Adaptive Mesh Refinement Strategy Research Articles

A finite volume parallel adaptive mesh refinement method for solid-liquid phase change

We present a finite volume adaptive mesh refinement method for solid-liquid phase change problems with convection. The refinement criterion consisted of three different error estimators for the solid-liquid interface, the flow field, and the temperature field respectively. For the solid-liquid interface, the cells undergoing phase change were refined based on the maximum difference in the liquid fraction over the cell faces. For the flow field and the temperature field, an error indicator was used based on the cell residual method. To maintain a high parallelization efficiency, a dynamic load balancing procedure was used. The adaptive mesh refinement strategy was verified through three different test cases, these are the gallium melting in both 2D and 3D cavities, and the molten salt reactor freeze valve. For all three cases, very good agreement was obtained between the adaptive mesh results and the reference solutions. In addition, more accurate results were obtained with the adaptive meshes compared to static meshes with a similar amount of mesh cells. This illustrated the potential of the current approach for developing computationally efficient numerical methods for solid-liquid phase change problems.

A posteriori-based, local multilevel mesh refinement for the Darcy porous media flow problem

In this work we develop an a posteriori-based adaptive local multilevel mesh refinement strategy for the Darcy porous media flow problem discretized with the finite volume method. Our approach is based on coupling the FIC “flux interface correction” method [1] and the equilibrated flux a posteriori error estimate [2]. The choice of the FIC method is motivated by the fact that it is well-adapted to problems discretized in conservative form since that the FIC provides corrections by balancing fluxes computed from both coarse and fin grids across the interface. The equilibrated flux a posteriori error estimate provides a guaranteed upper bound on the total error in the fluxes and takes advantage of the conservative scheme in such a way that the estimate can be easily coded and cheaply evaluated. We use this a posteriori estimate to detect automatically the zone of interest where the error is dominant in order to defined the local sub-grids. Numerous numerical experiments on practical problems illustrate the performance of our methodology. A comparison with a classical h-adaptive method is also carried out in this work.

Non-uniform knot (NUK) SIAC post-processing of flow fields produced through unstructured grid adaptation and optimization

As the finite element method (FEM) and the finite volume method (FVM), both their traditional and high-order variants, continue their proliferation into various applied engineering disciplines, adaptive mesh refinement and optimization strategies have increased in their importance when solving real-world computational fluid mechanics applications. The post-processing and visualization of the resulting flow fields present two significant analysis and visualization challenges. The first challenge is the handling of elemental continuity, which is often only C0 continuous (in continuous Galerkin methods) or piecewise discontinuous (in discontinuous Galerkin methods). The second challenge is that, depending on the flow regime and the geometric configurations for which adaptive meshing strategies are used, the meshes generated are often highly anisotropic. The (uniform knot) line-SIAC (L-SIAC) filter has been proposed as a way of handling elemental continuity issues in an accuracy-conserving manner with the added benefit of casting the data in a smooth context even if the representation is element discontinuous. In this paper, we demonstrate that the state-of-the-art adaptive L-SIAC filter, designed for mildly anisotropic meshes, suffers degradation in the quality of the post-processed solution when applied to the types of highly anisotropic meshes produced through adaptive mesh refinement and optimization. Hence, a new Non-Uniform Knot (NUK) L-SIAC filter is proposed that automatically conforms to the underlying mesh anisotropy. We demonstrate that the new filter behaves similarly to the adaptive L-SIAC filter when applied to uniform and mildly anisotropic meshes, and furthermore we show the superiority of the NUK L-SIAC filter when applied to highly anisotropic meshes. The newly formulated filter is applied to 2D canonical scalar fields and used to visualize 2D and 3D fluid flow simulation results.

Formation dynamics of the satellite droplet in the breakup of a symmetrical liquid bridge

Inkjet printing technology has played an irreplaceable role in life science, precision manufacturing, and other frontier fields in recent years. However, the further development of this technology is limited by the fact that its printing resolution is difficult to raise to a higher level. The emerging satellite droplet printing technology offers a new approach for inkjet printing to break through the bottleneck of printing resolution limitations. In this paper, a symmetrical satellite droplet printing strategy is proposed. The effects of the geometric parameters of the satellite droplet generating device, the physical properties of the ink, and the operating parameters on the liquid bridge breakup process and the size of the satellite droplet are systematically studied. The phase field method and adaptive mesh refinement strategy are applied to solve the two-dimensional symmetrical model. The results indicate that the length of the liquid bridge, the radius of the bridge, the viscosity of the ink, and the drainage velocity are all positively correlated with the satellite droplet size, while the surface tension coefficient has a negative correlation with the satellite droplet size. Furthermore, the three-phase contact line at the orifice end will slip toward the center if the initial radius of the liquid bridge is quite large. Based on these investigations and discussions, a corresponding effective working space for satellite droplet printing is obtained, which lays the foundation for the popularization and further development of satellite droplet printing technology.

