Adaptive Mesh Refinement Method Research Articles

Adaptive mesh refinement towards optimized mesh generation for large eddy simulation of turbulent combustion in a typical micro gas turbine combustor

Over the last years, several advanced micro Gas Turbine (mGT) cycle developments have been proposed, aiming at making the mGT more fuel and operational flexible. However, accurate data on real industrial combustors, assessing the performances and emissions of the combustion under unconventional diluted conditions or fuels involved in these novel cycles, are still missing. In this framework, Large Eddy Simulations, who allow to accurately assess the unsteady effects coupled to turbulent-chemistry interaction of reacting flows, offer an opportunity to better assess the combustion behavior under these specific conditions. However, the computational cost remains much higher compared to RANS simulations. The mesh generation process might be complex, especially when the region of interest is not intuitively known. Therefore, Adaptive Mesh Refinement (AMR) methods allow the mesh to be refined only in the region where finer cells are required to capture important phenomena, i.e. in the flame front. By dynamically refining the mesh all along the simulation, the mesh is optimized in terms of cell quantity and distribution for more accurate results at potentially lower computational costs. In this work, an adaptive mesh refinement method based on a predefined criterion is successfully applied to the LES of a typical industrial mGT combustor, the Turbec T100. The results show that the adaptation strategy allows to automatically generate a dynamic mesh that is able to capture correctly the flame over time for an increased computational cost of 15%. Therefore, the human meshing effort is reduced while the automatic meshing leads to an optimized mesh.

Droplet Injection for Multiphase Rainfall Simulations on Dynamically Refined Mesh for Effective Interface Capturing

This paper presents a volume of fluid (VOF) model for multiphase rainfall simulation that injects rain droplets as a continuous phase alongside the adaptive mesh refinement (AMR) method to resolve air-water interfaces. An approach based on multi-level domains and a pseudo-random algorithm is proposed to determine injection locations in a random and non-intrusive manner with the least bias. Face zones instead of faces are adopted as constituent elements for droplet injection to prevent droplet fragmentation due to a change of face IDs caused by AMR. Correspondingly, a new multi-level address system is introduced to establish the correspondence among subdomains at different levels. The model is applied to multiphase flow VOF simulation for parametric 2-D and 3-D rainfall analysis. The results are verified by the data reported in the literature. It demonstrates that the model can efficiently simulate realistic rainfall phenomena, capture the droplet interface, and preserve droplet injection uniformity.

Effect of the tip speed ratio on the wake characteristics of wind turbines using LBM‐LES

AbstractIn this paper, the wake characteristics of Zell 2000 wind turbine under different tip velocity ratios are studied by using the lattice Boltzmann method and large eddy simulation. The adaptive mesh refinement method is performed to capture the fine flow structure and wake characteristics development. In this paper, we mainly focus on the effect of the tip speed ratio on the flow structure and unsteady characteristics of wind turbine wake. The three‐dimensional flow vorticity structures, the section vorticity diagram, the pressure fluctuation of wake and the lift coefficient of wind turbine wake are utilized to explore the effect of the tip speed ratio on the unsteady physics mechanism of wind turbine wake. With the increase of the tip speed ratio, the distance between two adjacent vortex rings along the axial direction gradually decreases, as the position of the broken vortex circles gradually approaches the center of the blade, separated vortexes are rapidly generated, and the coherent structure appears closer to the wind turbine. A relationship is established between the tip speed ratios and the positions of the broken vortex circles. It is further found that the dominant frequency amplitude gradually increases with the increase of tip speed ratio and the pressure amplitude spectra of vortex increases with the decrease of the distance between the wake and the center of the blade axis. The above series of studies can provide significant physical insight into deep understanding the influence of the tip speed ratio on the wake characteristics of wind turbines.

