Computational Grid Research Articles

A blended shifted‐fracture/phase‐field framework for sharp/diffuse crack modeling

AbstractThe shifted fracture method (SFM) is an embedded method that enables sharp crack representations while using mesh‐fitted data structures. In the SFM, the true crack is embedded in the computational grid, but the crack interface conditions are approximated by, or shifted to, a surrogate crack composed of element boundaries (i.e., edges/faces in two/three dimensions). This avoids enriched degrees‐of‐freedom and cut elements, so that data structures and geometrical treatment are much simpler, while still maintaining mesh‐independent and accurate crack approximations. This article presents a continuous‐discontinuous model of fracture based on blending a phase‐field (PF) model with the SFM. The PF tracks the evolution of cracks inside a numerical fracture processing zone: diffuse cracks initiate, propagate, branch, and merge according to the field equations of energy minimization; no ad‐hoc criteria are needed. The PF damage variable is then used to define the geometry of the true crack. With computational efficiency in mind, the PF model is only solved in subdomains where additional crack growth is expected and the SFM representation is used elsewhere. The efficiency and accuracy of the proposed approach in capturing complex crack patterns are illustrated by a representative set of two‐dimensional numerical examples.

Machine learning-based assessment of storm surge in the New York metropolitan area

Storm surge generated from low-probability high-consequence tropical cyclones is a major flood hazard to the New York metropolitan area and its assessment requires a large number of storm scenarios. High-fidelity hydrodynamic numerical simulations can predict surge levels from storm scenarios. However, an accurate prediction requires a relatively fine computational grid, which is computationally expensive, especially when including wave effects. Towards alleviating the computational burden, Machine Learning models are developed to determine long-term average recurrence of flood levels induced by tropical cyclones in the New York metropolitan area. The models are trained and verified using a data set generated from physics-based hydrodynamic simulations to predict peak storm surge height, defined as the maximum induced water level due to wind stresses on the water surface and wave setup, at four coastal sites. In the generated data set, the number of low probability high-level storm surges was much smaller than the number of high probability low-level storm surges. This resulted in an imbalanced data set, a challenge that is addressed and resolved in this study. The results show that return period curves generated based on storm surge predictions from machine learning models are in good agreement with curves generated from high-fidelity hydrodynamic simulations, with the advantage that the machine learning model results are obtained in a fraction of the computational time required to run the simulations.

Modeling fracture propagation in poro-elastic media combining phase-field and discrete fracture models

We present a novel model for fluid-driven fracture propagation in poro-elastic media. Our approach combines ideas from dimensionally reduced discrete fracture models with diffuse phase-field models. The main advantage of this combined approach is that the fracture geometry is always represented explicitly, while the propagation remains geometrically flexible. We prove that our model is thermodynamically consistent. In order to solve our model numerically, we propose a mixed-dimensional discontinuous Galerkin scheme with a computational grid fully conforming to the fractures. As the fracture propagates, the diffuse phase-field acts as indicator to identify new fracture facets to be added to the discrete fracture network. Numerical experiments demonstrate that our approach reproduces classical scenarios for fracturing porous media.

Semi-analytic simulation of optical wave propagation through turbulence.

Split-step wave-optical simulations are useful for studying optical propagation through random media like atmospheric turbulence. The standard method involves alternating steps of paraxial vacuum propagation and turbulent phase accumulation. We present a semianalytic approach to evaluating the Fresnel diffraction integral with onephase screen between the source and observation planes and another screen in the observation plane. Specifically, we express the first phase screen's transmittance as a Fourier series, which allows us to bring phase screen effects outside of the Fresnel diffraction integral, thereby reducing the numerical computations. This particular setup is useful for simulating astronomical imaging geometries and two-screen laboratory experiments that emulate real turbulence with phase wheels, spatial light modulators, etc. Further, this is a key building block in more general semianalytic split-step simulations that have an arbitrary number of screens. Compared with the standard angular-spectrum approach using the fast Fourier transform, the semianalytic method provides relaxed sampling constraints and an arbitrary computational grid. Also, when a limited number of observation-plane points is evaluated or when many time steps or random draws are used, the semianalytic method can compute faster than the angular-spectrum method.

