Unstructured Tetrahedral Meshes Research Articles

Validation of two RANS solvers with flow data of the flat roof Michelstadt case

To further increase the confidence in the results of numerical simulations of flow and dispersion phenomena in urban environments thorough verification and validation of the numerical models is required. Wind tunnel measurements of an idealized Central-European city, Michelstadt, which are publicly available in the CEDVAL-LES database were used here to validate the open source code OpenFOAM® 1.7 and the commercial code Ansys® Fluent 13. The results of the flow field computations were compared graphically and with the metric hit rate to the experimental data. Unstructured tetrahedral and polyhedral meshes were used with different resolutions to investigate the advantages and shortcomings of the polyhedral meshing. With both codes and mesh types the qualitative agreement between numerical simulation and experiment is good for the mean velocities, with a minimum hit rate of 0.64 for the coarse polyhedral mesh. The Reynolds stresses on the other hand are consistently under-predicted with both codes on all meshes. Dispersion simulations were also investigated with one of the meshes. Validation of the two codes with this realistic urban geometry shows the capabilities and shortcomings of RANS CFD modelling for regulatory purposes in urban air quality modelling.

Effect of Fuel Particle Size on the Stability of Swirl Stabilized Flame in a Gas Turbine Combustor

AbstractCombustion stability is examined in a swirl stabilized aero gas turbine combustor using computational fluid dynamics. A 22.5° sector of an annular combustor is modeled for the study. Unstructured tetrahedral meshes comprising 1.2 × 10

Multiphase Flow of Immiscible Fluids on Unstructured Moving Meshes

In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization operations improve element quality and avoid element inversion. In the context of multiphase flow, we guarantee that every element is occupied by a single fluid and, consequently, the interface between fluids is represented by a set of faces in the simplicial complex. This approach ensures that the underlying discretization matches the physics and avoids the additional book-keeping required in grid-based methods where multiple fluids may occupy the same cell. Our Lagrangian approach naturally leads us to adopt a finite element approach to simulation, in contrast to the finite volume approaches adopted by a majority of fluid simulation techniques that use tetrahedral meshes. We characterize fluid simulation as an optimization problem allowing for full coupling of the pressure and velocity fields and the incorporation of a second-order surface energy. We introduce a preconditioner based on the diagonal Schur complement and solve our optimization on the GPU. We provide the results of parameter studies as well as a performance analysis of our method, together with suggestions for performance optimization.

Simulation analysis of airflow alteration in the trachea following the vascular ring surgery based on CT images using the computational fluid dynamics method

This study presents a computational fluid dynamics (CFD) model to simulate the three-dimensional airflow in the trachea before and after the vascular ring surgery (VRS). The simulation was based on CT-scan images of the patients with the vascular ring diseases. The surface geometry of the tracheal airway was reconstructed using triangular mesh by the Amira software package. The unstructured tetrahedral volume meshes were generated by the ANSYS ICEM CFD software package. The airflow in the tracheal airway was solved by the ESI CFD-ACE+ software package. Numerical simulation shows that the pressure drops across the tracheal stenosis before and after the surgery were 0.1789 and 0.0967 Pa, respectively, with the inspiratory inlet velocity 0.1 m/s. Meanwhile, the improvement percentage by the surgery was 45.95%. In the expiratory phase, by contrast, the improvement percentage was 40.65%. When the inspiratory velocity reached 1 m/s, the pressure drop became 4.988~Pa and the improvement percentage was 43.32%. Simulation results further show that after treatment the pressure drop in the tracheal airway was significantly decreased, especially for low inspiratory and expiratory velocities. The CFD method can be applied to quantify the airway pressure alteration and to evaluate the treatment outcome of the vascular ring surgery under different respiratory velocities.

A parallel non-conforming multi-element DGTD method for the simulation of electromagnetic wave interaction with metallic nanoparticles

The present work is about the development of a parallel non-conforming multi-element discontinuous Galerkin time-domain (DGTD) method for the simulation of the scattering of electromagnetic waves by metallic nanoparticles. Such nanoparticles most often have curvilinear shapes, therefore we propose a numerical modeling strategy which combines the use of an unstructured tetrahedral mesh for the discretization of the scattering structures with a structured (uniform cartesian) mesh for treating efficiently the rest of the domain. The overall goal is to increase the flexibility in the meshing process while decreasing the needs in computational resources for the target applications. The latter are here modeled by the system of 3D time-domain Maxwell equations coupled to a Drude dispersion model for taking into account the material properties of nanoparticles at optical frequencies. We propose an auxiliary differential equation (ADE) based DGTD method for solving the resulting system and present numerical results demonstrating the benefits of using non-conforming multi-element meshes in this particular application context.

