Adaptive Unstructured Grids Research Articles

Programming for the near future: Concepts and pragmatic considerations

This article deals with the concept, architecture, and scientific-organizational problems of creating a new generation of integrated software intended for predictive modeling in engineering, energy, materials science, biology, medicine, economics, nature management, ecology, sociology, etc. Mathematical formulations include interdisciplinary direct and inverse extremely resource-intensive tasks, which are solved using computational methods and technologies of scalable parallelization by hybrid programming on heterogeneous supercomputers with distributed and hierarchical shared memory. The project concept includes the development of an instrumental computational environment that supports all stages of a large-scale machine experiment: geometric and functional modeling, generating of adaptive unstructured grids of various types and orders, approximation of initial equations, solution of emerging algebraic problems, postprocessing of the obtained results, optimization methods for inverse tasks, and machine learning and decision-making on the results of calculations. The effective functionality of the instrumented computing environment is based on high-performance computing and intelligent big data tools. The architecture of the instrumental computational environment provides for automated expansion of the composition of implemented models and applied algorithms, adaptation to the evolution of supercomputer platforms, user-friendly interfaces and active reuse of external software products, and coordinated participation of different groups of developers, which together should provide a long life cycle and demand for the created ecosystem by a wide range of users from different professional fields.

Massively parallel FDTD full-band Monte Carlo simulations of electromagnetic THz pulses in p-doped silicon at cryogenic temperatures

In semiconductor samples with a low density of free charge carriers the current response to an intense electromagnetic pulse is weak and can be treated as a perturbation in the finite-difference-time-domain calculation of the electromagnetic field. Up to first order the electric field that drives the particles does not depend on their density and the particles can be simulated independently. This opens the door for massively parallel Monte Carlo simulations that can be processed efficiently on a computer cluster and a large number of particles can be simulated resulting in a very low noise level. By this full-band Monte Carlo finite-difference-time-domain approach the generation of higher harmonics in p-doped silicon at cryogenic temperatures is investigated. It is found that the higher harmonics are mostly due to the warped valence bands, which are discretized on adaptive unstructured tetrahedral grids in the k-space to avoid numerical artifacts.

A massively parallel accurate conservative level set algorithm for simulating turbulent atomization on adaptive unstructured grids

This article presents a massively parallel and robust strategy to perform the simulation of turbulent incompressible two-phase flows on unstructured grids in complex geometries. This strategy relies on a combination of a narrow-band accurate conservative level set (ACLS)/ghost-fluid framework with isotropic adaptive mesh refinement. This combination enables to accurately capture interface dynamics and topology, and the small physical scales at the liquid-gas interface are resolved at an affordable cost. The ACLS method, even if not strictly mass-conserving, ensures the exact conservation of a smoothed phase indicator, which minimizes the liquid mass conservation errors. In the accurate conservative level set framework, presented first in Desjardins et al. (2008) [25], the interface is defined as the iso-contour of a hyperbolic tangent function, which is advected by the fluid, and then reshaped using a reinitialization equation. Several forms of this reinitialization exist: the original ACLS form proposed by Desjardins et al. involves numerical estimation of the hyperbolic tangent gradient, which is difficult to compute accurately on unstructured meshes. It is thus susceptible to induce artificial deformation of the interface. A new form has been recently proposed in Chiodi and Desjardins (2017) [29], which takes advantage of a mapping onto a classical distance level set while much better preserving the interface shape. Nevertheless, the implementation of this new form on unstructured grids requires special care. In this work, a robust implementation of this new form on unstructured meshes is proposed and implemented in the YALES2 low-Mach flow solver. In order to compute interface normals and curvature, the signed-distance function is reconstructed in parallel at nodes in the narrow band around the interface using a Geometric-Projection Marker Method (GPMM). This method relies on the triangulation of the level set iso-contour and exact geometric projection to the closest surface elements. Spatial convergence, robustness and efficiency of the overall procedure are firstly demonstrated through classical interface transport test cases and two-phase flow examples. Eventually, to emphasize the significant computational gain using adaptive mesh refinement and the ability to compute complex turbulent flows with large density ratios, two Large-Eddy Simulations (LES) of atomizing liquid jets in air are presented, each one at various resolutions. The first one is a low-pressure water jet in quiescent air from a compound nozzle with full computation of the internal injector flow, while the latter is a high-pressure kerosene jet in crossflow. Both simulations are validated against experiments, demonstrating the potential of the method to access a deep numerical insight into jet instabilities and internal flow dynamics with 3D unstructured meshes.