Modeling the gravitational effects of ocean tide loading at coastal stations in the China earthquake gravity network based on GOTL software

Abstract The gravitational effects of ocean tide loading, which are one of the main factors affecting gravity measurements, consist of three components: (1) direct attraction from the tidal water masses, (2) radial displacement of the observing station due to the tidal load, and (3) internal redistribution of masses due to crustal deformation. In this study, software for gravitational effects of ocean tide loading was developed by evaluating a convolution integral between the ocean tide model and Green’s functions that describe the response of the Earth to tide loading. The effects of three-dimensional station coordinates, computational grid patterns, ocean tide models, Green’s functions, coastline, and local tide gauge were comprehensively considered in the programming process. Using a larger number of high-precision coastlines, ocean tide models, and Green’s functions, the reliability and applicability of the software were analyzed at coastal stations in the China Earthquake Gravity Network. The software can provide the amplitude and phase for ocean tide loading and produce a predicted gravity time series. The results can effectively reveal the variation characteristics of ocean tide loading in space and time. The computational gravitational effects of ocean tide loading were compared and analyzed for different ocean tide models and Green’s functions. The results show that different ocean tide models and Green’s functions have certain effects on the calculated values of loading gravity effects. Furthermore, a higher-precision local ocean tide model, digital elevation model, and local tidal gauge record can be further imported into our software to improve the accuracy of loading gravity effects in the global and local zones. The software is easy to operate and can provide a comprehensive platform for correcting the gravitational effects of ocean tide loading at stations in the China Earthquake Gravity Network.

Forecasting the energy characteristics of a reversible hydraulic machine for a head up to 250 m

BACKGROUND: At present, in the pressure zone of 50650 m for pumped storage power plants, hydroelectric units with classic single-stage radial-axial reversible hydraulic machines, which have a relatively simple design of the impeller and cylindrical guide vane, have received the most widespread energy performance, but are relatively quiet, large-sized and metal-intensive hydraulic machines. Numerical research and design of this type of machines are given special attention. The current trend is the design of flow parts based on numerical simulation of the flow. The most well-known commercial software products that implement finite volume numerical simulations are Ansys Fluent, Ansys CFX, StarCD, Numeca, Flow Vision and CADRUN. In the work under consideration, the calculations were performed using the Ansys CFX software package version 2021R1. Today, due to the lack of numerical capacity, the task of developing and using a technique that will allow obtaining an acceptable result with optimal time spent on data preparation and computational studies remains an urgent task.
 AIMS: The aim of the work was to present an economical methodology for numerical simulation of energy characteristics.
 METHODS: The methodology consists in describing the problem statement, the computational grids used, and the assumptions made for the optimal use of computing resources without a significant loss in the accuracy of the results.
 Object of computational research: The presented article investigates the flow part of a radial-axial pump-turbine designed for application to a maximum head of up to 250 m.
 RESULTS: Numerical modeling of power characteristics of on-pump and turbine modes is performed. A brief description of the problem statement, computational grids used, and assumptions made is given. A comparison of calculation results with experimental data of model tests is presented. The comparison results are presented in the relative form for the main parameters: pressure, efficiency, reduced rotational speed and flow rate.
 CONCLUSIONS: It is recommended to use SST model of turbulence in a stationary statement in order to predict the power characteristics of pump-turbines. The use of economical block-structured grids, as well as the performing of calculations only in the region of one blade of the guide vanes, one impeller blade and a suction pipe with the use of preliminary results of calculations in a spiral chamber allow using computational resources optimally without significant loss of accuracy of the results.

