Grid Refinement Research Articles

MTAINV3D: A Three-dimensional Adaptive Magnetotelluric Inversion Tool Using Unstructured Grids

Currently, 3D magnetotelluric inversion often uses a fixed inversion grid. Too sparse inversion grids cannot approximate the complex subsurface conductivity distribution, and may also lead to inversion results failing to converge. Too dense inversion grids will increase not only the computational cost, but also the non-uniqueness of the inversion. Aiming at the above problems, we have developed a three-dimensional magnetotelluric adaptive inversion strategy with unstructured finite element and limited memory BFGS (L-BFGS) algorithms. Firstly, based on the unstructured finite element method, the high accuracy forward responses of the 3D geo-electric model with arbitrary complex terrain and conductivity distributions can be obtained. Then, the forward and inversion meshes are decoupled by using the nested forward and inversion tetrahedral meshes. The Thikhonov regularization objective function with smooth constraints is established and minimized by L-BFGS optimization algorithm with inexact line search procedure, where the gradient of the objective function is solved by using the adjoint principle. Most importantly, an inversion grid adjustment strategy based on the dual constraints of sensitivity matrix and model gradient is proposed, which are used to guide the automatic refinement of inversion grid in the optimization process. Finally, a topographic model is used to validate and test the performance of the proposed adaptive inversion algorithm.

Globally optimal scheduling of an electrochemical process via data-driven dynamic modeling and wavelet-based adaptive grid refinement

Electrochemical recovery of succinic acid is an electricity intensive process with storable feeds and products, making its flexible operation promising for fluctuating electricity prices. We perform experiments of an electrolysis cell and use these to identify a data-driven model. We apply global dynamic optimization using discrete-time Hammerstein–Wiener models to solve the nonconvex offline scheduling problem to global optimality. We detect the method’s high computational cost and propose an adaptive grid refinement algorithm for global optimization (AGRAGO), which uses a wavelet transform of the control time series and a refinement criterion based on Lagrangian multipliers. AGRAGO is used for the automatic optimal allocation of the control variables in the grid to provide a globally optimal schedule within a given time frame. We demonstrate the applicability of AGRAGO while maintaining the high computational expenses of the solution method and detect superior results to uniform grid sampling indicating economic savings of 14.1%.

A node-splitting lattice spring model coupled with a J-integral formulation as a fracture criterion

A global energy minimization criterion based on Griffith’s theory is introduced for the node-splitting lattice spring model. The fracture criterion is computed by both direct numerical simulations of energy release rate G and through a J-integral formulation for comparison and validation. For mode I fractures, the standard implementation of J-integral formulation yields very good estimations of the energy release rate, but for mixed mode fracture the estimations deviates from the direct calculated energy release rate. The reasons for this discrepancy are elucidated and an approach to best approximate the J value is given. This method is compared with the more standard maximum tip stress threshold crack criterion, and shows a much better prediction of the energy release rate and is more robust under grid refinement.

Wall-Modeled Large-Eddy Simulation of Turbulent Boundary Layer with Spatially Varying Pressure Gradients

Wall-modeled large-eddy simulations of turbulent boundary layers subjected to spatially varying streamwise pressure gradients are conducted to assess the predictive performance of three wall models: ordinary differential equation equilibrium, integral nonequilibrium, and partial differential equation (PDE) nonequilibrium models. The test case is based on experiments conducted by Volino (Journal of Fluid Mechanics, Vol. 897, Aug. 2020, p. A2), where the flow is subjected successively to zero pressure gradient (ZPG), favorable pressure gradient (FPG), recovery ZPG, and adverse pressure gradient (APG) regions. Skin friction is overpredicted in FPG by all the wall models. For equilibrium and integral models, this overprediction is attributed to the strong deviation of mean velocity profiles within FPG from the log law, used explicitly in the equilibrium and implicitly in the integral model. The overprediction is more pronounced for the PDE model, which is attributed to dynamic correction of wall-model eddy viscosity for resolved stresses and a lack of correction for pressure gradient. Potential remedies to mitigate this problem are proposed. Grid refinement improves wall-stress predictions in both FPG and APG but only affects the outer profiles in APG, revealing that accurate wall-flux modeling is more critical for APG. Anisotropic grid analysis shows streamwise grid refinement to be more crucial than spanwise for the convergence of skin-friction, outer velocity, and Reynolds stress profiles.

