Unstructured Grids Research Articles

A high-performance computing applied to composition reservoir simulation using distributed memory and 3D hybrid unstructured grids

A high-performance computing applied to composition reservoir simulation using distributed memory and 3D hybrid unstructured grids

Predicting unsteady incompressible fluid dynamics with finite volume informed neural network

The rapid development of deep learning has significant implications for the advancement of computational fluid dynamics. Currently, most pixel-grid-based deep learning methods for flow field prediction exhibit significantly reduced accuracy in predicting boundary layer flows and poor adaptability to geometric shapes. Although graph neural network models for unstructured grid-based unsteady flow prediction have better geometric adaptability, these models suffer from error accumulation in long-term predictions of unsteady flows. More importantly, fully data-driven models often require extensive training time, greatly limiting the rapid update and iteration speed of deep learning models when facing more complex unsteady flows. Therefore, this paper aims to balance the demands for training overhead and prediction accuracy by integrating physical constraints based on the finite volume method into the loss function of the graph neural network. Additionally, it incorporates a twice-message aggregation mechanism inspired by the extended stencil method to enhance the unsteady flow prediction accuracy and geometric shape generalization ability of the graph neural network model on unstructured grids. We focus particularly on the model's predictive accuracy within the boundary layer. Compared to fully data-driven methods, our model achieves better predictive accuracy and geometric shape generalization ability in a shorter training time.

A three-dimensional numerical well-test model for pressure transient analysis in fractured horizontal wells with secondary fractures

During oil and gas reservoir development, multi-stage horizontal wells (MFHWs) and hydraulic fracturing techniques can effectively increase estimated ultimate recovery. However, there still lacks an understanding of the three-dimensional (3D) pressure transient behaviors of multi-stage fractured horizontal wells with secondary fractures. To narrow this gap, a three-dimensional numerical well-test model based on a discrete fracture model and unstructured tetrahedral grids is developed to study the pressure transient behaviors of MFHWs with secondary fractures. The pressure transient solutions of MFHWs with secondary fractures have been demonstrated by model verifications. The results show that the proposed model can accurately capture the complex transient flow around fractures, including early radial flow that is not easily captured by two-dimensional numerical well test models. The proposed model classifies the flow regimes of a MFHW as: wellbore storage and skin effects, early radial flow, bilinear flow, linear flow, elliptical flow, pseudo radial flow, and pseudo-boundary dominated flow. It is found that the fracture geometry has a relatively large effect on the shape of the pressure derivative curve in this work. The hydraulic fracture half-length has the greatest impact on the pressure transient behaviors of the MFHW, followed by fracture height and secondary fracture half-length, as found in this study. Additionally, fracture parameters are evaluated, and actual well testing data are interpreted, taking into account the fracture height. This work is meaningful to understand the three-dimensional pressure transient behaviors of MFHWs with secondary fractures.

Viewing electromagnetic scattering characteristics on air-brake of a stealth plane

Purpose This study aims to learn the dynamic radar cross-section (RCS) of a deflection air brake. Design/methodology/approach The aircraft model with delta wing, V-shaped tail and blended wing body is designed, and high-precision unstructured grid technology is used to deal with the surface of air brake and fuselage. The calculation method based on multiple tracking and dynamic scattering is presented to calculate RCS. Findings The fuselage has a low scattering level, and the opening air brake will bring obvious dynamic RCS effects to itself and the whole machine. The average indicator of air brake RCS can be lower than –0.6 dBm2 under the tail azimuth, while that of forward and lateral direction is lower. The mean RCS of fuselage is obviously higher than that of air brake, while the deflected air brake and its cabin can still provide strong scattering sources at some azimuths. When the air brake is opening, the change amplitude of the aircraft forward RCS can exceed 19.81 dBm2. Practical implications This research has practical significance for the dynamic electromagnetic scattering analysis and stealth design of the air brake. Originality/value The calculation method for aircraft RCS considering air brake dynamic deflection has been established.