An interface capturing method with a continuous function: The THINC method on unstructured triangular and tetrahedral meshes

A novel interface-capturing method is proposed to compute moving interfaces on unstructured grids with triangular (2D) and tetrahedral (3D) elements. Different from the conventional VOF (volume of fluid) method which involves geometric reconstructions of the interface, the present method is based on the algebraic reconstruction approach originally developed in the THINC (tangent of hyperbola interface capturing) scheme by Xiao et al. (2005) [17]. A continuous multidimensional hyperbolic tangent function is employed for retrieving the jump-like distribution of the indicator function, which avoids the explicit geometric representation of the interface and thus substantially reduces the algorithmic complexity in unstructured grids. Numerical diffusion and smearing are effectively eliminated, and the compact thickness of the jump transition layer in the volume fraction is retained throughout the computation even for largely deformed interface. The solution quality of the present scheme is comparable to the VOF method with PLIC (piecewise linear interface calculation) algorithm.

Accelerating the discontinuous Galerkin method for seismic wave propagation simulations using multiple GPUs with CUDA and MPI

We have successfully ported an arbitrary high-order discontinuous Galerkin method for solving the three-dimensional isotropic elastic wave equation on unstructured tetrahedral meshes to multiple Graphic Processing Units (GPUs) using the Compute Unified Device Architecture (CUDA) of NVIDIA and Message Passing Interface (MPI) and obtained a speedup factor of about 28.3 for the single-precision version of our codes and a speedup factor of about 14.9 for the double-precision version. The GPU used in the comparisons is NVIDIA Tesla C2070 Fermi, and the CPU used is Intel Xeon W5660. To effectively overlap inter-process communication with computation, we separate the elements on each subdomain into inner and outer elements and complete the computation on outer elements and fill the MPI buffer first. While the MPI messages travel across the network, the GPU performs computation on inner elements, and all other calculations that do not use information of outer elements from neighboring subdomains. A significant portion of the speedup also comes from a customized matrix–matrix multiplication kernel, which is used extensively throughout our program. Preliminary performance analysis on our parallel GPU codes shows favorable strong and weak scalabilities.

High-order accurate fluid–structure simulation of a tuning fork

The aeroacoustics of a tuning fork are investigated using a high-order fluid–structure interaction (FSI) scheme. The compressible Navier–Stokes equations are discretized using a discontinuous Galerkin arbitrary Lagrangian–Eulerian (DG-ALE) method on an unstructured tetrahedral mesh, and coupled to a non-linear hyperelastic neo-Hookean model of a tuning fork, discretized using continuous Galerkin finite elements on an unstructured tetrahedral mesh. The fluid and structure are both integrated implicitly in time using a partitioned approach based on an implicit–explicit Runge–Kutta method. We measure radial sound distributions which show good agreement with theoretical predictions and physical experiments in the open literature. In addition we demonstrate how to measure Q factors for several common modes, emphasizing that we can accurately capture the decay rates arising purely from the interaction of the tuning fork with the air and without any damping built into the structure model.

Parallel preconditioners for the unsteady Navier–Stokes equations and applications to hemodynamics simulations

We are interested in the numerical solution of the unsteady Navier–Stokes equations on large scale parallel architectures. We consider efficient preconditioners, such as the Pressure Convection-Diffusion (PCD), the Yosida preconditioner, the SIMPLE preconditioner, and the algebraic additive Schwarz preconditioner, for the linear systems arising from finite element discretizations using tetrahedral unstructured meshes and time advancing finite difference schemes. To achieve parallel efficiency, we introduce approximate versions of these preconditioners, based on their factorizations where each factor can be either inverted exactly or using an add-hoc preconditioner. We investigate their strong scalability for both classical benchmark problems and simulations relevant to hemodynamics, using up to 8192 cores.