Numerical investigation of the interaction between an interface and a decaying Lamb–Oseen vortex

The present study investigates the dynamics of the interface in the presence of a decaying Lamb–Oseen vortex, and four distinct wave patterns are observed: non-breaking waves with small periodic oscillations, plunging breakers, depression breakers, and gravity–capillary waves. The deformation of the interface is induced by a two-dimensional Lamb–Oseen vortex, and the study examines the influence of vortex strength and surface tension on the resulting flow. The wave dynamics are characterized as a function of the Reynolds and Weber numbers, and a phase diagram is presented in terms of (Re, We) to distinguish the different wave patterns. To ensure accurate reconstruction of the interface, the numerical methods used in this study feature a mass and momentum consistent advection method, high-order interpolation schemes, and a block-structured adaptive mesh refinement strategy. The study presents the characteristics of the air cavity entrained at the moment of wave impact for each wave pattern. Furthermore, the results provide insight into the nature of bubble entrainment within a vortex and reveals the bubble entrainment process via a breakup cascade. Meanwhile, it is also shown that the entrainment of bubble results in significant vortex distortion. Overall, this research contributes to enhance our understanding of wave dynamics and the intricate interaction between vortices and interfaces.

A [formula omitted] continuous multi-patch framework for adaptive isogeometric topology optimization of plate structures

This study proposes a novel computationally efficient methodology to perform topology optimization (TO) of fourth-order plate structures within the framework of multi-patch isogeometric analysis. This is realized by taking the multifold benefits of isogeometric PHT-Splines to (1) discretize the C1 continuous weak form of plate structures, (2) develop a C0 continuous density field for the material distribution in TO and inherently remove the need for filters, and (3) provide a hierarchical tree structure for the structural mesh to effortlessly implement an adaptive mesh refinement (AMR) strategy. Moreover, to ensure continuity between isogeometric patches, we adopt a strong C1 coupling between the boundaries. This is established by constructing new basis functions, defined as a linear combination of existing C0 functions at the patch interfaces. The density field in TO is further enhanced with a first-neighbourhood smoothening algorithm based on the Shepard function to generate printable topologies and alleviate the post-processing stages after optimization. An element-centre density, based on the control point densities of the isogeometric mesh, is used as the marking scheme for the AMR to determine the subdomains to be refined. Utilizing the Geometry Independent Field approximaTion, the design and adaptive analysis-optimization stages were independently discretized respectively through NURBS and PHT-Splines, allowing easy transfer of multi-patch geometries from industry-standard packages. Multiple numerical examples illustrate the stability of the multi-patch algorithm in optimizing the geometries effectively. The results also show considerable advantages in terms of solution accuracy such as precise field, smooth topology and computational efficiency.

Research on the Ghost Cell Immersed Boundary Method for Compressible Flow

In this paper, a kind of immersed boundary method, the discretized force with ghost cell method, is introduced to study compressible flow. Meanwhile, an adaptive mesh refinement scheme and a wall treatment for turbulent flow are proposed. With the help of in-house code, the accuracy of the method is verified based on several classic tests.

An enhanced compressible two-phase flow model with detailed chemistry under the adaptive mesh refinement frame

In the present study, an enhanced compressible two-phase flow model is advanced, considering the effect of chemical reactions within a detailed mechanism. In this model, two immiscible fluids (liquid and gaseous mixture) are accurately separated with the resolved interface. Unlike the classical five-equation two-phase flow model, the thermal properties of gases are no longer assumed to be constant but rather vary as functions of temperature. A modified mechanical relaxation procedure is proposed and employed at the gas-liquid interface to prevent the occurrence of nonphysical pressure oscillation. In the gaseous mixture, numerous gas components are included and resolved by their mass fraction among the gaseous mixture. In this model, the heat release effect is simulated by a detailed chemistry. Furthermore, the numerical results of several benchmark problems in one dimension and two dimensions demonstrate the efficacy of the proposed compressible multiphase flow model, such as the air shock tube, the gaseous detonation tube, the shock-droplet interaction, and especially the detonation-droplet interaction that has received little focused interest and investigations. Moreover, a self-developed adaptive mesh refinement strategy is performed for a high efficiency of numerical solving.