A robust phase-field method for two-phase flows on unstructured grids

A phase-field method for unstructured grids that is accurate, conservative, and robust is proposed in this work. The proposed method also results in bounded transport of volume fraction, and the interface thickness adapts automatically to local grid size. In addition to this, we present a novel formulation for two-phase flows on collocated grids that is provably energy stable, which is a critical feature for robust simulations of two-phase turbulent flows. The proposed method is first evaluated on canonical test cases, including scenarios like drop advection and drop in a shear flow. The accuracy of the proposed method in the presence of grid transitions, which is important for simulations in complex geometries using unstructured grids, is also evaluated. We assess the robustness of our method by performing simulations of a drop in homogeneous isotropic turbulence at infinite Reynolds number with varying density ratios. Furthermore, as a step toward verification and validation, simulations of test cases in complex geometries and conditions, such as, a damped surface wave, infinitesimal interface distortion on a liquid jet, and the atomization of a liquid jet from the engine combustion network's Spray A nozzle are presented. These simulations illustrate the accuracy, robustness, and applicability of the proposed method in various kinds of complex two-phase flow applications of engineering interest.

MachLine: Development of a Dirichlet-Based, Subsonic/Supersonic Panel Method for Unstructured Grids

To meet the growing need for fast supersonic flow solutions, the theory and implementation of a modern subsonic/supersonic, unstructured panel method are here presented. This work presents several improvements over legacy supersonic panel codes and available modern codes. Among these improvements are automatic methods for generating unstructured wakes, enforcing the Kutta condition at trailing edges, and placing interior control points. An efficient method for calculating domains of dependence on an unstructured mesh is also presented. For the first time in the literature regarding supersonic panel methods, a complete method for calculating influence coefficients is also described. The numerical sensitivities of the method are examined. Compared to analytic and experimental data, the method is accurate for small-perturbation flows. For example, the relative error in the root pressure coefficient on a straight wing in supersonic flow (M∞=1.5) was calculated to be within approximately 7% of the analytic solution for a range of angles of attack. For a delta wing in supersonic flow (M∞=1.62), the method is found to calculate lift slope and zero-lift drag to within 5% of experimental data. The method is also fast, having run times on the order of 1 minute for meshes with around 26,000 panels.

SNN-PDE: Learning Dynamic PDEs from Data with Simplicial Neural Networks

Dynamics of many complex systems, from weather and climate to spread of infectious diseases, can be described by partial differential equations (PDEs). Such PDEs involve unknown function(s), partial derivatives, and typically multiple independent variables. The traditional numerical methods for solving PDEs assume that the data are observed on a regular grid. However, in many applications, for example, weather and air pollution monitoring delivered by the arbitrary located weather stations of the National Weather Services, data records are irregularly spaced. Furthermore, in problems involving prediction analytics such as forecasting wildfire smoke plumes, the primary focus may be on a set of irregular locations associated with urban development. In recent years, deep learning (DL) methods and, in particular, graph neural networks (GNNs) have emerged as a new promising tool that can complement traditional PDE solvers in scenarios of the irregular spaced data, contributing to the newest research trend of physics informed machine learning (PIML). However, most existing PIML methods tend to be limited in their ability to describe higher dimensional structural properties exhibited by real world phenomena, especially, ones that live on manifolds. To address this fundamental challenge, we bring the elements of the Hodge theory and, in particular, simplicial convolution defined on the Hodge Laplacian to the emerging nexus of DL and PDEs. In contrast to conventional Laplacian and the associated convolution operation, the simplicial convolution allows us to rigorously describe diffusion across higher order structures and to better approximate the complex underlying topology and geometry of the data. The new approach, Simplicial Neural Networks for Partial Differential Equations (SNN PDE) offers a computationally efficient yet effective solution for time dependent PDEs. Our studies of a broad range of synthetic data and wildfire processes demonstrate that SNN PDE improves upon state of the art baselines in handling unstructured grids and irregular time intervals of complex physical systems and offers competitive forecasting capabilities for weather and air quality forecasting.

Three-dimensional finite-memory quasi-Newton inversion of the magnetotelluric based on unstructured grids

Abstract Simulation optimization of complex geological bodies is a necessary means to improve inversion accuracy and computational efficiency; thus, inversion of magnetotelluric (MT) based on unstructured grids has become a research hotspot in recent years. This article realizes the three-dimensional (3D) finite element forward modeling of MT based on the magnetic vector potential-electric scalar potential method, using unstructured grids as the forward modeling grid, which improves computational efficiency. The inversion uses the limited-memory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) method, and in the process of calculating the objective function gradient, the quasi-forward method is used to avoid solving the Jacobian matrix, which has the advantages of requiring small storage space and fast computational efficiency. Finally, the 3D LBFGS inversion algorithm of MT based on unstructured grids was realized, and the inversion studies of classic and complex models verified the effectiveness and the reliability of the algorithm proposed in this article.

