Unstructured Computational Grids Research Articles

Modeling Object Motion on Arbitrary Unstructured Grids Using an Invariant Principle of Computational Domain Topology: Key Features

This paper uses a finite volume algorithm to address the numerical modeling of fluid flow around moving bodies. The Navier–Stokes equations, which describe the flow of viscous compressible gas, along with key boundary conditions and discretization schemes, are presented. As the motion of boundaries typically leads to changes in the control volumes, the basic discretization schemes need to be adapted. This paper provides a detailed discussion on the adaptation of the initial system to deforming boundaries while preserving communication topology. The method for calculating the boundary velocity is a crucial element of the numerical scheme. The paper proposes an approach to reconstruct the boundary velocity vector using deformation analysis and the condition of geometric conservation. This approach ensures correct simulation results for arbitrary unstructured computational grids. A comparison of two approaches to reconstructing the boundary velocity vector for characteristic aviation problems in the direct formulation is presented. It is shown that the proposed approach allows for more accurate modeling of object motion on arbitrary grids using the “invariant” principle of the computational domain topology.

Parallelization of numerical solutions of shallow water equations by the finite volume method for implementation on multiprocessor systems and graphics processors

An overview of approaches to parallelization of grid-based numerical methods for solving shallow water equations for multiprocessor systems and graphics processors is presented. A multithreaded approach for shared-memory computing systems implemented on the basis of the OpenMP programming interface and a geometric decomposition approach with message-passing using the MPI library for distributed-memory computers are described. Multithreading for programming GPUs based on the OpenACC software interface is considered. For the COASTOX-UN system of two-dimensional modeling of hydrodynamics, sediment and radionuclide transport in river systems and coastal areas of the seas, the parallelization of its hydrodynamic model COASTOX-HD was carried out. In the developed numerical model, the shallow water equations are solved by finite-volume numerical methods on unstructured computational grids with triangular cells of variable size. The parallelization is implemented using a hybrid MPI+OpenACC approach targeting multiprocessor systems and GPUs. For multiprocessor computers, geometric decomposition and MPI-based messaging are used, and for GPUs, multithreading is implemented using OpenACC directives. The performance of the developed parallel hydrodynamic model was evaluated during the calculation of typical problems of hydrodynamics of shallow water bodies, river flood, and tsunami wave run-up on the coast on a Dell Precision Workstation 7920 multi-core workstation with two 20-core Intel Xeon Gold 6230 processors and NVIDIA Quadro RTX 5000 and NVIDIA GeForce RTX 3080 graphics cards. It is shown that the developed model has significantly accelerated the simulation on the considered multiprocessor system and the considered GPUs. The acceleration on GPUs depends on the size of the computational grid, increasing to saturation with an increase in the number of grid cells. It is established that for the developed parallel model, whose numerical schemes are related to algorithms with low computational intensity, the memory bandwidth of the NVIDIA architecture GPUs is a more important limiting factor of acceleration than their performance.

Моделирование ветрового волнения в море Лаптевых, Восточно-Сибирском и Чукотском морях

The paper presents an analysis of wind wave parameters in the Laptev, East Siberian and Chukchi seas based on the results of numerical experiments with the WAVEWATCH III wave model for a period from 1979 to 2021. Wave modeling was carried out using an unstructured computational grid with a high resolution (up to 800 m) in the coastal zone. The NCEP/CFSR/CFSv2 reanalysis was used as wind forcing. The maps of the long-term mean values of the wave height, wave length and period were obtained. For the several points in the central part of each sea, the mean annual values of wave heights are calculated and the analysis of interannual variability is carried out. The maximum significant wave height was 5–6 m in the Laptev Sea, 6–7 m in the East Siberian Sea, and 7–7.5 m in the Chukchi Sea. The analysis of interannual variability showed that there is a positive trend in wave height for all seas under consideration. The largest increase in the annual mean wave height is observed in the East Siberian Sea (from 0.4 to 1.4 m in the ice-free period). Keywords: Laptev Sea, Chukchi Sea, East Siberian Sea, wave modeling, Arctic wind waves, WAVEWATCH III

On Treatment of Some Physical Properties of Gas in Simulation of High-Voltage SF6 Circuit Breakers

Abstract Simulation of unsteady flow of SF6 gas in a simplified high-voltage circuit breaker model describing the nozzle, contacts and their nearest surrounding is presented. SF6 is considered as viscous, compressible, real gas described by Redlich-Kwong model. Heat transfer is taken into account due to the gas compressibility. The heat source, triggered by the electric arc between the contacts, was out of the scope of the current research, thus it was not included in the simulations presented. Turbulence, caused by the gas viscosity, is described using realizable k-ε model. In the simulation model, one of the contact sides – electrodes, is considered as moving at prescribed velocity. The part of the space ‘swept’ by the moving electrode is considered as the gas with imposed artificially increased viscosity in order to imitate the rigid body behaviour. Thus, no moving parts of the computational mesh are used in the model. The conservation equations of mass, momentum and energy, given in integral form, are solved using a finite-volume method on unstructured computational grids.