Simulation of coupled elasticity problem with pressure equation: hydroelastic equation

PurposeThe main aim of the current paper is to find a numerical plan for hydraulic fracturing problem with application in extracting natural gases and oil.Design/methodology/approach First, time discretization is accomplished via Crank-Nicolson and semi-implicit techniques. At the second step, a high-order finite element method using quadratic triangular elements is proposed to derive the spatial discretization. The efficiency and time consuming of both obtained schemes will be investigated. In addition to the popular uniform mesh refinement strategy, an adaptive mesh refinement strategy will be employed to reduce computational costs.FindingsNumerical results show a good agreement between the two schemes as well as the efficiency of the employed techniques to capture acceptable patterns of the model. In central single-crack mode, the experimental results demonstrate that maximal values of displacements in x- and y- directions are 0.1 and 0.08, respectively. They occur around both ends of the line and sides directly next to the line where pressure takes impact. Moreover, the pressure of injected fluid almost gained its initial value, i.e. 3,000 inside and close to the notch. Further, the results for non-central single-crack mode and bifurcated crack mode are depicted. In central single-crack mode and square computational area with a uniform mesh, computational times corresponding to the numerical schemes based on the high order finite element method for spatial discretization and Crank-Nicolson as well as semi-implicit techniques for temporal discretizations are 207.19s and 97.47s, respectively, with 2,048 elements, final time T = 0.2 and time step size τ = 0.01. Also, the simulations effectively illustrate a further decrease in computational time when the method is equipped with an adaptive mesh refinement strategy. The computational cost is reduced to 4.23s when the governed model is solved with the numerical scheme based on the adaptive high order finite element method and semi-implicit technique for spatial and temporal discretizations, respectively. Similarly, in other samples, the reduction of computational cost has been shown.Originality/valueThis is the first time that the high-order finite element method is employed to solve the model investigated in the current paper.

The adaptive hygrothermo–magneto–electro–elastic coupling improved enriched finite element method for functionally graded magneto–electro–elastic structures

In this study, the hygrothermo–magneto–electro–elastic coupling improved enriched finite element method (HC-IEFEM) is proposed to analyze functionally graded magneto–electro–elastic (FG-MEE) structures. The static behavior of FG-MEE structures in the hygrothermal environment is studied. In the enriched finite element method (EFEM) enhanced by interpolation cover functions, the improved shape functions are added to solve the rank defect problem. Quadrilateral elements are used in the analysis of FG-MEE structures in this study. This improved method has proven to be relatively more efficient and resistant to mesh distortion than the traditional finite element method (FEM). Besides, the adaptive mesh refinement (AMR) scheme is used to refine the mesh in local areas to improve numerical calculation efficiency. Numerical examples show that the adaptive HC-IEFEM can achieve relatively high accuracy for analyzing FG-MEE structures. The proposed HC-IEFEM can obtain high accuracy in the hygrothermal environment using a relatively coarse mesh through the improved shape function and AMR scheme. Therefore, the significant potential is demonstrated in analyzing FG-MEE structures in the hygrothermal environment using the proposed adaptive HC-IEFEM.

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.

A Posteriori Error Estimation for Parabolic Problems with Dynamic Boundary Conditions

This paper is concerned with adaptive mesh refinement strategies for the spatial discretization of parabolic problems with dynamic boundary conditions. This includes the characterization of inf–sup stable discretization schemes for a stationary model problem as a preliminary step. Based on an alternative formulation of the system as a partial differential–algebraic equation, we introduce a posteriori error estimators which allow local refinements as well as a special treatment of the boundary. We prove reliability and efficiency of the estimators and illustrate their performance in several numerical experiments.

Low-cycle fatigue crack growth in brittle materials: Adaptive phase-field modeling with variable-node elements

This work presents an adaptive phase field framework for the simulation of crack nucleation and propagation in brittle materials subject to low-cycle loading. We introduce a fatigue history strain parameter within the phase-field framework to capture the fatigue effect. The resulting coupled differential equations are solved using a staggered iteration scheme. In order to improve the computational efficiency of the phase-field model, an adaptive refinement scheme is introduced. This scheme utilizes an artificial threshold that takes into consideration of both phase-field variables and cumulative fatigue history field variables to determine the elements to be refined. The handling of the hanging nodes resulting from mesh refinement is accomplished through the application of the variable-node element technique, offering a flexible and efficient mesh integration technique. We validate our proposed numerical scheme through five representative numerical examples: single-edge cracked specimen, compact tension specimen, double-edge cracked panel, plate with a hole and plate with multi-cracks and hole. The results demonstrate that the adaptive mesh refinement scheme significantly reduces computational costs without compromising the accuracy of the numerical predictions.