Sensitivity of the Numerical Prediction of Turbulent Combustion Dynamics in the LIMOUSINE Combustor

The objective of this study is to investigate the sensitivity and accuracy of the reaction flow-field prediction for the LIMOUSINE combustor with regard to choices in computational mesh and turbulent combustion model. The LIMOUSINE combustor is a partially premixed, bluff body-stabilized natural gas combustor designed to operate at 40–80 kW and atmospheric pressure and used to study combustion instabilities. The transient simulation of a turbulent combusting flow with the purpose to study thermoacoustic instabilities is a very time-consuming process. For that reason, the meshing approach leading to accurate numerical prediction, known sensitivity, and minimized amount of mesh elements is important. Since the numerical dissipation (and dispersion) is highly dependent on, and affected by, the geometrical mesh quality, it is of high importance to control the mesh distribution and element size across the computational domain. Typically, the structural mesh topology allows using much fewer grid elements compared to the unstructured grid; however, an unstructured mesh is favorable for flows in complex geometries. To explore computational stability and accuracy, the numerical dissipation of the cold flow with mixing of fuel and air is studied first in the absence of the combustion process. Thereafter, the studies are extended to combustible flows using standard available ansys-cfx combustion models. To validate the predicted variable fields of the combustor's transient reactive flows, the numerical results for dynamic pressure and temperature variations, resolved under structured and unstructured mesh conditions, are compared with experimental data. The obtained results show minor dependence on the used mesh in the velocity and pressure profiles of the investigated grids under nonreacting conditions. More significant differences are observed in the mixing behavior of air and fuel flows. Here, the numerical dissipation of the (unstructured) tetrahedral mesh topology is higher than in the case of the (structured) hexahedral mesh. For that reason, the combusting flow, resolved with the use of the hexahedral mesh, presents better agreement with experimental data and demands less computational effort. Finally, in the paper, the performance of the combustion model for reacting flow is presented and the main issues of the applied combustion modeling are reviewed.

Grid-characteristic method using high-order interpolation on tetrahedral hierarchical meshes with a multiple time step

The purpose of the present paper is to develop a grid-characteristic method for high-performance computer systems using unstructured tetrahedral hierarchical meshes, a multiple time step and the high-order interpolation for simulating complex spatial dynamic processes in heterogeneous environments. This method has the precise formulation of contact conditions and is suitable for the physically correct solution of seismology and seismic prospecting problems in complex heterogeneous environments. The use of the hierarchical meshes allows us to take into account a large number of nonhomogeneous inclusions (cracks, cavities, etc.). The use of this grid-characteristic method makes it possible to use a multiple time step and thereby increase productivity and significantly reduce the computation time. The methods developed for high-order interpolation on unstructured tetrahedral meshes can solve the problems of seismology and seismic prospecting with approximation in space of up to the fifth degree (inclusive).

Direct volume rendering of unstructured tetrahedral meshes using CUDA and OpenMP

Direct volume visualization is an important method in many areas, including computational fluid dynamics and medicine. Achieving interactive rates for direct volume rendering of large unstructured volumetric grids is a challenging problem, but parallelizing direct volume rendering algorithms can help achieve this goal. Using Compute Unified Device Architecture (CUDA), we propose a GPU-based volume rendering algorithm that itself is based on a cell projection-based ray-casting algorithm designed for CPU implementations. We also propose a multicore parallelized version of the cell-projection algorithm using OpenMP. In both algorithms, we favor image quality over rendering speed. Our algorithm has a low memory footprint, allowing us to render large datasets. Our algorithm supports progressive rendering. We compared the GPU implementation with the serial and multicore implementations. We observed significant speed-ups that, together with progressive rendering, enables reaching interactive rates for large datasets.

Automatic mesh generation and transformation for topology optimization methods

This paper presents automatic tools aimed at the generation and adaptation of unstructured tetrahedral meshes in the context of composite or heterogeneous geometry. These tools are primarily intended for applications in the domain of topology optimization methods but the approach introduced presents great potential in a wider context. Indeed, various fields of application can be foreseen for which meshing heterogeneous geometry is required, such as finite element simulations (in the case of heterogeneous materials and assemblies, for example), animation and visualization (medical imaging, for example). Using B-Rep concepts as well as specific adaptations of advancing front mesh generation algorithms, the mesh generation approach presented guarantees, in a simple and natural way, mesh continuity and conformity across interior boundaries when trying to mesh a composite domain. When applied in the context of topology optimization methods, this approach guarantees that design and non-design sub-domains are meshed so that finite elements are tagged as design and non-design elements and so that continuity and conformity are guaranteed at the interface between design and non-design sub-domains. The paper also presents how mesh transformation and mesh smoothing tools can be successfully used when trying to derive a functional shape from raw topology optimization results.

