Mesh Refinement Research Articles

Formation of sodium-alginate droplets in an X-microdevice: Characterization of the pinching efficiency

Experiments and simulations are used jointly to gain a comprehensive insight into the pinching mechanism that generates alginate droplets in an X-microdevice operating in a hydrodynamic flow-focusing configuration. The X-microdevice is fed with an aqueous alginate solution into one inlet channel, while sunflower oil and Span80 are fed into the other two inlet channels. The use of the adaptive mesh refinement and volume of fluid method allows accurate tracking of the interface in numerical simulations. The sensitivities of numerical predictions to the contact angle and the surface tension are estimated through dedicated sets of simulations. Subsequently, numerical simulations and experiments are compared for different flow rates with a satisfactory agreement. We observe that the pinch-off mechanism may lead to the formation of several satellite drops in addition to the main droplet. A pinching performance indicator is suggested based on the amount of alginate that is encapsulated in the main droplet. The effect of operating conditions on the pinching efficiency, frequency, and droplet diameter is discussed to provide valuable information to optimize the droplets production. The pinching efficiency is closely related to the length and diameter of the liquid thread. At low flow rates, a short liquid thread is observed. This leads to the formation of few satellites and, thus, to high pinching efficiency but low droplet production. Increasing the dispersed-phase flow rate slightly reduces the efficiency but significantly increases the production.

Magnetic field and kinetic helicity evolution in simulations of interacting disk galaxies

Context. There are indications that the magnetic field evolution in galaxies is influenced by tidal interactions and mergers between galaxies. Aims. We carried out a parameter study of interacting disk galaxies with impact parameters ranging from central collisions to weakly interacting scenarios. The orientations of the disks were also varied. In particular, we investigated how magnetic field amplification depends on these parameters. Methods. We used magnetohydrodynamics for gas disks in combination with live dark-matter halos in adaptive mesh refinement simulations. The disks were initialized using a setup for isolated disks in hydrostatic equilibrium. Since we focused on the impact of tidal forces on magnetic field evolution, adiabatic physics was applied. Small-scale filtering of the velocity and magnetic field allowed us to estimate the turbulent electromotive force (EMF) and kinetic helicity. Results. Time series of the average magnetic field in central and outer disk regions show pronounced peaks during close encounters and mergers. This agrees with observed magnetic fields at different interaction stages. The central field strength exceeds 10 μG (corresponding to an amplification factor of 2–3) for small impact parameters. As the disks are increasingly disrupted and turbulence is produced by tidal forces, the small-scale EMF reaches a significant fraction of the total EMF. The small-scale kinetic helicity is initially antisymmetric across the disk plane. Though its evolution is sensitive to both the impact parameter and inclinations of the rotation axes with respect to the relative motion of the disks, antisymmetry is generally broken through interactions and the merger remnant loses most of the initial helicity. The EMF and the magnetic field also decay rapidly after coalescence. Conclusions. The strong amplification during close encounters of the interacting galaxies is mostly driven by helical flows and a mean-field dynamo. The small-scale dynamo contributes significantly in post-interaction phases. However, the amplification of the magnetic field cannot be sustained.

Large/small eddy simulations: A high-fidelity method for studying high-Reynolds number turbulent flows

Direct numerical simulations (DNS) are one of the main ab initio tools to study turbulent flows. However, due to their considerable computational cost, DNS are primarily restricted to canonical flows at moderate Reynolds numbers, in which turbulence is isolated from the realistic, large-scale flow dynamics. In contrast, lower fidelity techniques, such as large eddy simulations (LES), are employed for modeling real-life systems. Such approaches rely on closure models that make multiple assumptions, including turbulent equilibrium, small-scale universality, etc., which require prior knowledge of the flow and can be violated. We propose a method, which couples a lower-fidelity, unresolved, time-dependent calculation of an entire system (LES) with an embedded small eddy simulation (SES) that provides a high-fidelity, fully resolved solution in a sub-region of interest of the LES. Such coupling is achieved by continuous replacement of the large SES scales with a low-pass filtered LES velocity field. The method is formulated in physical space, with no assumptions of equilibrium, small-scale structure, and boundary conditions. A priori tests of both steady and unsteady homogeneous, isotropic turbulences are used to demonstrate the method's accuracy in recovering turbulence properties, including spectra, probability density functions of the intermittent quantities, and sub-grid dissipation. Finally, SES is compared with two alternative approaches: one embedding a high-resolution region through static mesh refinement and a generalization of the traditional volumetric spectral forcing. Unlike these methods, SES is shown to achieve DNS-level accuracy at a fraction of the cost of the full DNS, thus opening the possibility to study high-Re flows.