An adaptive h-refinement method for the boundary element fast multipole method for quasi-static electromagnetic modeling

Objective. In our recent work pertinent to modeling of brain stimulation and neurophysiological recordings, substantial modeling errors in the computed electric field and potential have sometimes been observed for standard multi-compartment head models. The goal of this study is to quantify those errors and, further, eliminate them through an adaptive mesh refinement (AMR) algorithm. The study concentrates on transcranial magnetic stimulation (TMS), transcranial electrical stimulation (TES), and electroencephalography (EEG) forward problems. Approach. We propose, describe, and systematically investigate an AMR method using the boundary element method with fast multipole acceleration (BEM-FMM) as the base numerical solver. The goal is to efficiently allocate additional unknowns to critical areas of the model, where they will best improve solution accuracy. The implemented AMR method’s accuracy improvement is measured on head models constructed from 16 Human Connectome Project subjects under problem classes of TES, TMS, and EEG. Errors are computed between three solutions: an initial non-adaptive solution, a solution found after applying AMR with a conservative refinement rate, and a ‘silver-standard’ solution found by subsequent 4:1 global refinement of the adaptively-refined model. Main results. Excellent agreement is shown between the adaptively-refined and silver-standard solutions for standard head models. AMR is found to be vital for accurate modeling of TES and EEG forward problems for standard models: an increase of less than 25% (on average) in number of mesh elements for these problems, efficiently allocated by AMR, exposes electric field/potential errors exceeding 60% (on average) in the solution for the unrefined models. Significance. This error has especially important implications for TES dosing prediction—where the stimulation strength plays a central role—and for EEG lead fields. Though the specific form of the AMR method described here is implemented for the BEM-FMM, we expect that AMR is applicable and even required for accurate electromagnetic simulations by other numerical modeling packages as well.

An adaptive mesh refinement method based on a characteristic‐compression embedded shock wave indicator for high‐speed flows

AbstractNumerical simulation of high‐speed flows often needs a fine grid for capturing detailed structures of shock or contact wave, which makes high‐order discontinuous Galerkin methods (DGMs) extremely costly. In this work, a characteristic‐compression based adaptive mesh refinement (AMR, h‐adaptive) method is proposed for efficiently improving resolution of the high‐speed flows. In order to allocate computational resources to needed regions, a characteristic‐compression embedded shock wave indicator is developed on incompatible grids and employed as the criterion for AMR. This indicator applies the admissible jumps of eigenvalues to measure the local compression of homogeneous characteristic curves, and theoretically can capture regions of characteristic‐compression which contain structures of shock, contact waves and vortices. Numerical results show that the proposed h‐adaptive DGM is robust, efficient and high‐resolution, it can capture dissipative shock, contact waves of different strengths and vortices with low noise on a rather coarse grid, and can significantly improve resolution of these structures through mild increase of computational resources as compared with the residual‐based h‐adaptive method.

Tsunami Inundation Modelling in a Built-In Coastal Environment with Adaptive Mesh Refinement: The Onagawa Benchmark Test

In tsunami studies, understanding the intricate dynamics in the swash area, characterised by the shoaling effect, remains a challenge. In this study, we employed the adaptive mesh refinement (AMR) method to model tsunami inundation and propagation in the Onagawa town physical flume experiment. Using the open-source flow solver Basilisk, we implemented the Saint-Venant (SV) equations, Serre–Green–Naghdi (SGN) equations, and a nonhydrostatic multilayer (ML) extension of the SGN equations. A hydraulic bore tsunami-like wave was used as the input boundary condition. The objective was to assess the efficiency of the AMR method with nonhydrostatic tsunami models in overcoming limitations in 2D and quasi-3D models in flume experiments, particularly with respect to improving accuracy in arrival time and run-up detection. The results indicate improved performance of the SGN and SV models in determining tsunami arrival times. The ML model demonstrated enhanced wave run-up simulations on complex built-in terrain. The refined roughness coefficient determined using the ML solver captured the arrival time well in the northern section of the Onagawa model, albeit with a 1 s delay. The AMR method offered a computationally stable solution with an 86.3% reduction in computational time compared to a constant grid. While effective, the nonhydrostatic models entail the use of a great deal of computational resources.