Simulation of two-phase flow in 3D fractured reservoirs using a projection-based Embedded Discrete Fracture Model on Unstructured tetrahedral grids (pEDFM-U)

The modeling of fluid flow in heterogeneous, anisotropic and fractured porous media is relevant in many applications, including hydrocarbon and groundwater extraction, dispersion of contaminants, hydrogen or carbon dioxide (CO2) storage. Thus, accurate and scalable simulation of fluid flow through these formations continues to be a great challenge. The presence of fractures that are explicitly modeled, ranging from flow barriers to highly conductive channels, significantly increases the complexity of the numerical simulation. The Embedded Discrete Fracture Model (EDFM) produces results that can be as accurate as those obtained using equidimensional Discrete Fracture Models (DFM) at a much lower computational cost for highly conductive fractures, but it is not adequate for impermeable barriers. In contrast, the pEDFM (projection-based Embedded Discrete Fracture Model) produces accurate results for both, channels and barriers by using additional matrix-fracture connectivities. In its current versions, it is restricted to cartesian and corner-point grid geometries and to the classical Two Point Flux Approximation (TPFA) scheme. In this work, for the first time, the pEDFM is extended to handle unstructured tetrahedral meshes (pEDFM-U). In addition, interface fluxes are approximated by using the Multipoint Flux Approximation method with a Diamond stencil (MPFA-D). This allows for simulation of highly heterogeneous and anisotropic geo-models. The developed method is robust and can deal with full permeability tensors on arbitrary tetrahedral meshes. The advective terms are discretized considering an implicit First Order Upwind (FOU) method. Our method is implemented within the DARSim (Delft Advanced Reservoir Simulation) open-source simulator framework. Through several test cases, the proposed method showed to be robust and capable to accurately capture the effects of both high and low permeability fractures for general tetrahedral meshes, under arbitrary heterogeneous and anisotropic permeability tensors for the rock matrix.

On polytope intersection by half-spaces and hyperplanes for unsplit geometric volume of fluid methods on arbitrary grids

Several tools with improved accuracy and computational efficiency, along with added capabilities, are presented for performing analytic and geometric operations involving intersections between half-spaces or hyperplanes and 2- or 3-polytopes (polygons or polyhedra, either convex or non-convex) that typically arise in advanced volume of fluid (VOF) methods on arbitrary grids. In particular, tools for the intersection between a polyhedron and a half-space, and for the computation of the interface position to cut off a given area/volume fraction from an arbitrary polygonal/polyhedral grid cell in PLIC (piecewise linear interface calculation) reconstruction have been improved in terms of accuracy and computational efficiency. In addition, specific tools are also proposed for (1) the intersection in 3D between a planar polygon and a half-space, and the computation of the resulting intersected area, which can be useful for unsplit methods based on wetted-area time-integration advection (WATIA) schemes, and for (2) the efficient computation of the geometric center of the set of clipped vertices and volume resulting from the intersection between an arbitrary polyhedron and a half-space, which can be useful for, respectively, several PLIC reconstruction methods and unsplit methods based on fluid-volume intersection advection (FVIA) schemes. Finally, a convenient strategy to perform the recursive intersections required during the advection step in advanced geometric VOF methods based on FVIA schemes is also proposed. To assess the performance and accuracy of the proposed tools, different tests were carried out for several convex and non-convex polytopes. Speedups of ×5 and improvements in accuracy of up to 5 orders of magnitude over previous tools have been achieved for certain geometries and operations. The proposed tools have been included in two advection methods (an FVIA method and a new WATIA method proposed in this work) and in a PLIC reconstruction method to demonstrate their improved performance and capabilities on structured and unstructured grids.

Computational Simulation of Wind Loads on Three Curved Eave Models with Different Height-Width Relationships

This work deals with the effects of wind loads on two industrial shed models with curved eaves aspect of different height-to-width ratios. Using Ansys Workbench software, the external pressure coefficients for the entire roof by applying refinement levels were determined. Also were studied the quality of the unstructured and tetrahedral grid according to recommendations to ensure greater efficiency in the simulation results. The results generated provided evidence that the wind in the transverse direction is more damaging in the windward region: for a wind at 45º the most critical region appeared both windward and leeward in the model with a ratio of h/b=0.5 (Model 1) and to windward in the models with a ratio of h/b=1 (Model 2) and h/b=1.5 (Model 3). The leeward suctions increased due to the reduction in the height-width ratio considering a wind direction of 45º. The increase in this ratio intensified the values of the external pressure coefficients in the windward region for the 90º wind direction.