Cartesian mesh adaptation: Immersed boundary method based on high-order discontinuous Galerkin method

Immersed boundary method (IBM) can easily distinguish fluid and solid regions in the computational region, thereby the workload of complex grid generation can be reduced. To accurately characterize the solid geometry, a large number of cells are required near the solid surface. The h-adaptive algorithm is adopted to reduce the requirement for the number of cells. In addition, considering the inherent adaptability to the h-adaptive Cartesian grids of the discontinuous Galerkin method, a high-order discontinuous Galerkin solver with an IBM is developed. To validate the h-adaptive algorithm and the solver, three cases are tested, including the steady flow past the National Advisory Committee for Aeronautics 0012 airfoil, the steady flow past a cylinder, and the unsteady flow past a cylinder. Compared with the non-adaptive cases, the h-adaptive cases need smaller total number of cells, and the numerical accuracy is significantly improved with an increasing degree of mesh refinement.

HEMLAB Algorithm Applied to the High-Lift Japan Aerospace Exploration Agency Standard Model

The high-lift Japan Aerospace Exploration Agency (JAXA) standard model (HL-JSM) has been numerically analyzed in order to further validate the HEMLAB code for realistic aircraft configurations. The numerical algorithm is based on highly efficient edge-based data structure for a vertex-based finite volume algorithm on hybrid meshes. The data pattern is arranged to meet the requirements of a vertex-based finite volume algorithm by considering data access patterns and cache efficiency. A fully implicit version of the numerical algorithm has also been implemented based on the Portable, Extensible Toolkit for Scientific Computation (PETSc) library in order to improve the robustness of the algorithm. The resulting algebraic equations, including the one-equation Spalart–Allmaras, are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the flexible generalized minimal residual method [FGMRES(m)] Krylov subspace algorithm. The numerical method is also combined with the metric-based anisotropic mesh refinement library Python Adaptive Mesh Geometry Suite–INRIA (pyAMG) from National Institute for Research in Digital Science and Technology in order to improve the numerical accuracy. The numerical algorithm is initially applied to the two-dimensional L1T2 (National High Lift Programme) high-lift system, and then the calculations around the HL-JSM are carried out at relatively high angles of attack. The numerical results with the anisotropic mesh refinement library pyAMG indicate significant improvements in numerical accuracy.

Sparse polynomial chaos expansion and adaptive mesh refinement for enhanced fracture prediction using phase-field method

Phase-field models (PFMs) have proven to accurately predict complex crack patterns such as crack branching, merging, and crack fragmentation, but they are computationally costly. This study stems from the high computational costs associated with non-adaptive PFMs for brittle fracture analysis, which require dense meshes. This makes training data generation for surrogate models prohibitively expensive. To address these challenges, this paper proposes an adaptive mesh refinement (AMR) informed sparse polynomial chaos expansion (PCE) framework. The AMR algorithm is incorporated into the fracture analysis workflow to maximize the computational efficiency in data generation, eliminating the need for pre-refinement. The AMR informed sparse PCE is calibrated with Bayesian compressive sensing (BCS) to efficiently map domain input parameters to quantities of interest (QoIs), even with limited training data. We employ a multi-output QoI approach to predict load–displacement relationships with high resolution. The novelty of this work lies in the integration of AMR into the PFM workflow and the application of sparse PCE for brittle fracture analysis. Benchmark tests demonstrate the proposed method’s superior accuracy and computational efficiency compared to conventional AMR method, marking a notable improvement in fracture mechanics.