NUMERICAL INVESTIGATION ON PULSE DETONATION ENGINE PERFORMANCE UNDER DIFFERENT EQUIVALENCE RATIO

Detonation-based engines have a higher thermal efficiency than deflagration-based engines and are therefore widely studied. In this study, the effect of initiation conditions on the detonation wave propagation and the performance of a pulse detonation engine, one type of detonation-based engine, was numerically investigated. Hydrogen-oxygen mixtures with equivalence ratios of φ=0.8, 1.0, and 1.2 were defined as initiation conditions with constant pressure and temperature. The numerical simulations were conducted using the transient explicit density-based solver in the ANSYS Fluent commercial software. The adaptability of the adaptive mesh refinement method in detonation-based engines was explored in the numerical studies, reducing the average total cell count by a factor of 2.617, and obtaining consistent results according to validation studies. The adaptive mesh refinement method was also used in numerical simulations where different equivalence ratios were defined. It was determined that an increase in the equivalence ratio resulted in an increase in the detonation wave velocity. Also, an increase in thrust distribution at the nozzle exit was observed before the blowdown stage, and the calculated thrust values for φ=0.8, φ=1.0, and φ=1.2 were 248.28 N, 264.5 N, and 270.83 N, respectively.

Dynamic evolution and morphological analysis of supersonic turbulence arising during the collision of prolate and spherical clouds

Our understanding of the formation and interaction processes of astronomical structures in the Universe and in galaxies has significantly expanded due to recent progress in improving the quality of observations, brought about by the emergence of new telescopes. Such processes are associated with the release of a significant amount of energy and may influence our vital activities. One example of energy flow release is magnetic storms, which are associated with processes occurring on the Sun. Such storms lead to disruptions of communication facilities, impact people, and can cause satellite and aircraft failures. There are objects in both near and deep space that are much more powerful than our star. In such objects, enormous energy flows are generated and released in the form of space jets. These energy flows occur in quasars, black holes, protostars, and during supernova explosions of types Ia, Ib, Ic, and II. During a supernova explosion, an immense amount of energy is released in the form of energy and high-energy particles. Such processes can have a significant impact on the safety of space flights. In this paper, the processes of formation of stellar systems within a turbulent interstellar medium are considered. This process is the result of complex processes that occur in the interstellar medium and denser gas formations – molecular clouds. At the same time, there are nonlinear interactions between turbulence and gravity, collisions between molecular clouds, interactions with shock waves, and so on. Supersonic turbulence is one of the main reasons for the formation of dynamic prestellar structures. The evolution of superdense substances formation begins when they gather in turbulent flows or are formed by supersonic collisions between molecular clouds. This process continues until these areas reach prestellar density. Depending on various factors, these superdense formations can either collapse and form new star systems or disintegrate, returning the substance to the interstellar medium. Until recently, the prevailing opinion was that a significant portions of molecular clouds were not gravitationally bound. Conclusions about this were made based on the virial theorem, which expresses the relationship between gravitational and kinetic energy. However, recent studies have refuted this. In this paper, the results of a simulation carried out to study the collision of large ellipsoidal and spherical molecular clouds in a three-dimensional setting. The simulation was conducted on high-resolution grids and utilized the adaptive mesh refinement (AMR) method.

