capable of capturing the propagation of droplet-induced crown with high spatial and temporal resolutions. A good agreement was reached between experimental and numerical data in terms of droplet-induced crown morphology and surface temperatures. Thermal boundary layer displacement thickness profiles from numerical analysis were used to understand the coupled nature of hydrodynamics and heat transfer within the thin liquid film. In summary, the results indicate that droplet Weber number is a significant factor in spreading-splashing transition and droplet-induced liquid film heat transfer.

Wall effect on interaction and coalescence of two bubbles in a vertical tube

While most studies on bubble dynamics are carried out in unconfined geometries, less attention has been paid to investigate confined bubbles and wall effects. This paper numerically investigates interaction and coalescence of two buoyancy-driven inline bubbles in a confined cylindrical vessel to study wall effects. An improved volume-of-fluid method is adopted, and high mesh resolution is achieved by dynamic adaptive mesh refinement. The confinement ratio, CR (the ratio of the radius of the cylindrical tube to the radius of the bubble), is introduced to quantitatively describe the wall proximity. In this paper, the interaction between bubbles is divided into three regimes according to the strength of the liquid influx behind the trailing bubble during bubble interaction (i.e., “weak interaction,” “intermediate interaction,” and “strong interaction”). If the CR is larger than a critical value (CR = 4 in this study), the wall effect can be neglected. It is found that wall proximity reduces the strength of the liquid influx behind the trailing bubble, which causes regime transition. In “strong interaction” and “intermediate interaction” regimes, if the CR is below another critical value, which is termed the second critical CR, “strong interaction” is degraded to “intermediate interaction,” and “intermediate interaction” can be degraded to “weak interaction.” A broader range of parameters is studied to explore the effect of confinement on bubble coalescence, and we further discovered that decreasing the CR does not necessarily postpone coalescence. This work provides insights into bubble motion and interaction influenced by the side wall.

GPU-native gas dynamic solver on octree-based AMR grids

GPU implementation of the Godunov-type gas dynamic solver on three-dimensional octree-based grids is proposed. In this implementation, all dynamic adaptive mesh refinement (AMR) procedures are performed entirely on GPU as opposed to most of other implementations where grid metadata is transferred to CPU for further updating. Conducted bench tests show that eliminating regular CPU–GPU grid data transferring in the proposed parallel AMR algorithms makes it possible to reduce the grid modification overhead to lower than 2% on Nvidia Tesla V100. The results concerned with both CUDA and OpenMP implementation performance are also presented.

Delayed approximate matrix assembly in multigrid with dynamic precisions

SummaryThe accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix‐free environment where we have to be able to quickly return matrix entries upon demand. Either way, the construction can become costly due to nontrivial material parameters entering the equations, multigrid codes requiring cascades of matrices that depend upon each other, or dynamic adaptive mesh refinement that necessitates the recomputation of matrix entries or the whole equation system throughout the solve. We propose that these constructions can be performed concurrently with the multigrid cycles. Initial geometric matrices and low accuracy integrations kickstart the multigrid iterations, while improved assembly data is fed to the solver as and when it becomes available. The time to solution is improved as we eliminate an expensive preparation phase traditionally delaying the actual computation. We eliminate algorithmic latency. Furthermore, we desynchronize the assembly from the solution process. This anarchic increase in the concurrency level improves the scalability. Assembly routines are notoriously memory‐ and bandwidth‐demanding. As we work with iteratively improving operator accuracies, we finally propose the use of a hierarchical, lossy compression scheme such that the memory footprint is brought down aggressively where the system matrix entries carry little information or are not yet available with high accuracy.