Efficient implementation of high order unstructured WENO schemes for cavitating flows

In this article we present a new efficient implementation of high order accurate Godunov-type WENO finite volume schemes on unstructured triangular and tetrahedral meshes for the simulation of real fluids with complex equations of state. The main focus of this paper is the efficient computation of flows in compressible mixtures of liquid and vapor in multiple space-dimensions, including the onset of cavitation. In the present article we use the full equation of state (EOS) for water, vapor and wet steam in thermal equilibrium based on the industrial and scientific standard IAPWS-IF97, as well as the real equation of state for n-heptane provided by Span and Wagner. Since the direct evaluation of these very complex EOS is computationally very expensive, we propose a new robust, accurate and particularly efficient approach for their evaluation in high order Godunov type finite volume schemes. It is based on the L2 projection of the EOS (ρ, e)→(p, T) onto the space of piecewise polynomials of degree q using an adaptive mesh refinement (AMR) approach together with Cartesian cut-cells, which adjusts the grid of the phase space (ρ, e) so that the L∞ error of the L2-projection of the EOS is less than a given error threshold ∊. For a thorough validation of our numerical approach we construct several quasi-exact solutions to the Riemann problem for water and n-heptane using the corresponding detailed equations of state. We furthermore present numerical convergence results of third and fourth order schemes for an unsteady two-dimensional test problem for water with real EOS. We furthermore show the onset of cavitation on a simple model problem with an initially purely liquid fluid at ambient conditions at rest using a strong heat source term in the energy equation as well as the development of a cavitation bubble due to strong rarefaction. Finally, some numerical test problems are solved with the new approach on unstructured triangular and tetrahedral meshes in multiple space dimensions.

Unstructured finite element method for the solution of the Boussinesq problem in three dimensions

SUMMARYWe present a numerical method for the monolithic discretisation of the Boussinesq system in three spatial dimensions. The key ingredients of the proposed methodology are the finite element discretisation of the spatial part of the problem using unstructured tetrahedral meshes, an implicit time integrator, based on adaptive predictor–corrector scheme (the explicit second‐order Adams–Bashforth method with the implicit stabilised trapezoid rule), and a new preconditioned Krylov subspace solver for the resulting linearised discrete problem. We test the proposed methodology on a number of physically relevant cases, including laterally heated cavities and the Rayleigh–Bénard convection. Copyright © 2013 John Wiley & Sons, Ltd.

A primal/dual representation for discrete Morse complexes on tetrahedral meshes

AbstractWe consider the problem of computing discrete Morse and Morse‐Smale complexes on an unstructured tetrahedral mesh discretizing the domain of a 3D scalar field. We use a duality argument to define the cells of the descending Morse complex in terms of the supplied (primal) tetrahedral mesh and those of the ascending complex in terms of its dual mesh. The Morse‐Smale complex is then described combinatorially as collections of cells from the intersection of the primal and dual meshes. We introduce a simple compact encoding for discrete vector fields attached to the mesh tetrahedra that is suitable for combination with any topological data structure encoding just the vertices and tetrahedra of the mesh. We demonstrate the effectiveness and scalability of our approach over large unstructured tetrahedral meshes by developing algorithms for computing the discrete gradient field and for extracting the cells of the Morse and Morse‐Smale complexes. We compare implementations of our approach on an adjacency‐based topological data structure and on the PR‐star octree, a compact spatio‐topological data structure.