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.

A Peaceman-type well model for the 3D Control Volume Finite Element Method and numerical simulations of supercritical geothermal resource utilization

While supercritical geothermal resources receive increasing attention, it has so far remained unclear if and how they could be utilized. In order to provide a tool that can simulate both the natural transient evolution of a supercritical resource near a magma intrusion and its response to possible operation schemes, we augmented the CSMP++ simulation platform with a Peaceman-type well model. For the purpose of generic porous medium simulations of the supercritical resource’s response to direct production, injection or other operation schemes, only a single in-/outflow interval per well is considered and flow in the wellbore is not simulated. The model’s semi-analytical source/sink function accounts for the rapid change in pressure near the wells in the reservoir simulation. As the implementation is based on the 3D Control Volume Finite Element Method it allows the use of unstructured computational grids in order to be able to include geologically realistic geometries. We validate that the well model provides robust solutions of well pressures and rates. Such robust solutions are also obtained for supercritical conditions where water is highly compressible and, therefore, does not strictly fulfil the assumptions used in the derivation of the Peaceman model. To illustrate how a magma-related supercritical resource responds to well operation, we first simulate the evolution of a geothermal system around and above a 2 km deep, explicitly represented magma body. During the system’s hottest phase, ca. 2700 years after its initiation and during progressive inward cooling of the magma body, a well completion interval is activated at 2.1 to 2.2 km depth where temperatures then reach 420 to 490 °C. For the relatively low host rock permeability used in the model (10−15 m2), injection and production rates remain quite limited at several kg/s. Yet, the evolving patterns of temperature, enthalpy, density and flow rates provide some first insights into supercritical resource response to operation.

MHD_NX: код идеальной МГД-устойчивости на двумерных неструктурированных сетках

The code developed by the authors for calculating the MHD stability of two-dimensional plasma configurations with an arbitrary magnetic field topology is presented. The choice of an appropriate version of the finite element method on hybrid unstructured computational grids and test calculations are discussed. Examples of using the code for modeling the plasma stability in Galatea traps and in divertor configurations of tokamak taking into account the plasma beyond the separatrix are given.

On numerical modeling of aerodynamics of urban developments on unstructured computational grids

On numerical modeling of aerodynamics of urban developments on unstructured computational grids

An Operational Numerical System for Oil Stranding Risk Assessment in a High-Density Vessel Traffic Area

In the Mediterranean Sea unique environmental characteristics and sensitive assets coexist with intense maritime traffic that is represented by frequent daily passages of vessels along the main waterways. In order to assess the risk of oil stranding in case of at-sea emergencies and provide key products for environmental agencies or policymakers preparedness, a geographically relocatable, operational numerical system is implemented and tested. The system relies on the application of oceanographic and particle tracking models and is able to provide, on a high-resolution and unstructured computational grid, a 3-days forecast of those variables known as the main drivers of oil slicks at sea. The risk of potential oil stranding is computed through a combination of anthropogenic hazard and shoreline vulnerability. The sources of hazard vary on time and space in relation to local maritime vessel traffic. The shoreline vulnerability is based on the current knowledge of slope, main grain size, geology of rocks, and occurrence of manmade structures at coast. The operational system is enriched by a web graphical user interface and includes automatic and on-demand working modes. Its functionality is demonstrated in the Strait of Bonifacio (western Mediterranean Sea), area with a high potential risk of oil stranding due to an intense maritime traffic. Risk assessment is hence computed for a test year, the 2018. Critical values of risk are found in correspondence of long stretches of littoral while many of them are currently characterized by a low anthropogenic pressure. The results emphasize the geomorphological features of the shorelines as reducing or amplifying factors to any potential impact of oil stranding at coast.