Determination of steam leaks through faulty labyrinth seals of a steam turbine

BACKGROUND: When calculating the axial force acting on the thrust bearing of a steam turbine, when calculating the dimensions of the unloading piston, when calculating the efficiency of the turbine stages, it is necessary to determine the amount of steam leakage through its diaphragm and end seals. Existing methods make it possible to calculate leaks only through serviceable, undamaged labyrinth seals of several standard designs. However, during the operation of steam turbines, due to off-design axial and radial displacements of the rotor, labyrinth seals are often damaged - deformed, crushed or broken.
 AIMS: The purpose of the study is to develop a method for calculating leaks using direct CFD modeling in serviceable and damaged seals with typical failures, verify the simulation results by comparison with known methods and experimental data, and determine critical steam leaks through faulty labyrinth turbine seals.
 MATERIALS AND METHODS: A method for calculating the steam flow rate through serviceable and faulty labyrinth seals of a steam turbine using the capabilities of modern CFD methods is proposed and verified. The computational domain of modeling the front-end seal of the turbine, the features of setting the boundary conditions, the adaptive computational grid, and the numerical mathematical model used are described.
 RESULTS: The results of a numerical study of steam leakage through serviceable and damaged labyrinth end seals of the turbine are presented: with bent ridges in the seals, with partial or complete absence of ridges. The operation of the front-end seal of the turbine was simulated with several typical failures. It is shown that partial damage to the ridges of the front-end seal of the turbine, which is often encountered during operation, leads to a significant increase in steam leakage. It has been established that with significant damage to the ridges, an increase in steam leakage can lead to the exhaustion of the capacity of the steam pressure regulator in the seal, which leads to a malfunction of the turbine thrust bearing unloading system.
 CONCLUSIONS: The proposed technique and the results obtained can be used to calculate steam leakage through serviceable and faulty diaphragm and end labyrinth seals of turbines, when calculating the value of the axial force acting on the turbine thrust bearing in variable operating modes, the technique is useful in assessing the efficiency of the thrust bearing unloading system.

Direct numerical simulation of shock wave/turbulent boundary layer interaction in a swept compression ramp at Mach 6

Swept compression ramps widely exist in supersonic/hypersonic vehicles and have become a typical standard model for studying three-dimensional (3D) shock wave/turbulent boundary layer interactions (STBLIs). In this paper, we conduct a direct numerical simulation of swept compression ramp STBLI with a 34° compression angle and a 45° sweep angle at Mach 6 using a heterogeneous parallel finite difference solver. Benefitting from the powerful computing performance of the graphics processing unit, the computational grid number exceeds 5 × 106 with the spatiotemporal evolution data of hypersonic 3D STBLI obtained. The results show that the flow of the hypersonic swept compression ramp follows the quasi-conical symmetry. A supersonic crossflow with helical motion appears in the interaction region, and its velocity increases along the spanwise direction. Fluids from the high-energy-density region pass through the bow shock at the head of the main shock and crash into the wall downstream of the reattachment, resulting in the peaks in skin friction and heat flux. The peak friction and heating increase along the spanwise direction because of the spanwise variation in the shock wave inclination. In the interaction region, the unsteadiness is dominated by the mid-frequency motion, whereas the low-frequency large-scale motion is nearly absent. Two reasons for the lack of low-frequency unsteadiness are given: (1) The separation shock is significantly weaker than the reattachment shock and main shock; and (2) because of the supersonic crossflow, the perturbations propagating at the sound speed are not self-sustaining but flow along the r-direction and toward the spanwise boundary.

Numerical Simulation of Roughness Effects of Ice Accretion on Wind Turbine Airfoils

One of the emerging problems in modern computational fluid dynamics is the simulation of flow over rough surfaces. A good example of these rough surfaces is wind turbine blades with ice formation on its leading edge. Instead of resolving the airflow field using a fine computational grid near the wall, rough wall functions (RWFs) can be used to model the flow behavior in case of the presence of roughness. This work aims to investigate the performance of state-of-the-art RWFs to show which of these models can provide the most accurate results with the lowest computational cost possible. This aim is achieved by comparing coefficients of lift and pressure resulting from CFD simulations with wind tunnel results of an airfoil with actual ice profiles collected from the site. The RWFs are used to simulate airflow field over the airfoil profiles with ice profile attached to its leading edge using OpenFOAM CFD framework. The comparison of the numerical simulations and the wind tunnel measurements showed that the Colebrook RWF provided the best agreement between simulation and experimental results while using about 20% of the number of cells used with smooth RWF.