Embedded direct numerical simulation of ignition kernel evolution and flame initiation in dual-fuel spray assisted combustion

The flame initiation process in dual-fuel spray assisted combustion is presently not fully understood. Here, diesel spray assisted combustion of premixed methane/oxidizer/EGR is explored in the post-ignition phase by scale-resolved simulations. The modified dual-fuel ECN Spray A forms the baseline configuration. An extensive local grid refinement (approaching DNS limit) around one of the first high-temperature ignition kernels is carried out in order to examine the validity of hypothesized flame initiation and deflagration. A high quality LES is used to solve the spray dynamics, while the embedded quasi-DNS (eq-DNS) region offers detailed information on the ignition kernel evolution. The finite-rate chemistry is directly integrated, utilizing 54 species and 269 reactions. Local combustion modes are investigated for the ignition kernel development toward spontaneous ignition and premixed flame propagation using various approaches, including the reaction front displacement speed, energy transport budget, and chemical explosive mode analysis. Furthermore, a new criterion based on reaction flux analysis is introduced, which is compatible with dual-fuel combustion. The spatial and temporal scales associated with the ambient methane consumption and consequent flame initiation are characterized. For the first time in dual-fuel spray assisted simulations, numerical evidence is provided on the initiation of premixed flames, and the corresponding timescale is reported. Particularly, there is a transient mixed-mode combustion phase of approximately 0.2 ms after the spray second stage ignition wherein extinction, ignition fronts, and quasi-deflagrative structures co-exist. After such a transient period, the combustion mode becomes essentially deflagrative. Finally, interactions between turbulence and premixed flame front are characterized mostly in the corrugated regime.

Sensitivity of simulated wind power under diverse spatial scales and multiple terrains using the weather research and forecasting model

During the process of grid refinement and downscaling in the Weather Research and Forecasting (WRF) model, the horizontal grid resolution inevitably enters the realm of uncertainty known as the Terra Incognita. Within this region, conventional mesoscale Planetary Boundary Layer schemes fail to achieve the desired optimized outcomes following grid refinement. This study conducted a series of sensitivity analyses to explore the performance of the WRF model in simulating wind speed and direction at different spatial scales under various conditions. By comparing 10 min mean values for flat and complex terrains and then evaluating the performance of the model using statistical scoring. The results indicate that for wind resource assessment, the mesoscale boundary exceeds the height of the atmospheric boundary layer during the simulation period. For flat terrains, nesting is not recommended. Instead, nesting into Terra Incognita and microscale is preferred for complex terrains. The model demonstrates overall accuracy in wind direction estimation but tends to underestimate wind speed. Notably, the accuracy of simulations at 70 m above ground is higher than that at 10 m. The assessment of wind speed and direction exhibits distinct patterns across various wind speed ranges, wind direction, and atmospheric stabilities.

Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil–water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery. In contrast to water, polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening, polymer convection, diffusion, adsorption retention, inaccessible pore volume and reduced effective permeability. Meanwhile, the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution, formation damage, and proppant breakage. In this paper, we present an oil–water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior, and non-uniform fracture characteristics in fractured polymer flooding. The hydraulic fracture is firstly divided into two parts: high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section. A hybrid grid system, including perpendicular bisection (PEBI) and Cartesian grid, is applied to discrete the partial differential flow equations, and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution. The combination of polymer behavior characterizations and numerical flow simulations are applied, resulting in the calculation for the distribution of water saturation, polymer concentration and reservoir pressure. Compared with the polymer flooding well with uniform fracture conductivity, this non-uniform fracture conductivity model exhibits the larger pressure difference, and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section. The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately, and yields fracture half-lengths that better match engineering reality, enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity. The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology, as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