CFD–DEM–VDGM method for simulation of particle fluidization behavior in multi-ring inclined-hole spouted fluidized bed

The simulation of particle fluidization behavior in a complex geometry with a large number of particles is challenging owing to the complexity of unstructured computational grids and high computational intensity. In this study, a virtual dual-grid model (VDGM) is proposed to calculate the solid volume fraction in unstructured grids and speed up the calculation. The VDGM is coupled with a computational fluid dynamics–discrete element method model to simulate particle fluidization behavior in a multi-ring inclined-hole spouted fluidized bed with 4.2 million particles under a high temperature of 1423 K. A computational fluid dynamics–discrete element method–virtual dual-grid model (CFD–DEM–VDGM) coupling model is implemented based on commercial software Fluent and EDEM. The time step settings in Fluent and EDEM and the pattern of particle data transfer in Fluent are improved to speed up the calculation. It is discovered that the VDGM can calculate the solid volume fraction in unstructured grids of complex geometry and speed up the calculation effectively. The calculation speed increased by more than 10 times compared with that of the segmentation sampling method. The new pattern of particle data transfer in Fluent can reduce data transfer time by more than 90%. The fluidization behavior of 4.2 million high-density particles in the multi-ring inclined-hole spouted fluidized bed is obtained and analyzed in detail. The CFD–DEM–VDGM coupling method is validated for the bed expansion height and spouting cycle time in a spouted fluidized bed via experimental results.

3D-CFD Study of Oblique Streamlining Membranes on the Roof-Top of a Low-Rise Building, Targeting Pedestrian Comfort-A Case Study

Considering the cubic nature of the most frequent geometries among the urban elements and their configurations, the manipulation of the free stream wind flow around the enormous objects, as well as within relatively narrow corridors, such as street canyons is significant in many regards. One of its instances could be mentioned as pedestrian comfort. In this case study, the implementation of an Oblique Streamlining Membrane (OSM) has been studied on a sub-branch of a low rise, but bulky, building, over which a roof-top outdoor food court area has been primarily designed. The OSM serves as the streamlining mechanism, preventing the roof-top area from the intense fluctuations of the wind flow after the flow is separated from the inlet corner side of the building in question. The optimization of sub-geometries and the proof of the concept for the OSM flow controlling mechanism were the subject of the current manuscript, for which a 3D numerical Reynolds Average Navier-Stokes (RANS) scheme has been used. An unstructured computational grid has been applied around the 3D geometry of the entire building and its sub-branching details, which is in contrast with most studies on full-scale geometries, tending to have simplifications on the body to reach a more generalized set of results. All cases have been numerically tested with and without the presence of the OSM. This comparison has been the grounds for proving the effectivity of the said flow controlling mechanism to eliminate high gradient fluctuations of the separated flow off the roof corners. This has led to pedestrian/resident comfort on the roof-top food court area located on top of the building.

Black Sea wind wave climate with a focus on coastal regions

This study is dedicated to the wind waves parameters distribution on the Black Sea with a focus on coastal areas. Wind waves were simulated using the SWAN model forced by the NCEP CFSR and NCEP CFSv2 reanalyses for the period 1979–2016. An unstructured computational grid with resolution varying between 15 km and 200 m was applied. Modelling results were validated against in situ and remote sensing data. For the entire sea, distributions of total and seasonal maxima of wave parameters are analyzed. Maximal significant wave heights exceed 8.5 m and are found in the southwestern areas of the sea. Maximal wave lengths (over 160 m) and periods (over 10.5 s) are located in the eastern part of the sea. Total and seasonal time series extracted for 12 locations along the coasts of the Black Sea were studied. Maximal values of significant wave heights (over 6 m) correspond to areas along the northeastern and southwestern coasts of the Black Sea and the southern coast of the Crimean Peninsula. Maximal values of wave lengths and wave periods (over 140 m and 10 s) are located along the northeastern and southern coasts of the Black sea.

Three-Dimensional Unstructured Grid Finite-Volume Model for Coastal and Estuarine Circulation and Its Application

We developed a three-dimensional unstructured grid coastal and estuarine circulation model, named the General Ocean Model (GOM). Combining the finite volume and finite difference methods, GOM achieved both the exact conservation and computational efficiency. The propagation term was implemented by a semi-implicit numerical scheme, the so-called θ scheme, and the time-explicit Eulerian–Lagrangian method was used to discretize the nonlinear advection term to remove the major limitation of the time step, which appears when solving shallow water equations, by the Courant–Friedrichs–Lewy stability condition. Because the GOM uses orthogonal unstructured computational grids, allowing both triangular and quadrilateral grids, considerable flexibility to resolve complex coastal boundaries is allowed without any transformation of governing equations. The GOM was successfully verified with five analytical solutions, and it was also validated when applied to the Texas coast, showing an overall skill value of 0.951. The verification results showed that the algorithm used in GOM was correctly coded, and it is efficient and robust.