A non-uniform compound strip method for effective buckling analysis of stiffened structures

In this paper, a versatile compound strip method (CSM) with non-uniform spline functions is developed for buckling analysis of stiffened structures. The proposed method further extends the existing CSM by permitting the flexible modification of local knots to place the stiffeners along the strip arbitrarily. In addition, a reasonable knot arrangement can achieve an accurate solving procedure with improved convergence. The displacements of stiffeners are expressed compatibly by the fundamental parameters of skin according to the beam-plate model. Consequently, the reinforcement of stiffeners is naturally incorporated by adding the beam stiffness matrix to the corresponding strips. Based on the first-order shear deformation plate theory and non-uniform spline functions, the semi-analytical formulations of stiffened structures are established. The present method provides the possibility to achieve the local mesh refinement in the finite strip methods. The convergence and validation study is demonstrated through the comparisons with the results of the existing literature solution and finite element method. In conclusion, a more efficient and applicable CSM is proposed to analyze the buckling behaviors of stiffened structures.

Unilateral buckling of thin plates by complementarity eigenvalue analyses

In this work, the analysis by the finite element method of thin plates subjected to buckling in the presence of unilateral punctual obstacles, that is, supports that allow the plate to move in one direction but prevent the motion in the opposite direction, is addressed. An appropriate algorithm based on the solution of a semi-smooth system of equations, that results from the formulation of the unilateral buckling problem as a complementarity eigenvalue problem, is used. Rectangular and square plates are analysed under various membrane loadings, including compression and shear. The conformal Bogner–Fox–Schmit (BFS) finite element is employed to compute the bifurcation loads and the corresponding instability modes in scenarios with and without unilateral obstacles. For each plate and type of loading, the six lowest bifurcation loads and corresponding modes are computed for different levels of mesh refinement. The results confirm that the convergence of bifurcation loads obtained using the BFS element is monotonically decreasing as the mesh is refined. It is also confirmed that, when unilateral obstacles are present, the lowest bifurcation load, known as the critical load, can never be lower than the one of the homologous problem without unilateral obstacles.

Local spline refinement driven by fault jump estimates for scattered data approximation

We present new fault jump estimates to guide local refinement in surface approximation schemes with adaptive spline constructions. The proposed approach is based on the idea that, since discontinuities in the data should naturally correspond to sharp variations in the reconstructed surface, the location and size of jumps detected in the input point cloud should drive the mesh refinement algorithm. To exploit the possibility of inserting local meshlines in one or the other coordinate direction, as suggested by the jump estimates, we propose a quasi-interpolation (QI) scheme based on locally refined B-splines (LR B-splines). Particular attention is devoted to the construction of the local operator of the LR B-spline QI scheme, which properly adapts the spline approximation according to the nature and density of the scattered data configuration. A selection of numerical examples outlines the performance of the method on synthetic and real datasets characterized by different geographical features.

Physics-motivated cell-octree adaptive mesh refinement in the Vlasiator 5.3 global hybrid-Vlasov code

Physics-motivated cell-octree adaptive mesh refinement in the Vlasiator 5.3 global hybrid-Vlasov code

Mixed-mode thermo-mechanical fracture: An adaptive multi-patch isogeometric phase-field cohesive zone model

This work presents an adaptive phase-field cohesive zone model (PF-CZM) for simulating mixed-mode crack nucleation and growth in isotropic rock-like materials subjected to thermo-mechanical interactions. The proposed approach combines an adaptive multi-patch isogeometric analysis (MP-IGA) and length-scale insensitive PF-CZM. The formulation captures the distinct critical energy release rates for Mode-I and Mode-II fractures, which is crucial for predicting mixed-mode thermo-mechanical fracture behavior in isotropic rock-like materials. The PF-CZM governing equations are solved with isogeometric analysis based on locally refined non-uniform rational B-splines (LR NURBS), and the complex structural geometry is exactly described with multiple LR NURBS patches. The field variables, such as displacement, phase-field, and temperature at the interface of adjacent patches, are coupled using Nitsche’s method. To enhance the computational efficiency while maintaining accuracy, a refinement-correction adaptive scheme combined with the structured mesh refinement strategy is developed. The proposed framework is validated against recent numerical and experimental results in the literature, particularly in the context of capturing complex behavior of mixed-mode crack propagation in isotropic rock-like materials subjected to thermo-mechanical loading.