Multiscale finite volume method with adaptive unstructured grids for flow simulation in heterogeneous fractured porous media

Multiscale finite volume method with adaptive unstructured grids for flow simulation in heterogeneous fractured porous media

Consistent scalar transport with front capturing methods: application to two-phase heat transfer

Accurate numerical simulations of heat transfers in 3D liquid-gas flows are of first importance in multiple industrial applications such as droplet evaporation in combustion chambers, spray cooling or propellant behavior in cryogenic tanks. Liquid-gas flows are characterized by the discontinuity of properties (e.g. viscosity, thermal diffusivities, ...) and flow variables (e.g. pressure, energy, chemical composition) across the interface. Robust and accurate algorithms are then necessary to transport the flow variables consistently with the interface. This work presents an algebraic interface capturing method which enables a consistent transport of scalars with the interface. This two-fluid approach ensures conservation of the transported scalars while controlling accurately the flux at the interface. The interface represented by a hyperbolic tangent profile is transported and reinitialized without geometric reconstruction. The scalars are transported separately in each phase and a reinitialization step is performed in order to impose the correct flux at the interface. The method is implemented in the YALES2 low-Mach number flow solver and takes advantage of adaptive unstructured grids to handle complex geometries. It has been assessed on various test cases and compared to analytical solutions.

3D numerical modelling of braided channel formation

A numerical model was used to compute the formation of a braided channel system. The model calculated the water flow field from the fully 3D Navier-Stokes equations on a non-orthogonal unstructured adaptive grid. The sediment transport was computed from the Engelund-Hansen formula. A free surface algorithm based on local pressure gradients was used. The model was applied to an idealized geometry of an initially straight alluvial channel, where the evolution of the braided channel system over time was computed. The complex processes and geometry for this case made it very well suited for testing the numerical model. The purpose of the study was also to explain avulsion processes of a braided river in more detail. Figures are presented with water depth, velocity, water level and secondary currents during an avulsion. The effect of the water level changes and the secondary currents are shown. The geometry, sediment size and water discharge used in the numerical model was identical to a laboratory study. Reasonable agreement was found when comparing the active braiding intensity (BIA) computed by the numerical model with measurements from the flume experiment. Parameter tests include sediment transport formula, grid size, secondary current damping and grid parameters related to wetting/drying. The results using the Engelund-Hansen formula show a higher degree of braiding than the van Rijn or Mayer-Peter Müller formula. The secondary current strength is also shown to be very important for the braiding process and the BIA values.

A high‐order Runge‐Kutta discontinuous Galerkin method with a subcell limiter on adaptive unstructured grids for two‐dimensional compressible inviscid flows

SummaryA robust, adaptive unstructured mesh refinement strategy for high‐order Runge‐Kutta discontinuous Galerkin method is proposed. The present work mainly focuses on accurate capturing of sharp gradient flow features like strong shocks in the simulations of two‐dimensional inviscid compressible flows. A posteriori finite volume subcell limiter is employed in the shock‐affected cells to control numerical spurious oscillations. An efficient cell‐by‐cell adaptive mesh refinement is implemented to increase the resolution of our simulations. This strategy enables to capture strong shocks without much numerical dissipation. A wide range of challenging test cases is considered to demonstrate the efficiency of the present adaptive numerical strategy for solving inviscid compressible flow problems having strong shocks.

A front tracking method for simulation of two-phase interfacial flows on adaptive unstructured meshes for complex geometries

A novel numerical algorithm and modeling framework of a front tracking method based on adaptive anisotropic unstructured meshes for simulating two-phase interfacial flows is presented. In the traditional front tracking methods, a fixed uniform Eulerian Cartesian mesh is used for solving the fluid flow, and adaptive unstructured grid markers are used for tracking the phase-interface front. In the new algorithm, an adaptive anisotropic unstructured mesh is used for solving the fluid flow, as well as for tracking the phase-interface front. Special attentions are focused on developing an algorithm for physical variable interpolation between the two sets of unstructured meshes for both the fluid flow and the front movement. A modeling framework for the described numerical algorithm is implemented on the platform of the commercial CFD package ANSYS Fluent through user-defined functions. The advanced ANSYS Fluent fluid flow solver feature of using adaptive unstructured mesh is integrated with the front tracking method, which can handle complex boundary geometries and has high numerical efficiency. These advanced features are demonstrated through three numerical test examples of simulating a single gas bubble rising freely in a viscous liquid, a buoyancy-driven liquid droplet rising in a periodically constricted capillary tube, and a pressure-driven droplet passing through a small throat hole in a pipe. The accuracy of the simulation results is demonstrated through the comparison with those observed in experiments or obtained using other simulation methods.