κmonty: a Monte Carlo Compton scattering code including non-thermal electrons

ABSTRACT Low-luminosity active galactic nuclei are strong sources of X-ray emission produced by Compton scattering originating from the accretion flows surrounding their supermassive black holes. The shape and energy of the resulting spectrum depend on the shape of the underlying electron distribution function (DF). In this work, we present an extended version of the grmonty code, called κmonty. The grmonty code previously only included a thermal Maxwell–Jütner electron DF. We extend the grmonty code with non-thermal electron DFs, namely the κ and power-law DFs, implement Cartesian Kerr–Schild coordinates, accelerate the code with mpi, and couple the code to the non-uniform adaptive mesh refinement grid data from the general relativistic magnetohydrodynamics code bhac. For the Compton scattering process, we derive two sampling kernels for both DFs. Finally, we present a series of code tests to verify the accuracy of our schemes. The implementation of non-thermal DFs opens the possibility of studying the effect of non-thermal emission on previously developed black hole accretion models.

Hydrodynamic force and torque fluctuations in a random array of polydisperse stationary spheres

We report data on the fluctuations of hydrodynamic force and torque exerted on polydisperse stationary spheres randomly distributed in a cubic tri-periodic box. We generate our data with an accurate Particle-Resolved/Direct Numerical Simulation (PR-DNS) method that relies on an Immersed Boundary/lattice Boltzmann method implemented on a Cartesian octree grid (Cheng and Wachs, 2022). The local grid refinement capability offered by the octree grid enables us to properly resolve the flow dynamics even around the smallest stationary spheres in the system in the case of a wide sphere diameter distribution. We verify that our data are indeed accurate and reliable through a thorough comparison with results produced by other numerical methods and with data published in the literature. We evaluate the accuracy and limitations of various average drag models on different levels of polydispersity. We consider two Reynolds numbers Re=1 and Re=100 representative of low and moderate inertia. We analyze results in terms of hydrodynamic force and torque fluctuations around the average value and relate these fluctuations to the flow disturbances created by the neighboring particles, i.e., the local microstructure. Finally, we discuss the implications of the presented results on the extension of hydrodynamic force and torque models recently proposed in the literature that take advantage of the local microstructure to predict fluctuations in the case of arrays of monodisperse stationary spheres to the case of arrays of polydisperse stationary spheres.

An Eulerian based geometry conforming grid-block dynamic mesh refinement for the lattice Boltzmann method

An algorithm for a three-dimensional fine-grid block encompassing a moving solid body using a multi-relaxation time model of the lattice Boltzmann method is proposed and developed. In this numerical framework, a geometry-conforming fine block shifts a coarse lattice unit as the object translates by same amount. The effective utilization of higher-order spatial interpolation has been demonstrated in place of the commonly used low-order temporal interpolation in traditional grid refinement techniques within the lattice Boltzmann method. The successful application of this method has been showcased through three distinct cases: the settling of a solid sphere in a fluid tank under the influence of gravity, hovering motion of an elliptic airfoil, and the “clap and fling” motion of an insect wing. In this regard, various interpolation schemes based on the location of nodes in the overlapping zones of fine and coarse block are discussed. In addition, two cases were evaluated, case 1 where distributions are interpolated and case 2 where macroscopic variables are directly interpolated. It was observed that both interpolations gave same computational accuracy for low Reynolds number [∼O(102)]. However, as Re is increased [∼O(103)], direct interpolation of macroscopic variables proved erroneous and resulted in a large deviation in fluid forces and is not recommended. The geometry-conforming dynamic mesh refinement results in a substantial decrease in computation time, approximately 90%, along with a memory reduction of about 80% compared to the fully refined counterpart.

Developments regarding Type II secondary sonic booms and topography

Type II secondary sonic booms are those that reflect from the primary boom carpet, enter the stratosphere, and turn back toward the ground if the upper atmospheric winds are favorable. A study initially described by the authors at the Forum Acusticum meeting in September 2023 predicted that the Type II secondary sonic boom rays could be profoundly affected by small angle changes in the topography of the ground. The current work provides an update on those ray tracing predictions, namely, that the amplitudes of Type II secondary sonic booms are substantially reduced by the topography. Such results may explain why secondary sonic booms historically have been reported for supersonic operations over water but not for over land. A grid refinement study will also be summarized. [Work supported by the FAA through ASCENT Project 57 under the supervision of Sandy Liu. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the FAA.]