New Adaptive Mesh Refinement Strategy for Entry Guidance via Sequential Convex Programming

This study focuses on the entry guidance problem, which is a highly nonlinear and constrained optimal control problem. The entry guidance problem is formulated as a nonlinear trajectory optimization problem with six-degrees-of-freedom dynamics, path constraints, and boundary constraints. The formulated problem is discretized and solved using sequential convex programming (SCP) with successive linearization. However, during the discretization process, conventional collocation methods encounter a challenge with high-frequency jittering in the control and bank angle profiles near active path constraints. Because the considered problem especially involves tight path constraints, the solution jittering issue becomes severe. Therefore, this study proposes a novel mesh refinement strategy to address this problem. Unlike conventional mesh refinement strategies based on interpolation error, the proposed approach resolves the convergence and solution jittering issue of the SCP framework by linking the direct and indirect methods with the costate estimation under successive linearization. Along with the development, we introduce a novel costate estimation method and provide proof of its validity. We present numerical simulation results of the proposed method and conduct a comparison with conventional approaches. The results obtained demonstrate successful mitigation of the solution jittering issue and a significant improvement in solution accuracy regarding compliance with the necessary conditions of optimality.

Boosting galactic outflows with enhanced resolution

ABSTRACT We study how better resolving the cooling length of galactic outflows affect their energetics. We perform radiative-hydrodynamical galaxy formation simulations of an isolated dwarf galaxy ($M_{\star }=10^{8}\, \mbox{M}_\mathrm{\odot }$) with the ramses-rtz code, accounting for non-equilibrium cooling and chemistry coupled to radiative transfer. Our simulations reach a spatial resolution of $18 \, \mathrm{pc}$ in the interstellar medium (ISM) using a traditional quasi-Lagrangian scheme. We further implement a new adaptive mesh refinement strategy to resolve the local gas cooling length, allowing us to gradually increase the resolution in the stellar-feedback-powered outflows, from $\ge 200 \, \mathrm{pc}$ to $18 \, \mathrm{pc}$. The propagation of outflows into the inner circumgalactic medium is significantly modified by this additional resolution, but the ISM, star formation, and feedback remain by and large the same. With increasing resolution in the diffuse gas, the hot outflowing phase ($T \gt {8} \times 10^{4} \, \mathrm{K}$) systematically reaches overall higher temperatures and stays hotter for longer as it propagates outwards. This leads to two-fold increases in the time-averaged mass and metal outflow loading factors away from the galaxy ($r=5\, \mathrm{kpc}$), a five-fold increase in the average energy loading factor, and a ≈50 per cent increase in the number of sightlines with $N_{\rm{O {\small VI}}} \ge 10^{13}\, \mathrm{cm}^{-2}$. Such a significant boost to the energetics of outflows without new feedback mechanisms or channels strongly motivates future studies quantifying the efficiency with which better-resolved multiphase outflows regulate galactic star formation in a cosmological context.

MHD modelling of coronal streamers and their oscillations

Context. The present work investigates solar coronal dynamics in particular streamer waves. Streamer waves are transverse oscillations of the streamer stalk, often generated by the passage of a coronal mass ejection (CME). Recent observational studies infer that the streamer wave is an eigenmode of the streamer plasma slab and an excellent candidate for coronal seismology. Aims. In the present work, we aim to numerically investigate the theoretical concepts of the physics and properties of streamer waves and to complement the observational statistical analysis of these events. Methods. We used the magnetohydrodynamics (MHD) module of MPI-AMRVAC. An adaptive mesh refinement scheme was employed to achieve high resolution for the streamer structure. All the simulations were computed on the same base grid with the same numerical methods. We considered a dipole magnetic field on the Sun and a uniformly accelerating solar wind. We introduced a θ-velocity perturbation within our computational domain in the plane of a streamer to excite the transverse motion. Results. A numerical model for the streamer wave phenomena was constructed in the framework of 2.5D MHD. We performed a parameter study and identified a sensitivity of the streamer dynamics to the background solar wind speed, the characteristics of the perturbation, and the input parameters for the model, such as temperature and magnetic field. We performed a statistical analysis and compared the obtained modelling results with the database of such events from observations from three different coronagraphs. We observed a narrow range of phase speeds and a correlation between wavelength and period. This is consistent with the observations and supports the idea that the streamer wave is an eigenmode of the streamer plasma slab. The measured phase speed is consistently significantly higher than the speed calculated from the measured period and wavelength. The simple fit, when the difference between these two speeds is exactly the background solar wind speed, only matches a small fraction of the data. The obtained results indicate that further investigation is required into the Doppler shift effect in the MHD theory for coronal seismology.