Robust and accurate Roe-type Riemann solver with compact stencil: Rotated-RoeM scheme

In this study, we aim to develop a robust and accurate Riemann solver to resolve strong shock waves with compact stencil information by applying the rotated hybrid concept to the RoeM scheme. The original RoeM scheme offers good robustness from the perspective of avoiding shock instability, also called the carbuncle phenomenon, in hypersonic flows by introducing Mach-number-based functions. These functions rely on multi-dimensional shock discontinuity sensing terms to capture grid-aligned shock waves, thus necessitating sharing of values of cells adjacent to each vertex. Consequently, constructing a data structure that can handle such a wide stencil is necessary, particularly for implementations on unstructured grids. Moreover, communication of this stencil information on parallel computation can increase computational costs.To overcome these complexities, the rotated hybrid concept is applied to the RoeM scheme, to replace the multi-dimensional terms while still resolving the grid-aligned shock instability. In addition, a Mach-number-based weighting function is introduced to distinguish between the flow around the boundary layer and the onset of shock instability. The damping characteristic of the proposed scheme is compared to that of the original RoeM scheme by conducting a linear perturbation analysis. The findings reveal that the proposed scheme effectively controls spurious oscillations across strong shock waves. Numerous test cases are presented to demonstrate the robustness and accuracy of the proposed approach. Notably, the proposed scheme successfully resolves thermal boundary layers and accurately predicts the heat transfer rate around stagnation points in hypersonic flows.

Numerical Simulation of Storm Surge Inundation in Estuarine Area Considering Multiple Influencing Factors

With global climate change, the risk of extreme storms and storm surges in estuarine areas is increasing; thus, storm surge inundation research and prediction have become important issues to ensure sustainable development in estuarine areas. The Jitimen estuary in Guangdong Province, China, was chosen as our study area. In this study, a numerical model for simulating storm surge inundation in small regions based on unstructured triangular grids was established, and the model accuracy was validated. The typhoon characteristics in the study area were statistically analyzed based on historical data. Three experimental schemes, involving factors influencing storm surge inundation, such as typhoon landfall location, intensity, and direction, were used to evaluate the differences in the numerical results. The results showed that when the typhoon landfall direction remained unchanged and the highest tide levels at the Sanzao tide gauge station were similar, the differences between the numerical results for the typhoon landfall location and typhoon intensity schemes were less than 5%, and the inundation characteristics were similar. However, when the typhoon location and intensity were unchanged and the highest tide levels at the Sanzao tide gauge station were similar, the numerical results for the typhoon landfall direction scheme significantly differed; this result was caused by the difference in the duration of the high tide level (exceeding 3 m); these results indicated that the topographic characteristics and the typhoon landing direction had a greater impact on storm surge inundation. The results from this study can aid in the prediction of storm surge inundation information for the Jitimen estuary area when the typhoon landing direction and the maximum tide level are known.

A Posteriori Local Subcell Correction of High-Order Discontinuous Galerkin Scheme for Conservation Laws on Two-Dimensional Unstructured Grids

A Posteriori Local Subcell Correction of High-Order Discontinuous Galerkin Scheme for Conservation Laws on Two-Dimensional Unstructured Grids

A residual graph convolutional network for setting initial flow field in computational fluid dynamics simulations

The computational cost of computational fluid dynamics (CFD) simulation is relatively high due to its computational complexity. To reduce the computing time required by CFD, researchers have proposed various methods, including efficient time advancement methods, correction methods for discrete control equations, multigrid methods, reasonable initial field setting methods, and parallel methods. Among these methods, the initial field setting method can provide significant performance improvements, but there is little work on it. Existing CFD industrial software typically uses inflow conditions for the initial flow field or applies empirical methods, which can cause instability in the CFD calculation process and make convergence difficult. With the rapid development of deep learning, researchers are increasingly attempting to replace CFD simulations with deep neural networks and have achieved significant performance improvements. However, these methods still face some challenges. First, they can only predict the computational flow field on regular grids. They cannot directly make predictions for irregular grids such as multi-block grids and unstructured grids, so the final flow field can only be obtained through interpolation and similar methods. Second, although these methods have been claimed to provide high accuracy, there is still a significant gap in performance with CFD and they cannot yet be applied to real scenarios. To address these issues, we propose a Residual Graph Convolutional Network for Initial Flow Field Setting (RGCN-IFS) in CFD simulations. This method converts the grid into a graph structure and uses an improved graph neural network to predict the flow field. In this way, we can predict the flow field on any type of grid. More importantly, this method does not directly replace CFD simulations, but it rather serves in an auxiliary role, providing appropriate initial flow fields for the CFD calculations, improving the convergence efficiency while ensuring calculation accuracy, and directly bridging the accuracy gap between intelligent surrogate models and CFD simulations.