Large-Eddy Simulation Study of Flow and Combustion Dynamics in a Full-Scale Hydrogen-Air Rotating Detonation Combustor-Stator Integrated System

Abstract A first-of-its-kind large-eddy simulation (LES) study is conducted to numerically investigate the combustion dynamics as well as aero-thermal phenomena in a full-scale non-premixed hydrogen-air rotating detonation engine (RDE) integrated with nozzle guide vanes (NGV) acting as the turbine stator. The LES framework incorporates hydrogen-air detailed chemical kinetics and adaptive mesh refinement. A comparative analysis is carried out for two operating conditions with different fuel/air mass flow rates but global equivalence ratio of unity. The LES model is validated against experimental data with respect to detonation wave speed/height, wave dynamics, and axial static pressure distribution. Numerical results indicate significant deflagrative combustion occurring in the fill region near the inner wall due to formation of recirculation zones in the injection near-field driven by the backward facing step. The leading detonation wave is found to be trailed by an azimuthal reflected-shock combustion wave, which consumes unburned vitiated reactants that leak through the main detonation wave. The detonation wave characteristics do not change appreciably with the presence of NGV. The exit flow is found to be nearly fully subsonic and supersonic for the low and high mass flux conditions, respectively. The presence of NGV renders the flow more axial, and significantly impacts the exit Mach number and total pressure. The low mass flux operating point, despite exhibiting more deflagrative losses within the combustor, yields overall lower pressure drop from plenum to exhaust, mainly attributed to lower pressure drop across the injectors.

An adaptive lattice Green's function method for external flows with two unbounded and one homogeneous directions

We solve the incompressible Navier-Stokes equations using a lattice Green's function (LGF) approach, including immersed boundaries (IB) and adaptive mesh refinement (AMR), for external flows with one homogeneous direction (e.g. infinite cylinders of arbitrary cross-section). We hybridize a Fourier collocation (pseudo-spectral) method for the homogeneous direction with a specially designed, staggered-grid finite-volume scheme on an AMR grid. The Fourier series is also truncated variably according to the refinement level in the other directions. We derive new algorithms to tabulate the LGF of the screened Poisson operator and viscous integrating factor. After adapting other algorithmic details from the fully inhomogeneous case [1], we validate and demonstrate the new method with transitional and turbulent flows over a circular cylinder at Re=300 and Re=12,000, respectively.

An optimally convergent Fictitious Domain method for interface problems

We introduce a novel Fictitious Domain (FD) unfitted method for interface problems associated with a second-order elliptic linear differential operator, that achieves optimal convergence without the need for adaptive mesh refinements nor enrichments of the Finite Element spaces. The key aspect of the proposed method is that it extends the solution into the fictitious domain in a way that ensures high global regularity. Continuity of the solution across the interface is enforced through a boundary Lagrange multiplier. The subdomains coupling, however, is not achieved by means of the duality pairing with the Lagrange multiplier, but through an L2 product with the H1 Riesz representative of the latter, thus avoiding gradient jumps across the interface. Thanks to the enhanced regularity, the proposed method attains an increase, with respect to standard FD methods, of up to one order of convergence in energy norm. The Finite Element formulation of the method is presented, followed by its analysis. Numerical tests on a model problem demonstrate its effectiveness and its superior accuracy compared to standard unfitted methods.