Blade shape optimization of an aircraft propeller using space mapping surrogates

Propeller performance greatly influences the overall efficiency of the turboprop engines. The aim of this study is to perform a propeller blade shape optimization for maximum aerodynamic efficiency with a minimal number of high-fidelity model evaluations. A physics-based surrogate approach exploiting space mapping is employed for the design process. A space mapping algorithm is utilized, for the first time in the field of propeller design, to link two of the most common propeller analysis models: the classical blade-element momentum theory to be the coarse model; and the high-fidelity computational fluid dynamics tool as the fine model. The numerical computational fluid dynamics simulations are performed using the finite-volume discretization of the Reynolds-averaged Navier–Stokes equations on an adaptive unstructured grid. The optimum design is obtained after few iterations with only 56 computationally expensive computational fluid dynamics simulations. Furthermore, an optimization method based on design of experiments and kriging response surface is used to validate the results and compare the computational efficiency of the two techniques. The results show that space mapping is more computationally efficient.

Finite volume methods for numerical simulation of the discharge motion described by different physical models

This paper deals with the numerical solution of an ionization wave propagation in air, described by a coupled set of convection-diffusion-reaction equations and a Poisson equation. The standard three-species and more complex eleven-species models with simple chemistry are formulated. The PDEs are solved by a finite volume method that is theoretically second order in space and time on an unstructured adaptive grid. The upwind scheme and the diamond scheme are used for the discretization of the convective and diffusive fluxes, respectively. The Poisson equation is also discretized by the diamond scheme. The results of both models are compared in details for a test case. The influence of physically pertinent boundary conditions at electrodes is also presented. Finally, we deal with numerical accuracy study of implicit scheme in two variants for simplified standard model. It allows us in the future to compute simultaneously and efficiently a process consisting of short time discharge propagation and long-term after-discharge phase or repetitively pulsed discharge.

Image-based modeling of blood flow in cerebral aneurysms treated with intrasaccular flow diverting devices.

Modeling the flow dynamics in cerebral aneurysms after the implantation of intrasaccular devices is important for understanding the relationship between flow conditions created immediately posttreatment and the subsequent outcomes. This information, ideally available a priori based on computational modeling prior to implantation, is valuable to identify which aneurysms will occlude immediately and which aneurysms will likely remain patent and would benefit from a different procedure or device. In this report, a methodology for modeling the hemodynamics in intracranial aneurysms treated with intrasaccular flow diverting devices is described. This approach combines an image-guided, virtual device deployment within patient-specific vascular models with an immersed boundary method on adaptive unstructured grids. A partial mesh refinement strategy that reduces the number of mesh elements near the aneurysm dome where the flow conditions are largely stagnant was compared with the full refinement strategy that refines the mesh everywhere around the device wires. The results indicate that using the partial mesh refinement approach is adequate for analyzing the posttreatment hemodynamics, at a reduced computational cost. The results obtained on a series of four cerebral aneurysms treated with different intrasaccular devices were in good qualitative agreement with angiographic observations. Promising results were obtained relating posttreatment flow conditions and outcomes of treatments with intrasaccular devices, which need to be confirmed on larger series.

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.

Design of adaptive unstructured grids using differential methods

Design of adaptive unstructured grids using differential methods

Comparison of Fixed and Adaptive Unstructured Grid Results for Drag Prediction Workshop 6

Fixed and adapted grid solutions on the NASA Common Research Model (CRM) in wing–body (WB) and wing–body–nacelle–pylon (WBNP) configurations are compared for three Reynolds-averaged Navier–Stokes flow solvers. The flow solvers were run on a sequence of fixed unstructured grids built for the 6th AIAA CFD Drag Prediction Workshop (DPW-6) and compared with solutions generated on solution adaptive grids. The fixed and adaptive mesh generation processes and resulting grids and solutions are presented and discussed. Both approaches achieve asymptotic grid convergence of less than two counts of drag. The fixed grid approach is based on gridding guidelines developed over many years of CFD application experience on similar applications and required an expert user several weeks of effort to develop a grid family conforming to the guidelines. In contrast, the adaptive grid approach is automatic, relying on an estimate of solution discretization error to guide grid construction. The adaptive grids were generated with less than 2 days of user interaction, requiring very few user decisions and almost no expert knowledge.

A GPU accelerated level set reinitialization for an adaptive discontinuous Galerkin method

GPU accelerated high order reconstruction of signed distance function of the level set method is studied. The flow based reinitialization equation is discretized in space by using a nodal discontinuous Galerkin method on adaptive unstructured grids. Artificial diffusion with a modal decay rate based regularity estimator is used to damp out high frequency solution components near kinks, where mesh adaptivity is applied. A two rate Adams-Bashforth time integrator is developed to avoid time step restrictions resulting from artificial diffusion stabilization and local mesh refinement. Platform independence of the solver is achieved by using an extensible multi-threading programming API that allows runtime selection of different computing devices (GPU and CPU) and threading interfaces (CUDA, OpenCL and OpenMP). Overall, a highly scalable numerical scheme that preserves the simplicity of the original level set method is obtained. Performance and accuracy of the method to construct signed distance function on highly disturbed initial data with smooth and non-smooth interfaces are tested through distinct two- and three-dimensional problems.