A second-order-accuracy finite difference scheme for numerical computation on two-dimensional three-neighboring-node unstructured grids

The computation of the finite difference method in curvilinear coordinates usually necessitates coordinate transformation. Eliminating geometric errors induced by coordinate transformation can be achieved with geometric conservation law. However, no research has been conducted to implement a difference scheme on two-dimensional three-neighboring-node unstructured meshes and achieve a second-order accuracy. In this paper, a new finite difference method is proposed for a numerical simulation on these meshes, and it can achieve a second-order accuracy with the use of the gradient interpolation and the discrete criterion, freezing the metrics and Jacobian at local nodes. The results of several numerical tests demonstrate that the method achieved reliable performance and robustness on unique and randomized unstructured grids for a complex flow with discontinuity, subsonic inflow, and diffraction. The method had comparable accuracy to the second-order difference scheme on structured grids.

A typhoon-induced storm surge numerical model with GPU acceleration based on an unstructured spherical centroidal Voronoi tessellation grid

A typhoon-induced storm surge numerical model with GPU acceleration based on an unstructured spherical centroidal Voronoi tessellation grid

Unsteady aerodynamic characteristics of a morphing tail configuration

Morphing aircraft is an important trend in the future development of next-generation aircraft. This paper focuses on aircraft with a small aspect ratio flying wing configuration that includes morphing tails. The unsteady aerodynamic characteristics of the morphing tail configuration are numerically simulated using the unstructured overset grid technique and the dual-time method, focusing on the effects of the tail deflection angle over time, Mach number, and side slip angle on the unsteady aerodynamic characteristics of the entire aircraft and tails. The second derivative of the tail deflection angle with time should be continuous, and the maximum angular velocity and maximum angular acceleration should be minimized. The hysteresis loop area is closely related to the Mach number. The sideslip angle aggravates the nonlinearity of the unsteady aerodynamic characteristics of the entire aircraft. The unsteady aerodynamic characteristics during tail morphing are affected by static (wing downwash effect and projected area effect) and dynamic (flow field hysteresis effect, additional motion effect, and wall implication effect) characteristics. The enclosed research provides a reference for the aerodynamic and control system designs of morphing tail configurations.

Memory of HF radar surface-current assimilation on different forecasting variables of ocean circulation models

In this study, using nudging method, the current data from a pair of HF radar along Jiangsu coast was assimilated to unstructured grid models based on FVCOM. Several experiments were conducted to examine the effect of radar data on surface velocity, elevation and sea surface salinity forecast. The results show that the gain of assimilation on surface velocity and elevation forecasts disappeared fast within a few hours, while salinity forecasts can be influenced for more than 10 days. This fast diminishing of the gain of data assimilation on current and elevation can be attributed to the fast wave propagation from elsewhere to the radar coverage area.

Metocean conditions at two Norwegian sites for development of offshore wind farms

This paper examines metocean data from NORA3, a state-of-the-art wind and wave hindcast dataset for Northern Europe. Two offshore Norwegian areas, Utsira Nord (UN) and Sørlige Nordsjø II (SN2), are investigated. Both areas offer significant potential for the offshore wind sector. UN is situated in deep-sea water, suitable for floating offshore wind turbines. In contrast, SN2 lies in intermediate waters and ranks among the North Sea’s most promising regions allocated for offshore wind. Data from NORA3, originally on a 3-km resolution grid, are resampled into unstructured grids spanning from 1982 to 2022. This refined dataset offers a climatology time scale with superior spatial and temporal resolution compared to most other hindcast and reanalysis databases. The study examines mean wind speed and direction across seven levels, ranging from 10 m to 750 m above the surface. Analyses of extreme wind and wave conditions have been conducted. Results reveal that UN experiences higher extreme wave heights than SN2 while the extreme wind speeds may be substantially larger at SN2 than UN. Moreover, this study establishes joint distribution models that encompass several parameters, including mean wind speed, significant wave height, wave spectral peak period, and direction difference between wind and waves. Thus, this metocean data is valuable for designing and analyzing floating wind farms over their lifecycles.