Multi‒scale numerical investigations on the atomization performance of liquid‒liquid pintle injector

Three‒dimensional atomization field of the radial annular slot type liquid‒liquid pintle injector under different total momentum ratio (TMR) is simulated based on the volume of fluid to discrete particle model (VOF to DPM) method and the octree adaptive mesh refinement (AMR). The typical spray morphology of the injector is obtained, the variation of spray angle, breakup length of liquid film, amplitude of disturbance waves before liquid film breaking and its causes are analyzed. The results show that the injector can form a hollow conical spray during operation, and there are two recirculation zones near the inner surface of liquid film. According to the characteristics of the spray morphology, the spray can be divided into four areas: undisturbed liquid film, disturbed liquid film, fluctuating breakup zone and small droplets accumulation zone. The simulated spray angle is close to the model proposed by Heister when TMR is smaller than 0.6 and is close to the model proposed by Boettcher when TMR exceeds 0.6, with the maximum relative error of 9.5%. TMR has little influence on the amplitude of disturbance waves before liquid film breaking, while the breakup length of liquid film increases at first and then decreases with the increase of TMR. The breakup length is relatively large when TMR is close to 1, within the range of 20∼22 mm, while it is relatively small when TMR is far away from 1, within the range of 12∼15mm.

Progressive failure analysis of laminar composites under compression using smeared crack-band damage model and full layerwise theory

This paper presents an original finite element (FE) model that integrates the smeared crack band (SCB) approach and full layerwise plate theory (FLWT). The model enhances the computational efficiency of progressive failure analysis (PFA) of laminar composites in compression, by utilizing the layerwise approach which reduces a 3D model to a 2D one. The model distributes damage throughout the FE domain, with fracture mechanisms represented by material stiffness degradation controlled by damage variables (based on equivalent strains specifically defined for each failure mode). Mesh dependency issues are addressed by scaling fracture energy using a characteristic element length, and failure initiation and modes are determined using the 3D Hashin failure criterion.Accurately describing lamina response in fiber direction under compression requires linear-brittle softening with a stress plateau. The study showed that a model considering 30 % of residual stress accurately predicts maximum stress regardless of mesh refinement, demonstrating results’ minor dependence from the selected element size.The model accuracy has been confirmed by comparing the obtained results against experimental and benchmark data from the literature. The size effect study demonstrated a decrease in maximum stress of the open-hole laminates in compression with increasing specimen in-plane size. This trend is consistent with experimental and reference numerical observations, confirming the model accuracy and applicability even for relatively coarse meshes. Therefore, computational efficiency is improved, with preserved accuracy of conventional solid finite element models.

High-fidelity numerical simulation of longitudinal thermoacoustic instability in a high-pressure subscale rocket combustor

A detailed analysis of thermoacoustic combustion instability in a subscale rocket combustor at high pressure is reported in this paper using the high-fidelity large-eddy simulation (LES). Self-sustained longitudinal combustion instability is observed in the experiments for this combustor configuration. The computational setup follows the past experimental study of a rig called the Continuously Variable Resonance Combustor (CVRC). In this combustor, both stable combustion and unstable combustion dynamics have been observed by varying the oxidizer injector length. A combustor configuration with an oxidizer injector length of 12 cm is chosen for this study based on the experimental evidence of longitudinal combustion instability. An autonomous meshing using the modified cut-cell Cartesian grid generation approach, coupled with on-the-fly Adaptive Mesh Refinement (AMR) is employed in this study. Chemical reactions during turbulent combustion in this configuration are modeled by solving the species transport equations with a detailed chemistry solver using a kinetic mechanism with 21 species and 84 steps. Similar to the findings of the experiments, we observe a self-sustained combustion instability in the present study, which is characterized by a limit cycle behavior of the acoustic fluctuations. The spectral analysis of these acoustic fluctuations shows good agreement with experimental data for the frequency of the three dominant modes. We further analyze the features of time-averaged and instantaneous reacting flow to study the effects of combustion instability on the flame holding dynamics, vortex shedding, mixing, and combustion regime due to flame movement along the longitudinal direction of the combustor during a limit cycle. These phenomena are effectively captured through the integration of AMR with complex chemistry in the present study. A particular focus of the study is on understanding the role of minor species (OH, HO2, and CH2O) in the physical and state-space in sustaining the flame during the combustion instability. Additionally, the physical mechanisms responsible for the production and dissipation of enstrophy are examined to demonstrate that their contribution can create significant fluctuations in the reacting flow field, which can assist in sustaining the combustion instability.