Effect of unsteady supersonic flow on detonation under different hot jet initiation conditions

To understand the actual operation of detonation engines, it is of great significance to simulate the detonation characteristics after being affected by unsteady supersonic flow. Adaptive mesh refinement method and single-step chemical reaction model were used for simulation calculations. The Navier–Stokes equations and hybrid sixth-order weighted essentially non-oscillatory centered difference scheme was adopted in this study. Three different amplitudes of disturbances (0.1, 0.2, and 0.3) and two hot jet injection times were analyzed. The results showed that a moderate disturbance can improve the stability of detonation wave under the ideal hot jet injection time. It allows detonation wave to stay in the combustion chamber for a longer time, which is beneficial for the release of thrust performance. Although the stability of detonation wave is significantly different between the low and high-amplitude disturbances, the residence time of detonation wave is close to the steady flow case under ideal initiation conditions. When the ignition time is insufficient, successful detonation can occur with low and medium-amplitude disturbances. However, the ignition delay was significantly prolonged with medium-amplitude disturbance. There was also greater instability, which is detrimental to the thrust release. When the inflow has a high-amplitude disturbance, the detonation wave fails to ignite due to insufficient energy.

Low-Thrust Transfer Orbit Optimization Using Sequential Convex Programming and Adaptive Mesh Refinement

In this paper, a mesh-adaptive Hermite–Simpson sequential convex programming (SCP) method is proposed for solving low-thrust orbit transfer problems efficiently and accurately. First, we develop a Hermite–Simpson convex programming method that utilizes quadratic polynomial control interpolation to improve discretization accuracy. Then, a mesh-adaptive Hermite–Simpson SCP method is proposed by incorporating an improved adaptive mesh refinement method into the Hermite–Simpson SCP method for solving optimal control accurately and efficiently. The proposed method is applied to two-dimensional time-optimal and three-dimensional fuel-optimal low-thrust orbit transfer problems to show its features, and its performance is compared against several existing methods. Numerical simulations show that the proposed method achieves more accurate solutions while being computationally more efficient compared to the trapezoidal SCP method. In comparison to the GPOPS-II software, the proposed method produces solutions of comparable accuracy but is more computationally efficient.

Dynamical energy dissipation of relativistic magnetic bullets

ABSTRACT To demonstrate the magnetic energy dissipation via relativistic shocks, we carry out spherically symmetrical one-dimensional special relativistic magnetohydrodynamic simulations of highly magnetized outflows with an adaptive mesh refinement method. We first investigate the details of the dynamical energy dissipation via interaction between a single ejecta and an external medium. The energy dissipation time-scales, which affect the early behaviour of the afterglow emission in gamma-ray bursts, are estimated for a wide range of magnetization. In addition, we demonstrate the internal shock dissipation in multiple interactions between magnetically dominated relativistic ejecta and kinetically dominated non-relativistic winds. Our numerical results show that ∼10 per cent of the magnetic energy in the ejecta can be converted into the thermal energy of the relativistic and low-magnetized outflows via shocks in the rarefaction waves or the winds. Such hot and less magnetized outflows are relevant for observed non-thermal emissions in blazars or gamma-ray bursts.

Multi-scale Simulation of Subsequent Tsunami Waves in Japan Excited by Air Pressure Waves Due to the 2022 Tonga Volcanic Eruption

The 2022 Hunga Tonga-Hunga Ha’apai eruption generated tsunamis that propagated across the Pacific Ocean. Along the coast of Japan, nearshore amplification led to amplitudes of nearly 1 m at some locations, with varying peak tsunami occurrence times. The leading tsunami wave can generally be reproduced by Lamb waves, which are a type of air-pressure wave generated by an eruption. However, subsequent tsunamis that occurred several hours after the leading wave tended to be larger for unknown reasons. This study performs multi-scale numerical simulations to investigate subsequent tsunami waves in the vicinity of Japan induced by air pressure waves caused by the eruption. The atmospheric pressure field was created using a dispersion relation of atmospheric gravity wave and tuned by physical parameters based on observational records. The tsunami simulations used the adaptive mesh refinement method, incorporating detailed bathymetry and topography to solve the tsunami at various spatial scales. The simulations effectively reproduced the tsunami waveforms observed at numerous coastal locations, and results indicate that the factors contributing to the maximum tsunami amplitude differ by region. In particular, bay resonance plays a major role in determining the maximum amplitude at many sites along the east coast of Japan. However, large tsunami amplification at some west coast locations was not replicated, probably because it was caused by amplification during oceanic wave propagation rather than meteorological factors. These findings enhance our understanding of meteotsunami complexity and help distinguish tsunami amplification factors.