Penalized Wall Function Method for Turbulent Flow Modeling

A novel penalized wall function method for simulations of wall-bounded compressible turbulent flows is proposed. The new approach is based on the Reynolds-averaged Navier–Stokes (RANS) equations to model the outer region of the turbulent boundary layer, while the inner part is approximated by the equilibrium wall function model. The differential formulation to match the external and the wall function solutions is reformulated in a form of the generalized characteristic-based volume penalization method to model the transfer of the shear stress from the outer region of the boundary layer to the wall and to impose the wall-stress boundary conditions on the RANS solution. The exchange location is specified implicitly through a localized source term in the boundary layer equation, written as a function of the normalized distance from the wall. The wall-stress condition is determined by solving an auxiliary equation for the wall-stress, ensuring the correct matching of the RANS and the wall function solutions at the exchange layer. The proposed method noticeably reduces the near-wall mesh resolution requirements without significant modification of the RANS solver and removes the ill-defined explicit matching procedure, commonly used by traditional wall function-based methods. The penalized wall function approach is implemented using the vertex-centered control volume method on unstructured computational grids. The effectiveness of the developed penalized wall function method is demonstrated for twodimensional bump-in-channel flow for the Spalart–Allmaras turbulence model.

Numerical simulation of separated flow past a square cylinder based on a two-fluid turbulence model

The paper presents the numerical results of the transverse flow around an infinite square beam based on the two-fluid turbulence model for the Reynolds number Re = 21400. This problem has a periodic solution, so the non-stationary system of equations of the turbulence model was solved. For the difference approximation of the initial equations, the control volume method and the computational grid arranged in a checkerboard pattern were used. Coarse, fine, and condensed computational grids were used in the work. Their influence on the numerical results is shown. The SIMPLE procedure was applied to correct the velocity through pressure. For the numerical implementation of the equations of the two-fluid model, the two-step Peaceman-Rachford scheme was used. In the work, instantaneous and averaged results for longitudinal and transverse velocities, pressure, pressure coefficient and turbulent stresses are obtained. These results are presented in the form of profiles, as well as in the form of dependences on time and distance in the longitudinal direction. The instantaneous and averaged flow patterns are also presented. The obtained numerical results are compared with the experimental data and the results of other known turbulent models. It is shown that the two-fluid model describes this turbulent flow well.

Construction of Tidal Information Database on the Southern Coast of Korea and Prediction of the Tide

The construction of the tidal information database study was conducted through numerical simulations for the southern coast of Korea. Because Korea has a complex coastline, the grid size of the numerical model was set to 0.1min(approx. 200m) to improve the accuracy of tidal prediction. The NAO.99jb, one of the ocean tide models, was employed in the study to increase the accuracy of the database. The numerical model applied to the database construction was calibrated and validated using observation data from the Korea hydrographic and oceanographic agency. To construct a high-resolution tidal information database, we conducted harmonic analysis for each computational grid point using numerical simulation results. In order to evaluate the tide and tidal current prediction performance of the tidal information database, numerical simulation results were used and compared. The results show that the predictive performance of the harmonic constant database is sufficient, so it can be used where rapid tidal prediction is required.

Computational fluid dynamics grid technology development

This paper reviews the development of computational fluid dynamics, especially computational aerodynamics. This paper summarizes the achievements of CFD in grid technology, analyzes the existing problems and perplexities, and prospects its development trend. The CFD grid technology includes structured grid, unstructured grid, hybrid grid and overlapping grid.

The sweep method for radiative transfer in arepo

ABSTRACT We introduce the radiative transfer code Sweep for the cosmological simulation suite arepo. Sweep is a discrete ordinates method in which the radiative transfer equation is solved under the infinite speed of light, steady state assumption by a transport sweep across the entire computational grid. Since arepo is based on an adaptive, unstructured grid, the dependency graph induced by the sweep dependencies of the grid cells is non-trivial. In order to solve the topological sorting problem in a distributed manner, we employ a task-based-parallelism approach. The main advantage of the sweep method is that the computational cost scales only with the size of the grid and is independent of the number of sources or the distribution of sources in the computational domain, which is an advantage for radiative transfer in cosmological simulations, where there are large numbers of sparsely distributed sources. We successfully apply the code to a number of physical tests such as the expansion of H ii regions, the formation of shadows behind dense objects, the scattering of light, and its behaviour in the presence of periodic boundary conditions. In addition, we measure its computational performance with a focus on highly parallel, large-scale simulations.