Three-dimensional multi-relaxation-time lattice Boltzmann front-tracking method for two-phase flow**Project supported by the National Natural Science Foundation of China (Grant No. 11572062), the Fundamental Research Funds for the Central Universities, China (Grant No. CDJZR13248801), the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT13043), and Key Laboratory of Functional Crystals and Laser Technology, TIPC, Chinese Academy

We developed a three-dimensional multi-relaxation-time lattice Boltzmann method for incompressible and immiscible two-phase flow by coupling with a front-tracking technique. The flow field was simulated by using an Eulerian grid, an adaptive unstructured triangular Lagrangian grid was applied to track explicitly the motion of the two-fluid interface, and an indicator function was introduced to update accurately the fluid properties. The surface tension was computed directly on a triangular Lagrangian grid, and then the surface tension was distributed to the background Eulerian grid. Three benchmarks of two-phase flow, including the Laplace law for a stationary drop, the oscillation of a three-dimensional ellipsoidal drop, and the drop deformation in a shear flow, were simulated to validate the present model.

Influence research of profile chords ratio on aerodynamic characteristics of tandem compressor cascade

Efficiency improvement of gas turbine compressors is ensured by the extensive use of tandem blade rows in straightener blades of the last stages of multistage axial compressors. Their installation provides large flow deflection angles in the unstalled flow of blade rows and, consequently, a low level of losses in the design mode of the compressor. The problem of influence research of the first- and second-row blade chords ratio in tandem blade rows in a wide range of angles of attack is relevant and is of practical interest in developing recommendations for ensuring the gas-dynamic stability of gas turbine compressors. To solve the problem, the method of the computational experiment was used and characteristics of tandem compressor cascade with different first- and second-row blade chords ratios were calculated in the paper. The calculation results of the characteristics of tandem cascade were compared with the characteristics of an equivalent single compressor cascade. For the computational domain of the studied tandem and equivalent single cascades, small adaptive unstructured grid and the second-order design scheme with the local use of the first-order design scheme (High resolution) was applied. The Menter's SST model was used to solve the problems. The results showed that the aerodynamic characteristics of the tandem compressor cascades essentially depend on the first- and second-row blade chords ratio. With positive angles of attack, the quality parameter of tandem cascades is higher than that of single, with the first- and second-row blade chords ratio, corresponding to the position of the slot x щ =(0,3 ... 0,4)b ∑ . With negative angles of attack, the quality parameter of tandem cascades is higher than that of single, with the first- and second-row blade chords ratio, corresponding to the position of the slot x щ =(0,5 ... 0,7)b ∑ .

Unstructured Adaptive Grid Refinement for Flow Feature Capture

An unstructured grid adaptation technology has been developed for capturing flow features effectively. The face-based hierarchical data structure is used at grid refinement procedure. The difference of suitable flow properties between cell and its neighbors for flow features detection. The results of different simulation cases show the strengths of unstructured grid adaptation technology. The flow features such as shock wave and vortex are resolved better with grids refinement. The grid adaptation also improves the computational accuracy of aerodynamic characteristics and loads.

A Full 3-D Dynamically Adaptive Unstructured Grid Finite-Volume Approach to Simulate Multiple Branching in Streamer Propagation

Electron-spot-induced multiple branching and trajectory deviation of streamer microdischarges in air was simulated using a 3-D unstructured adaptive mesh finite-volume approach along with the air plasma streamer model proposed by Morrow et al. Images illustrating the effect of electron spots on the propagation trajectory, i.e., deviation, simple branching, multiple branching, are presented and commented.

A geometry-based adaptive unstructured grid generation algorithm for complex geological media

In this paper a novel unstructured grid generation algorithm is presented that considers the effect of geological features and well locations in grid resolution. The proposed grid generation algorithm presents a strategy for definition and construction of an initial grid based on the geological model, geometry adaptation of geological features, and grid resolution control. The algorithm is applied to seismotectonic map of the Masjed-i-Soleiman reservoir. Comparison of grid results with the “Triangle” program shows a more suitable permeability contrast. Immiscible two-phase flow solutions are presented for a fractured porous media test case using different grid resolutions. Adapted grid on the fracture geometry gave identical results with that of a fine grid. The adapted grid employed 88.2% less CPU time when compared to the solutions obtained by the fine grid.