Study on volumetric heat and mass transfer coefficient in a spray drying process utilizing pressure swirl nozzle: A numerical and experimental approach

This paper applies a sectional and cumulative approach to estimate the volumetric heat and mass transfer coefficients (hV and kV) to characterize the behaviour of the spray drying process. The investigation utilizes a tailor-made spray dryer equipped with a pressure swirl nozzle with a 0.2 mm orifice diameter, utilizing Mannitol solution as the precursor and air as the carrier gas. A comprehensive numerical analysis is conducted using the Adaptive Mesh Refinement (AMR) technique alongside selective experiments. The study considers precursor mass flow rates of 1 g/s, 1.2 g/s, and 1.5 g/s, along with carrier gas velocities of 0.88 m/s and 1.19 m/s at a temperature of 250 °C. Comparisons between predicted and estimated hV and kV are performed, leading to the proposal of a method for identifying constant rate and falling rate periods. The analyses contribute to delineating the solvent evaporation zone, solid particles heating zone, spray penetration length, and drying length. Additionally, experimental temperature measurements in both axial and radial directions at 12 grid points in the chamber are conducted to validate the numerical results, showing acceptable deviation.

A hp-adaptive finite element approach for 3D controlled source electromagnetic forward modeling

Accurate and efficient 3D controlled-source electromagnetic (CSEM) forward modeling is crucial for deciphering CSEM responses in complex geological contexts and for assessing the efficacy of survey designs. It also serves as the foundation for 3D inversion, a critical technique for interpreting CSEM data. We present a novel hp-adaptive finite element method for 3D CSEM forward modeling. This method enhances the traditional h-adaptive approach, which only refines the mesh while keeping the polynomial degree of the basis functions constant, by enabling simultaneous refining mesh and increasing polynomial degree of basis functions. High-order elements yield superior approximations when the solution exhibits sufficient smoothness, while mesh refinement enhances accuracy in regions with less smooth solutions. The adaptive refinement process is guided by a goal-oriented error estimator that relies on the residual of the governing equation and the continuity of electromagnetic fields. The hp-adaptive strategy, which determines whether to refine elements or increase their polynomial degree, is based on the refinement levels of the elements. Constraints are applied to hanging nodes, introduced during the refinement process, to ensure the continuity of the finite element space. We validate the accuracy, efficiency, and convergence of the hp-adaptive method through tests on two layered models. Further simulations on a topographic model and a realistic model corroborate its effectiveness. Our findings indicate that the hp-adaptive method outperforms the traditional h-adaptive method in terms of accuracy, convergence rate and computational cost, making it a promising technique for 3D CSEM forward modeling.

Numerical Simulation of Non-Darcy Flow in Naturally Fractured Tight Gas Reservoirs for Enhanced Gas Recovery

In this work, we analyze non-Darcy two-component single-phase isothermal flow in naturally fractured tight gas reservoirs. The model is applied in a scenario of enhanced gas recovery (EGR) with the possibility of carbon dioxide storage. The properties of the gases are obtained via the Peng–Robinson equation of state. The finite volume method is used to solve the governing partial differential equations. This process leads to two subsystems of algebraic equations, which, after linearization and use of an operator splitting method, are solved by the conjugate gradient (CG) and biconjugate gradient stabilized (BiCGSTAB) methods for determining the pressure and fraction molar, respectively. We include inertial effects using the Barree and Conway model and gas slippage via a more recent model than Klinkenberg’s, and we use a simplified model for the effects of effective stress. We also utilize a mesh refinement technique to represent the discrete fractures. Finally, several simulations show the influence of inertial, slippage and stress effects on production in fractured tight gas reservoirs.