Flow simulation in 3D fractured porous medium using a generalized pipe-based cell-centered finite volume model with local grid refinement

The presence of fractures in porous media strongly influences the fluid flow behavior. This work presents an efficient and simple numerical model to address the hydrodynamic behavior of complex fractured porous media, aiming at balancing computational efficiency and accuracy. Fractures are mapped to a set of cells having implicit aperture, where local grid refinement (LGR) is adopted around the fracture to improve accuracy with lower computational burden. The fluid flow in the matrix, fracture, and exchange between fracture-matrix, are described by a generalized equivalent pipe-network model. The numerical scheme and implementation are verified against established numerical solutions. Results show that this method is efficient in capturing main phenomena of the fluid transport in fractured porous media, without sacrificing computational accuracy. Heterogeneous and anisotropic features of fluid flow are well captured. Particularly, the convergence of the LGR is in a higher order than the global grid refinement (GGR). This model also provides great flexibility in handling a multitude of fracture input data, e.g., planar fractures obtained from statistical data and non-planar fractures from digital images represented with point clouds. Balancing computational accuracy and efficiency, this method provides an effective approach for simulating flow transport in fracture porous medium.

Exploring the ability of the variable-resolution Community Earth System Model to simulate cryospheric–hydrological variables in High Mountain Asia

Abstract. Earth system models (ESMs) can help to improve the understanding of climate-induced cryospheric–hydrological impacts in complex mountain regions, such as High Mountain Asia (HMA). Coarse ESM grids, however, have difficulties in representing cryospheric–hydrological processes that vary over short distances in complex mountainous environments. Variable-resolution (VR) ESMs can help to overcome these limitations through targeted grid refinement. This study investigates the ability of the VR Community Earth System Model (VR-CESM) to simulate cryospheric–hydrological variables such as the glacier surface mass balance (SMB) over HMA. To this end, a new VR grid is generated, with a regional grid refinement up to 7 km over HMA. Two coupled atmosphere–land simulations are run for the period 1979–1998. The second simulation is performed with an updated glacier cover dataset and includes snow and glacier model modifications. Comparisons are made to gridded outputs derived from a globally uniform 1∘ CESM grid, observation-, reanalysis-, and satellite-based datasets, and a glacier model forced by a regional climate model (RCM). Climatological biases are generally reduced compared to the coarse-resolution CESM grid, but the glacier SMB is too negative relative to observation-based glaciological and geodetic mass balances, as well as the RCM-forced glacier model output. In the second simulation, the SMB is improved but is still underestimated due to cloud cover and temperature biases, missing model physics, and incomplete land–atmosphere coupling. The outcomes suggest that VR-CESM could be a useful tool to simulate cryospheric–hydrological variables and to study climate change in mountainous environments, but further developments are needed to better simulate the SMB of mountain glaciers.

Effect of interpolation kernels and grid refinement on two way-coupled point-particle simulations

The predictive capability of two way–coupled point-particle Euler–Lagrange model in accurately capturing particle-flow interactions under grid refinement, wherein the particle size can be comparable to the grid size, is systematically evaluated. Two situations are considered, (i) uniform flow over a stationary particle, and (ii) decaying isotropic turbulence laden with Kolmogorov-scale particles. Particle-fluid interactions are modeled using only the standard drag law, typical of large density-ratio systems. A zonal, advection-diffusion-reaction (Zonal-ADR) model is used to obtain the undisturbed fluid velocity needed in the drag closure. Two main types of interpolation kernels, grid-based and particle size–based, are employed. The effect of interpolation kernels on capturing the particle-fluid interactions, kinetic energy, dissipation rate, and particle acceleration statistics are evaluated in detail. It is shown that the interpolation kernels whose width scales with the particle size perform significantly better under grid refinement than kernels whose width scales with the grid size. Convergence with respect to spatial resolution is obtained with the particle size–based kernels with and without correcting for the self-disturbance effect. While the use of particle size–based interpolation kernels provide spatial convergence and perform better than kernels that scale based on grid size, small differences can still be seen in the converged results with and without correcting for the particle self-disturbance. Such differences indicate the need for self-disturbance correction to obtain the best results, especially when the particles are larger than the grid size.