Simulation Analysis of the Effect of Slit/Slot Pintle Geometry on Atomization of Bipropellant Engine

In order to optimize the slit/slot geometry design of a bipropellant pintle injector, the impinging spray development of a pintle injector was numerically investigated. The VOF (volume of fluid) and LES (large eddy simulation) methods were employed for an analysis to capture the gas–liquid interface by means of the AMR (adaptive mesh refinement) method. In those simulation cases, different flowrates, slot numbers, pintle diameters, slot thicknesses and slot shapes were compared for an analysis. In a comparison of visualization and quantification, a high flowrate and large pintle diameter were shown to be more positive features for improving the atomization quality and mixing effect. As for the slot parameters and shape, the spray development was mainly determined by the flow proportion between the slit jet and slot jet. The simulation results indicated that dominant slot jets cause a more dispersed spatial distribution, which is more conducive to the subsequent improvement of combustion efficiency in a limited space. However, an excessive increase in the number of slot jets can weaken the overall atomization quality and mixing effect, so it is suggested to ensure a balance for geometry design optimization.

Minimum-time lane changing problem of vehicle handling inverse dynamics based on adaptive mesh refinement and collocation optimization method

In order to solve the problems of multiple constraints, many different calculations of nonlinear equations which lead to major errors in the process of vehicle lane changing with minimum time, an adaptive mesh refinement and collocation optimization method is proposed. Firstly, the problem of vehicle lane changing with minimum time has been divided into nonlinear programming problems in different grids. The Lagrange interpolation polynomial was used to approximate the solution of the optimization problem in the grid, and the absolute and relative errors were resolved. Then, a mesh was determined for the unsmooth part according to the curvature of the trajectory, and the location and number of meshes were further determined according to the relationship between the maximum relative error and the allowable error. At the same time, the solution accuracy was improved by adding an adaptive calculation to the smooth interval which does not meet the tolerance error. Finally, the simulation example of comparison with the traditional optimization method was proposed. The results showed that the algorithm presented in the paper had a higher solution efficiency under the same calculation accuracy.

Numerical solution to phase-field model of solidification: A review

Recent advances in improving the computational efficiency of the phase-field simulations of solidification microstructures are reviewed. The parallel progress of four typical approaches, namely, multigrid, adaptive mesh refinement method, semi-implicit Fourier spectral method, and graphical processing units (GPUs) architecture, is highlighted. Large-scale spatiotemporal simulations are successfully performed to cover essential aspects of multiphysics with the capability of these algorithms. Focus is put on the principles, applications, and comparison of the four algorithms, while solidification theories and discretization methods are outlined.

A phase-field Lattice Boltzmann method for liquid-vapor phase change problems based on conservative Allen-Cahn equation and adaptive treegrid

A phase-field Lattice Boltzmann method (LBM) based on Allen-Cahn (A-C) equation with a modified adaptive mesh refinement (AMR) method is presented to simulate the liquid-vapor phase change problem. Three Lattice Boltzmann equations are solved: one for the conservative Allen-Cahn equation, one for the incompressible Navier-Stokes equations, and one for the energy equation. These three equations are written in the form of multiple-relaxation-time, together with the equilibrium and forcing terms using the set of Hermite polynomials. The adaptive mesh refinement technique with quadtree grid data structure is implemented to capture the liquid-vapor interface in simulations, in which the mesh can be locally refined by subdividing blocks identified by user-defined criterion. The Lax-Wendroff finite-difference scheme is adopted to calculate the whole computational domain continuously under nonuniform grids. The present method is validated by the classical Stefan problem and then performed to simulate the film boiling heat transfer. The numerical experiments verify the ability of the proposed method to capture the correct evolution of the interface, guarantee the numerical accuracy and remarkably save the computational cost.