Metric assisted stochastic sampling search for gravitational waves from binary black hole mergers

We present a novel gravitational-wave detection algorithm that conducts a matched-filter search stochastically across the compact binary parameter space rather than relying on a fixed bank of template waveforms. This technique is competitive with standard template-bank-driven pipelines in both computational cost and sensitivity. However, the complexity of the analysis is simpler, allowing for easy configuration and horizontal scaling across heterogeneous grids of computers. To demonstrate the method we analyze approximately one month of public LIGO data from July 27 00:00 2017 UTC–Aug 25 22:00 2017 UTC and recover eight known confident gravitational-wave candidates. We also inject simulated binary black hole signals to demonstrate the sensitivity.Received 1 November 2021Accepted 4 October 2022DOI:https://doi.org/10.1103/PhysRevD.106.084033© 2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasClassical black holesGravitational wave detectionGravitational wave sourcesGravitation, Cosmology & Astrophysics

Load Balancing Based on Firefly and Ant Colony Optimization Algorithms for Parallel Computing.

With the wide application of computational fluid dynamics in various fields and the continuous growth of the complexity of the problem and the scale of the computational grid, large-scale parallel computing came into being and became an indispensable means to solve this problem. In the numerical simulation of multi-block grids, the mapping strategy from grid block to processor is an important factor affecting the efficiency of load balancing and communication overhead. The multi-level graph partitioning algorithm is an important algorithm that introduces graph network dynamic programming to solve the load-balancing problem. This paper proposed a firefly-ant compound optimization (FaCO) algorithm for the weighted fusion of two optimization rules of the firefly and ant colony algorithm. For the graph, results after multi-level graph partitioning are transformed into a traveling salesman problem (TSP). This algorithm is used to optimize the load distribution of the solution, and finally, the rough graph segmentation is projected to obtain the most original segmentation optimization results. Although firefly algorithm (FA) and ant colony optimization (ACO), as swarm intelligence algorithms, are widely used to solve TSP problems, for the problems for which swarm intelligence algorithms easily fall into local optimization and low search accuracy, the improvement of the FaCO algorithm adjusts the weight of iterative location selection and updates the location. Experimental results on publicly available datasets such as the Oliver30 dataset and the eil51 dataset demonstrated the effectiveness of the FaCO algorithm. It is also significantly better than the commonly used firefly algorithm and other algorithms in terms of the search results and efficiency and achieves better results in optimizing the load-balancing problem of parallel computing.

Efficient formulation of a two‐noded geometrically exact curved beam element

AbstractThe article extends the formulation of a 2D geometrically exact beam element proposed by Jirásek et al. (2021) to curved elastic beams. This formulation is based on equilibrium equations in their integrated form, combined with the kinematic relations and sectional equations that link the internal forces to sectional deformation variables. The resulting first‐order differential equations are approximated by the finite difference scheme and the boundary value problem is converted to an initial value problem using the shooting method. The article develops the theoretical framework based on the Navier–Bernoulli hypothesis, with a possible extension to shear‐flexible beams. Numerical procedures for the evaluation of equivalent nodal forces and of the element tangent stiffness are presented in detail. Unlike standard finite element formulations, the present approach can increase accuracy by refining the integration scheme on the element level while the number of global degrees of freedom is kept constant. The efficiency and accuracy of the developed scheme are documented by seven examples that cover circular and parabolic arches, a spiral‐shaped beam, and a spring‐like beam with a zig‐zag centerline. The proposed formulation does not exhibit any locking. No excessive stiffness is observed for coarse computational grids and the distribution of internal forces is not polluted by any oscillations. It is also shown that a cross effect in the relations between internal forces and deformation variables arises, that is, the bending moment affects axial stretching and the normal force affects the curvature. This coupling is theoretically explained in the Appendix.