Mechanisms of detonation initiation in multi-focusing systems

The work is dedicated to the experimental and numerical study of the mechanisms of gaseous detonation initiation in a stoichiometric hydrogen–oxygen mixture due to the reflection of a shock wave from a complex-shaped end wall. Several elliptic surfaces of different geometries, including distributed ones, were considered. We refer to such reflectors with multiple elliptical surfaces as multi-focusing systems. The experiments were carried out in a shock tube. Visualization of the process was carried out with a high-speed schlieren system. In the experiments, the ignition delay times and the critical incident shock wave Mach number for detonation initiation were measured. Two-dimensional Euler simulations, on a fully unstructured computational grid, were carried out to determine the mechanism of detonation initiation. The numerical approach was verified using the experimentally measured ignition delay times. Reasonable agreement between the simulations and experiments for the critical Mach number of detonation initiation and for the efficiency of various multi-focusing systems for detonation initiation was achieved. Different regimes of detonation initiation depending on the incident shock wave Mach number were observed.

Micro gas turbine combustion chamber CFD modelling

The interest in micro gas turbines has been steadily increasing. As a result, the researchers’ attention has been focused on obtaining optimal configurations for micro gas turbines depending on the applications in which they are used. Micro gas turbines are suitable for both civil and military applications. Presently, they are often used in the development of Unmanned Air Vehicles (UAVs). Micro gas turbines have the following advantages: a wider range of options regarding the used fuel and a significant system weight reduction. This paper presents the CFD modelling results regarding an annular type combustion chamber. This combustion chamber is part of a 80 daN micro gas turbine, destined to equip a small scale multifunctional airplane. The combustion chamber is equipped with eight pressure-swirl injectors, using Jet-A as fuel. A 3D RANS numerical integration of the Navier-Stokes equations has been carried out, using an Eddy Dissipation combustion Model (EDM) and the k-ε turbulence model, implemented in a numerical simulation conducted using the commercial software ANSYS CFX. An unstructured computational grid, generated using ICEM CFD, has been used. The fuel is injected directly in the fire tube in the form of droplets. The initial fuel droplet’s diameter has been considered to be 50µm and the fuel spraying cone angle has been set at 90°. The fuel droplet break-up and evaporation processes have been simulated using numerical models available in ANSYS CFX library. A two steps reaction mechanism, which takes into consideration the formation of NO, has been used. The results thus obtained are encouraging. The flame developed in the central area of the fire tube, its walls thus not being subjected to high temperatures. Also, the maximum temperatures were obtained in the primary zone of the fire tube. The temperature then decreased in the fire tube’s secondary zone and dilution zone, until it reached an average value of 1200 K at the combustion chamber exit. Regarding the pressure, based on the numerical simulation results, a 5% pressure loss has been obtained. The numerical results will be validated by conducting combustion tests on a testing rig which will be developed inside the institute’s Combustion Chamber Laboratory.

A CFD-DEM-IBM method for Cartesian grid simulation of gas-solid flow in complex geometries

The use of CFD-DEM method to accurately simulate gas-solid flows in complex geometries is challenging, mainly due to the complexity related to the use of unstructured computational grids. In order to solve this problem, researchers have simulated gas-solid fluidized beds with complex geometries using CFD-DEM-IBM method with Cartesian grids. In present study the gas-solid flows in complex geometries were simulated using Cartesian grids following the basic idea of CFD-DEM-IBM method (De Jong et al., 2012), where the interactions between gas phase and complex geometries were firstly modelled using the immersed boundary method (IBM) implemented by Tuković and Jasak (2012) in OpenFOAM®. It was found that the computational efficiency is quite low. To improve the efficiency of the CFD-DEM-IBM solver, a new IBM method was then proposed by removing the neighboring immersed boundary cells from the interpolated extended stencil in the reconstruction of the velocity and pressure fields near the wall, and further proposing a new zero-gradient boundary condition to replace the original Neumann boundary condition for reconstructing the pressure field. Single-phase flow past a stationary cylinder, single-phase pipe flow, gas-solid flow in a cylindrical fluidized bed and fluidized bed with immersed tubes were simulated with four different IBM imposition methods to assess the accuracy and efficiency of sharp-interface CFD-DEM-IBM solver. It was shown that (i) the results of CFD-DEM-IBM simulations agree well with the reported experimental, analytical and/or numerical results available in literature; and (ii) the computational efficiency of newly proposed CFD-DEM-IBM solver is one or two order of magnitudes faster than that of the original IBM of Tuković and Jasak (2012) in OpenFOAM®, due to the fact that internal iterations are not needed anymore during the reconstruction of velocity and pressure fields.