Variability of the slow solar wind: New insights from modelling and PSP-WISPR observations

Aims. We analyse the signature and origin of transient structures embedded in the slow solar wind, and observed by the Wide-Field Imager for Parker Solar Probe (WISPR) during its first ten passages close to the Sun. WISPR provides a new in-depth vision on these structures, which have long been speculated to be a remnant of the pinch-off magnetic reconnection occurring at the tip of helmet streamers. Methods. We pursued the previous modelling works of Réville et al. (2020, ApJ, 895, L20; 2022, A&A, 659, A110) that simulate the dynamic release of quasi-periodic density structures into the slow wind through a tearing-induced magnetic reconnection at the tip of helmet streamers. Synthetic WISPR white-light (WL) images are produced using a newly developed advanced forward modelling algorithm that includes an adaptive grid refinement to resolve the smallest transient structures in the simulations. We analysed the aspect and properties of the simulated WL signatures in several case studies that are typical of solar minimum and near-maximum configurations. Results. Quasi-periodic density structures associated with small-scale magnetic flux ropes are formed by tearing-induced magnetic reconnection at the heliospheric current sheet and within 3 − 7 R⊙. Their appearance in WL images is greatly affected by the shape of the streamer belt and the presence of pseudo-streamers. The simulations show periodicities on ≃90 − 180 min, ≃7 − 10 h, and ≃25 − 50 h timescales, which are compatible with WISPR and past observations. Conclusions. This work shows strong evidence for a tearing-induced magnetic reconnection contributing to the long-observed high variability of the slow solar wind.

On the Stability of IMEX Upwind gSBP Schemes for 1D Linear Advection-Diffusion Equations

AbstractA fully discrete energy stability analysis is carried out for linear advection-diffusion problems discretized by generalized upwind summation-by-parts (upwind gSBP) schemes in space and implicit-explicit Runge-Kutta (IMEX-RK) schemes in time. Hereby, advection terms are discretized explicitly, while diffusion terms are solved implicitly. In this context, specific combinations of space and time discretizations enjoy enhanced stability properties. In fact, if the first- and second-derivative upwind gSBP operators fulfill a compatibility condition, the allowable time step size is independent of grid refinement, although the advective terms are discretized explicitly. In one space dimension it is shown that upwind gSBP schemes represent a general framework including standard discontinuous Galerkin (DG) schemes on a global level. While previous work for DG schemes has demonstrated that the combination of upwind advection fluxes and the central-type first Bassi-Rebay (BR1) scheme for diffusion does not allow for grid-independent stable time steps, the current work shows that central advection fluxes are compatible with BR1 regarding enhanced stability of IMEX time stepping. Furthermore, unlike previous discrete energy stability investigations for DG schemes, the present analysis is based on the discrete energy provided by the corresponding SBP norm matrix and yields time step restrictions independent of the discretization order in space, since no finite-element-type inverse constants are involved. Numerical experiments are provided confirming these theoretical findings.

Numerical simulation of optimization of volume fracturing parameters for horizontal wells in tight oil

ABSTRACT A comprehensive workflow for optimizing the fracturing parameters of horizontal wells in tight oil reservoirs is demonstrated. A numerical simulation model with geologic characterization data from Cangdong Sag Basin reservoirs was constructed. Geometrical parameters of the fractures were calculated through a volumetric model of the fracture network. The fracture lengths, heights, and network radius were optimized using dynamic local grid refinement. The equivalent stimulated reservoir volume considering fracture propagation was then simulated. Based on the simulation results of the mechanism model, after considering factors such as interfracture interference, fracturing operation duration, cost, and construction safety, the following optimal ranges of fracturing parameters are recommended: number of fracturing fractures = 8–11 levels, half-length of fracturing fractures = 130–160 m, and conductivity of fracturing fractures = 14–20 D∙cm. Based on the actual situation of the work area, it is recommended that the number of fracturing fractures be 9, the half-length of the fracture be 150 m, and the fracture conductivity be 18 D∙cm to achieve higher horizontal well production and provide a certain data reference for the efficient development of similar dense oil reservoirs.