Free-surface flow simulations with floating objects using lattice Boltzmann method

ABSTRACTIn tsunami inundations or slope disasters of heavy rain, a lot of floating debris or driftwood logs are included in the flows. The damage to structures from solid body impacts is more severe than the damage from the water pressure. In order to study free-surface flows that include floating debris, developing a high-accurate simulation code of free-surface flows with high performance for large-scale computations is desired. We propose the single-phase free-surface flow model based on the cumulant lattice Boltzmann method coupled with a particle-based rigid body simulation. The discrete element method calculates the contact interaction between solids. An octree-based AMR (Adaptive Mesh Refinement) method is introduced to improve computational accuracy and time-to-solution. High-resolution grids are assigned near the free surfaces and solid boundaries. We conducted two kinds of tsunami flow experiments in the 15 and 70 m water tanks at Hachinohe Institute of Technology and Kobe University to validate the accuracy of the proposed model. The simulation results have shown good agreement with the experiments for the drifting speed, the number of trapped wood pieces, and the stacked angles.

Phase-field lattice Boltzmann simulation of three-dimensional settling dendrite with natural convection during nonisothermal solidification of binary alloy

Understanding the motion and growth behaviors of equiaxed dendrites during solidification is important for predicting macrosegregation. In this study, we develop a phase-field lattice Boltzmann (PF-LB) simulation method for the settling and growth of an equiaxed dendrite during the nonisothermal solidification of a binary alloy. The PF-LB computations are accelerated by employing parallel computation using multiple graphic processing units (GPUs) and the octree block-structured adaptive mesh refinement method, which incorporates multiple mesh and time increment methods. By using the developed method, we can simulate the three-dimensional long-distance settling dendrite while considering the effects of latent heat release and natural convection. From the simulation results, we confirm that the natural convection due to the high solute concentration around a dendrite reduces the settling velocity. In addition, we observe that the temperature increase owing to latent heat release slows dendrite growth, which in turn slightly slows the settling velocity. From these results, we confirm that the effects of latent heat release and natural convection are not negligible in the quantitative evaluation of settling dendrites.

An Evaluation of Accuracy and Efficiency of a 3D Adaptive Mesh Refinement Method with Analytical Velocity Fields

Appropriate mesh refinement plays a vital role in the accuracy and convergence of computational fluid dynamics solvers. This work is an extension of the previous work that further demonstrates the accuracy of the 3D adaptive mesh refinement method by comparing the accuracy measures between the ones derived from the analytical fields and those identified by the refined meshes. The adaptive mesh refinement method presented in this study is based on the law of mass conservation for three-dimensional incompressible or compressible steady fluid flows. The assessment of the performance of the adaptive mesh refinement method considers its key features such as drawing closed streamline and identification of singular points, asymptotic planes, and vortex axis. Several illustrative examples of the applications of the 3D mesh refinement method with a multi-level refinement confirm the accuracy and efficiency of the proposed method. Furthermore, the results demonstrate that the adaptive mesh refinement method can provide accurate and reliable qualitative measures of 3D computational fluid dynamics problems.

Triangular metric-based mesh adaptation for compressible multi-material flows in semi-Lagrangian coordinates

In this paper, we propose an adaptive mesh refinement method for 2D multi-material compressible non-viscous flows in semi-Lagrangian coordinates.The mesh adaptation procedure is local and relies on a discrete metric field evaluation. The remapping method is second-order accurate and we prove its stability. We propose a multi-material treatment using two ingredients: the local remeshing is performed in a way that reduces as much as possible the creation of mixed cells and an interface reconstruction method that can be used to avoid the diffusion of the material interfaces.The obtained method is almost Lagrangian and can be implemented in a parallel framework. We provide some numerical tests which attest the validity of the method and its robustness.