Adaptive solution of the domain decomposition+L2-jumps method applied to the neutron diffusion equation on structured meshes

At the core scale, neutron deterministic calculations are usually based on the neutron diffusion equation. Classically, this equation can be recast in a mixed variational form, and then discretized by using the Raviart-Thomas-Nédélec Finite Element. The goal is to extend the Adaptive Mesh Refinement (AMR) strategy previously proposed in [1] to the Domain Decomposition+L2 jumps which allows non conformity at the interface between subdomains. We are able to refine each subdomain independently, which eventually leads to a more optimal refinement. We numerically investigate the improvements made to the AMR strategy.

Multiscale modeling of liquid jet breakup in crossflow using an Eulerian/Lagrangian approach

Liquid atomization is a very complex issue, involving multiple length and time scales over several orders of magnitude. To better understand the atomization characteristics of the main injection in a lean premix prevaporize (LPP) combustor, a volume of fluid (VOF)–particle conversion algorithm Lagrangian particle tracking (LPT) coupled approach was proposed to simultaneously reproduce the primary and secondary breakup processes. A VOF model with an adaptive mesh refinement strategy was used to resolve the liquid disintegration on a large scale. The small liquid structures qualified as droplets were transformed into discrete particles based on particle conversion criteria. Next, these particles were tracked using the LPT method to simulate the secondary breakup process. The proposed coupled method used in the Eulerian/Lagrangian framework was validated against liquid jet in crossflow experimental data. The numerical results achieved good agreement with the experimental data. Finally, the proposed method was used to predict the atomization characteristics of the main injection in an LPP combustor under various aerodynamic conditions. Qualitative and quantitative information about liquid deformation and spray characteristics were obtained, which varied depending on the aerodynamic parameters.

Adaptive Mesh Refinement Strategies for Cost-Effective Eddy-Resolving Transient Simulations of Spray Dryers

The use of adaptive meshing strategies to perform cost-effective transient simulations of spray drying processes is evaluated. These simulations are often computationally expensive, given the large differences between the characteristic times of the central jet and those of the unsteady flow developed at its periphery. Managing the computational cost through the control of the grid resolution by regions is inadequate in many of these applications since the grid resolution requirements change dynamically within the domain. These conditions are related to the unsteady nature of the flow in both the central jet and the flow recirculation zones. Therefore, the application of adaptive mesh refinement (AMR) strategies is recommended. In this paper, general AMR criteria based on relative errors are evaluated by testing three mesh adaptation criteria: velocity gradient, pressure gradient, and vorticity. This evaluation is performed using a low-cost turbulence model with eddy resolution (DDES) in two different types of drying chambers, in which experimental measurements are available. The use of AMR exerts appreciable effects on decreasing computational costs and contributes to the capture of large eddies in critical regions. The present approach provides an appropriate balance between solution accuracy and computational cost. By using a correct AMR configuration, it is possible to obtain results similar to those obtained on a fixed grid but reducing the computational costs by 3 to 5 times.

Mesh coarsening using the phantom-node method in the phase field model

The phantom-node method is applied in the phase field model for mesh coarsening to improve computational efficiency. When the adaptive mesh refinement scheme is used, the fine mesh still remains along the path where crack already passed. However, structural properties such as stiffness, damage and strain energy of an element completely partitioned by the crack path remain almost unchanged during the rest of the simulation. Using the phantom-node method, the fine mesh in the crack path domain is recovered into a coarse mesh. This numerical scheme significantly reduces the number of degrees of freedom involved in the computation. Using the mesh coarsening method together with the adaptive mesh refinement and adaptive update schemes, the computational cost is further reduced. Through several numerical examples, the performance of the proposed method is demonstrated.