Mathematical modeling of detonation initiation and propagation in the complex-shaped domains

The present work is devoted to the development of the numerical algorithm for the mathematical modeling of gaseous detonation initiation and propagation and the complex-shaped domains using fully unstructured computational grids and high-order numerical schemes. Mathematical model is based on two-dimensional Euler equations supplemented with the one-stage chemical kinetics model. Numerical algorithm is based on the finite volume approach, AUSM numerical flux and the reconstruction of the grid-functions on unstructured grids. The canonical problem of cellular detonation formation is considered as the test case. The influence of grid resolution and the properties of the numerical scheme on the results of modeling is investigated. The problem of the critical geometrical conditions determination for the detonation initiation and propagation in the asymmetrical tube with variable cross-section area filled with stoichiometric hydrogen–air mixture is considered. The problem in consideration relates to the utilization of the industrial waste.

Large-eddy simulation of flow over an axisymmetric body of revolution

Wall-resolved large-eddy simulation (LES) is used to simulate flow over an axisymmetric body of revolution at a Reynolds number,$Re=1.1\times 10^{6}$, based on the free-stream velocity and the length of the body. The geometry used in the present work is an idealized submarine hull (DARPA SUBOFF without appendages) at zero angle of pitch and yaw. The computational domain is chosen to avoid confinement effects and capture the wake up to fifteen diameters downstream of the body. The unstructured computational grid is designed to capture the fine near-wall flow structures as well as the wake evolution. LES results show good agreement with the available experimental data. The axisymmetric turbulent boundary layer has higher skin friction and higher radial decay of turbulence away from the wall, compared to a planar turbulent boundary layer under similar conditions. The mean streamwise velocity exhibits self-similarity, but the turbulent intensities are not self-similar over the length of the simulated wake, consistent with previous studies reported in the literature. The axisymmetric wake shifts from high-$Re$to low-$Re$equilibrium self-similar solutions, which were only observed for axisymmetric wakes of bluff bodies in the past.

Дослідження впливу інтерференції лопаткових вінців на втрати в ступені осьового компресора

Мета: дослідження втрат повного тиску у вхідному напрямному апараті, в робочому колесі й напрямному апараті ступеня осьового компресора з урахуванням їх газодинамічної інтерференції. Метод дослідження: дослідження виконано методом чисельного моделювання тривимірної течії в ступені осьового компресора. Побудовано неструктуровану адаптивну розрахункову сітку. Газодинамічний розрахунок течії в ступені осьового компресора виконано з використанням системи рівнянь Нав’є – Стокса, яка замикалася моделлю турбулентної в’язкості SST. Результати: було проведено серію газодинамічних розрахунків течії при різних значеннях осьової швидкості на вході в ступінь компресора. Колова швидкість на периферійному радіусі на розрахунковому режимі складала u=238.64 м/с. Коефіцієнт швидкості на вході в ступінь змінювався в діапазоні =0.35…0.7. За результатами розрахунку побудовано залежності коефіцієнтів втрат повного тиску від коефіцієнта швидкості на вході для вхідного напрямного апарату, робочого колеса і напрямного апарату. Аналіз результатів дослідження показує, що найбільший внесок у загальний баланс втрат повного тиску вносять втрати в напрямному апараті. Обговорення: унаслідок газодинамічної інтерференції робочого колеса і напрямного апарату відбувається збільшення втрат в напрямному апараті. Взаємний вплив лопаткових вінців робочого колеса і напрямного апарату призводить до суттєвої трансформації швидкостей і тисків в міжлопаткових каналах. Як наслідок, має місце перерозподілення втрат, обумовлених коловою і радіальною нерівномірністю потоку, кінцевими перетіканнями і дією відцентрових сил. Можна очікувати, що зменшення рівня втрат в ступені осьового компресора можна забезпечити шляхом впливу на пограничний шар в кінцевому зазорі робочого колеса.

Numerical Study of Detonation Wave Propagation in the Variable Cross-Section Channel Using Unstructured Computational Grids

The work is dedicated to the numerical study of detonation wave initiation and propagation in the variable cross-section axisymmetric channel filled with the model hydrogen-air mixture. The channel models the large-scale device for the utilization of worn-out tires. Mathematical model is based on two-dimensional axisymmetric Euler equations supplemented by global chemical kinetics model. The finite volume computational algorithm of the second approximation order for the calculation of two-dimensional flows with detonation waves on fully unstructured grids with triangular cells is developed. Three geometrical configurations of the channel are investigated, each with its own degree of the divergence of the conical part of the channel from the point of view of the pressure from the detonation wave on the end wall of the channel. The problem in consideration relates to the problem of waste recycling in the devices based on the detonation combustion of the fuel.