Modeling of current characteristics of segmented Langmuir probe on DEMETER

We model the current characteristics of the DEMETER Segmented Langmuir probe (SLP). The probe is used to measure electron density and temperature in the ionosphere at an altitude of approximately 700 km. It is also used to measure the plasma flow velocity in the satellite frame of reference. The probe is partitioned into seven collectors: six electrically insulated spherical segments and a guard electrode (the rest of the sphere and the small post). Comparisons are made between the predictions of the model and DEMETER measurements for actual ionospheric plasma conditions encountered along the satellite orbit. Segment characteristics are computed numerically with PTetra, a three-dimensional particle in cell simulation code. In PTetra, space is discretized with an unstructured tetrahedral mesh, thus, enabling a good representation of the probe geometry. The model also accounts for several physical effects of importance in the interaction of spacecraft with the space environment. These include satellite charging, photoelectron, and secondary electron emissions. The model is electrostatic, but it accounts for the presence of a uniform background magnetic field. PTetra simulation results show different characteristics for the different probe segments. The current collected by each segment depends on its orientation with respect to the ram direction, the plasma composition, the magnitude, and the orientation of the magnetic field. It is observed that the presence of light H+ ions leads to a significant increase in the ion current branch of the I-V curves of the negatively polarized SLP. The effect of the magnetic field is demonstrated by varying its magnitude and direction with respect to the reference magnetic field. It is found that the magnetic field appreciably affects the electron current branch of the I-V curves of certain segments on the SLP, whereas the ion current branch remains almost unaffected. PTetra simulations are validated by comparing the computed characteristics and their angular anisotropy with the DEMETER measurements, as simulation results are found to be in good agreement with the measurements.

Evaluation of known-boundary and resistivity constraints for improving cross-borehole DC electrical resistivity imaging of discrete fractures

There is a need to better characterize discrete fractures in contaminated hard rock aquifers to determine the fate of remediation injections away from boreholes and also to evaluate hydraulic fracturing performance. A synthetic cross-borehole electrical resistivity study was conducted assuming a discrete fracture model of an existing contaminated site with known fracture locations. Four boreholes and two discrete fracture zones, assumed to be the dominant electrical and hydraulically conductive pathways, were explicitly modeled within an unstructured tetrahedral mesh. We first evaluated different regularization constraints starting with an uninformed smoothness-constrained inversion, to which a priori information was incrementally added. We found major improvements when (1) smoothness regularization constraints were relaxed (or disconnected) along boreholes and fractures, (2) a homogeneous conductivity was assumed along boreholes, and (3) borehole conductivity constraints that could be determined from a specific conductance log were applied. We also evaluated the effect of including borehole packers on fracture zone model recovery. We found that the fracture zone conductivities with the inclusion of packers were comparable to similar trials excluding the use of packers regardless of electrical potential changes. The misplacement of fracture regularization disconnects (FRDs) can easily be misinterpreted as actual fracture locations. Conductivities within these misplaced disconnects were near the starting model value, and removing smoothing between boreholes and assumed fracture locations helped in identifying incorrectly located FRDs. We found that structural constraints used after careful evaluation of a priori information are critical to improve imaging of fracture electrical conductivities, locations, and orientations.

Sensitivity field distributions for segmental bioelectrical impedance analysis based on real human anatomy

In this work, an adaptive unstructured tetrahedral mesh generation technology is applied for simulation of segmental bioimpedance measurements using high-resolution whole-body model of the Visible Human Project man. Sensitivity field distributions for a conventional tetrapolar, as well as eight- and ten-electrode measurement configurations are obtained. Based on the ten-electrode configuration, we suggest an algorithm for monitoring changes in the upper lung area.

A study of the flow field characteristics around star-shaped artificial reefs

In this paper, a three-dimensional numerical model is devised to calculate the unsteady flow field around star-shaped artificial reefs. The model is based on Reynolds-averaged Navier–Stokes (RANS) equations embedded within a renormalization group (RNG) k–ε turbulence model. The RANS equations are solved using the finite volume method (FVM) with an unstructured tetrahedral mesh. The pressure and velocity coupling is solved at each time step with the SIMPLEC algorithm. Non-invasive particle image velocimetry (PIV) laboratory measurements are employed to verify the simulation results. Good agreement is found between the simulation and experimental results with respect to the major flow fields. Based on the flow-field verification, the influence of arrangement and spacing on the flow field of one and two artificial reefs are discussed in light of the numerical method. A large-scale slow flow region is obtained when the reef is arranged in the second form. In the parallel combination, a slight mutual effect exists between the two reefs when the spacing is larger than 3.0L. In the streamwise combination, the interaction of two reefs is at its strongest at spacings of 3.0L to 4.0L.