Large eddy simulation of tip-leakage cavitating flow around twisted hydrofoil with effects of tip clearance and skew angle

Tip-leakage cavitating flow around hydrofoils has attracted much research interest, but the complex structures of tip separation vortex (TSV) and tip-leakage vortex (TLV) have not been clearly resolved and discussed with the effects of tip clearance and skew angle yet. In the present work, large eddy simulation (LES) with multi-level octree grid refinement is used to investigate the tip-leakage flows around a series of twisted hydrofoils with various skew angle and tip clearance. High resolution is guaranteed by the normalized grid sizes of y+<1, Δx+∼50 and Δz+∼10, through which the predicted flow meets the criterion that at least 80% of the turbulent kinetic energy is resolved. The TSVs are identified to grow from the entire lower edge of the tip and twine with the TLV into a primary vortex tube, which leads to counter-rotating induced vortices (IV) strongly twisted around the primary vortex in the case of medium tip clearance but weakened for small one. Cavitation effect significantly accelerates the roll-up process of the vortices so that the primary vortex is formed earlier. The tip-leakage flow turns from wake-like to jet-like when the clearance is reduced, but the jet velocity diminishes markedly for extremely small clearance. The hydrofoil skewness barely makes a lift on the vortex tube, distinctive from the effect of tip clearance variation. The adverse pressure gradient induced by the skew angle has significant effect on the laminar–turbulent​ transition of the flow. The tip vortex flow induces strongly characterized laminar ant turbulent flow regions on the suction side, which continuously changes with the variation of the skewness.

Accelerated convergence for city-scale flow fields using immersed boundaries and coupled multigrid

Fast and accurate prediction of Chemical, Biological and Radiological (CBR) dispersion patterns and toxic extents is important for public safety as conventional and non-conventional airborne threats released into the built environment can pose serious dangers to human health ranging from difficulty breathing and eye irritation to incapacitation and death. Computational fluid dynamics (CFD) is routinely used for gas dispersion modeling when increased accuracy over traditional Gaussian-based methods is required, although CFD requires greater modelling efforts. The combination of structured Cartesian meshes and immersed boundary methods reduces this effort and has been resurging in popularity over the past decade.Due to a lack of related literature, a simple and robust methodology was developed by the authors to treat immersed boundaries at multigrid levels, and this integration focused on a segregated multigrid approach using structured Cartesian meshes with adaptive mesh refinement. In the current work, a coupled multigrid treatment is adapted to the integrated immersed boundary methodology and adaptive mesh approach and compared to the segregated technique in terms of convergence rates. To accelerate convergence, the coupled approach selectively applies grid refinement at coarse grid levels, and by design, neither methodology detects the immersed boundaries on coarse grid levels.The two multigrid approaches are compared at three flow scales: wind tunnel, mock-urban and full-urban. At the wind tunnel scale, the coupled multigrid solver shows 39.3 times speed up over single grid and 10.4 times improvement over the baseline segregated approach. At the full urban scale, the coupled approach is shown to converge wind fields with a 6.3 times speed improvement over the previous segregated approach and therefore is suitable for CFD-based CBR assessment tools.

Computational Evaluation of Rotor Alone Noise

Transonic 2-Dimensional flow past the rotor was simulated to predict the pressure variation past the rotor through the CFD software ANSYS-Fluent. The mesh generated was found to have a direct impact on capturing the shock and effect of change in the angle of attack through the flow past the rotating blades were found to vary the strength of the passage shock between the blades. The effect of blade geometry on the fan noise radiated near field and far field were investigated. Through the effect of grid refinement, change of chord length and thickness the noise generated by the rotor was found to reduce considerably to an extent. The effect of blade geometry on the fan noise was also studied. The results were in good agreement with the available data from the literature which was evident from the N-waveform.