Deep learning for fast photoacoustic wave simulations

Photoacoustic tomography involves absorption of pulsed light and subsequent generation of ultrasound, which when detected using an array of sensors can produce clinically useful images. Simulation tools for photoacoustic wave propagation have played a key role in advancing photoacoustic imaging by providing quantitative and qualitative insights into parameters affecting image quality. Classical methods for numerically solving the photoacoustic wave equation rely on a fine discretization of space and can become computationally expensive for large computational grids. In this work, we apply Fourier Neural Operator (FNO) networks as a fast data-driven deep learning method for solving the 2D photoacoustic wave equation in a homogeneous medium. Comparisons between the FNO network and pseudo-spectral time domain approach demonstrated that the FNO network generated comparable simulations with small errors and was an order of magnitude faster. Moreover, the FNO network was generalizable and could generate simulations not observed in the training data.

Development and Validation of a Three‐Dimensional Variably Saturated Flow Model for Future Water Resource Assessment at a Global Scale—Targeting Saturated Groundwater Flow in Plains

A three-dimensional variably saturated flow model was developed for assessing future global water resources and parameterized for groundwater pumping. We applied this model to an actual watershed to verify its validity as an Earth System Model. For global applicability, the parameterization method for multi-layered groundwater pumping was developed and verified through comparison with observations and MODFLOW results. The parameterization proposed in this study is applicable even when multiple groundwater pumping wells are present within one horizontal computational grid and when the well spans multiple vertical grids. This method can be applied at the global scale without parameters such as the well radius, for which data may be difficult to obtain. The parameterization recreated seasonal and annual variations in the observed values. Furthermore, the results were comparable to those of MODFLOW. However, the calculation results were overestimated relative to the observed values. This overestimation was likely to be due to active groundwater pumping in the Central Valley before the start of the unsteady-state calculation. Therefore, the groundwater level at the beginning of the unsteady-state calculation was calculated using observed values, improving reproducibility. Furthermore, as observed groundwater levels are unlikely to be available at the global scale, steady-state calculations were conducted over 15 and 60 years considering groundwater pumping. However, the results were not as reproducible as those obtained using observed groundwater levels. These results suggest that the groundwater level set at the beginning of the calculation is important for global-scale groundwater flow calculation.

Subgrid-scale modeling of tsunami inundation in coastal urban areas

Numerical tsunami inundation simulations using high-resolution (HR) topographical data are important to predict tsunami damage in urban areas at individual building levels accurately but are challenging due to the high computational cost. To address this issue, a subgrid-scale (SGS) model of tsunami inundation, called the individual drag force model (iDFM), is developed. In this model, the sum of the building drag forces in a computational mesh is fed back to the flow field by taking into account spatial information about multiple structures in the mesh. To evaluate the model performance, idealized numerical experiments using simple urban topography with several types of spatial layout patterns and hindcast physical experiments focusing upon Onagawa Town affected by the 2011 Tohoku, Japan tsunami as a historical event are conducted. Results are compared with HR tsunami simulations using building-resolved topographical data, called the structure resolving model (SRM). In general, the iDFM (and other SGS models) characterizes the effects of structures as resistance elements that reduce the fluid velocity in momentum conservation. On the other hand, the SRM evaluates these effects as topography and feeds them back into not only momentum conservation but also mass conservation and wet/dry boundary conditions. Therefore, the iDFM can model the overall inundation characteristics, such as the limits of inundation, more than 10 2 times efficiently compared with the SRM, although it cannot capture local phenomena driven by structures, such as surface rising due to blocking and contracting current between structures. In both numerical and historical tsunami (Onagawa) cases, there were small differences between the modeled inundation characteristics, such as the maximum surface elevation and fluid velocity, and the time series of inundation leading edges determined by the iDFM due to the computational grid cell sizes. The observed differences between the idealized numerical experiment and the historical tsunami case can be affected by the drag coefficient and the Froude number during the tsunami run-up.