Hybrid Unstructured Meshes Research Articles

Flow Characteristic Study on Wake Flow of High-speed vehicles

Based on the general CFD software NNW-FlowStar of national numerical wind tunnel engineering, this paper adopts anisotropic unstructured hybrid mesh to simulate the wake field characteristics of aircraft in high-speed flight. NNW-FlowStar software in high resolution numerical format, gaussian type node gradient calculation method, massively parallel and a series of numerical algorithm in terms of development and improvement to ensure the fine simulation of the hypersonic flow field. The numerical method can clearly aircraft wake flow field, the main shock, the corner expansion area, shear layer and the shock wave, clearly shows the wake flow field structure. With the increase of Mach number, the wake flow is getting more and more strong, the backwater area range is more and more small, after the stagnation point, the shock wave is also much greater compressibility.

Decay Dose Shielding Analysis with Hybrid Unstructured Mesh/Constructive Solid Geometry Monte Carlo Calculation and ADVANTG Acceleration

The target segments of the Oak Ridge National Laboratory Second Target Station (STS) neutron production facility become highly activated due to spallation reactions or nuclei transmutation by primary protons and emitted neutrons. Once the target segments are removed from their location within the core vessel, decay dose rates must be accurately quantified to determine the shielding configurations of remote-handling tools and transport casks and to aid in planning maintenance activities. For this analysis, we utilized a hybrid unstructured mesh (UM)/constructive solid geometry approach for calculating spallation products and neutron fluxes, activation calculations using the AARE package that includes the CINDER2008 activation code to calculate the decay photon source at different cooling times, and the ADVANTG code to accelerate the final decay photon transport calculation. Both Type 316 stainless steel (SS-316) and lead were investigated as candidates for shielding materials. The decay photon transport calculation through the thick SS-316 or lead shields exhibited between 25 and 30 orders-of-magnitude attenuations in the radial direction, depending on the shield. Such a difficult shielding calculation required advanced variance reduction. ADVANTG has some missing features, which limits its usability in spallation neutron source applications. It does not support volumetric sources created for MCNP6.2 UM capability. An approximate source was created for this problem. Not only was this approximate source needed for running the ADVANTG calculation to generate the weight windows, but also it was essential to develop source biasing (SB) parameters that were crucial for dramatically accelerating the decay photon transport in this problem. With this approximate source, the analysis was completed in a very reasonable computational time, and the design of the STS remote-handling equipment was finalized. This paper compares the efficiency of Monte Carlo simulations with different weight window and SB parameters calculated using different approximate ADVANTG calculations.

Development of a Two-Dimensional Hybrid Sediment-Transport Model

This paper presents the development of a two-dimensional hydrodynamic sediment transport model using the finite volume method based on a collocated unstructured hybrid-mesh system consisting of triangular and quadrilateral cells. The model is a single-phase nonequilibrium sediment-transport model for nonuniform and noncohesive sediments in unsteady turbulent flows that considers multiple sediment-transport processes such as deposition, erosion, transport, and bed sorting. This model features a hybrid unstructured mesh system for easy mesh generation in complex domains. To avoid interpolation from vertices in conventional unstructured models, this model adopted a second-order accurate edge-gradient evaluation method to consider the mesh irregularities based on Taylor’s series expansion. In addition, the multipoint momentum interpolation corrections were integrated to avoid possible nonphysical oscillations during the wetting-and-drying process, common in unsteady sediment transport problems, to ensure both numerical stability and numerical accuracy. The developed sediment transport model was validated by a benchmark degradation case for the erosion process with armoring effects, a benchmark aggradation case for the deposition process, and a naturally meandering river for long-term unsteady sediment-transport processes. Finally, the model was successfully applied to simulate sediment transport in a reservoir that was significantly affected by typhoon events.

Efficient Lagrangian particle tracking algorithms for distributed-memory architectures

This paper focuses on the solution of the dispersed phase of Eulerian–Lagrangian one-way coupled particle laden flows. An efficient two-constraint domain partitioning for 2D and 3D unstructured hybrid meshes is proposed and implemented in distributed memory architectures. A preliminary simulation, using a set of representative particles, is performed first to suitably tag the cells with a weight proportional to the probability of being crossed by a particle. In addition, an innovative parallel ray-tracing location algorithm is presented. A global identifier is assigned to each particle resulting in a significant reduction of the overall communication among processes.The proposed approaches are verified against two steady reference cases for ice accretion simulation: a NACA 0012 profile and a NACA 64A008 swept horizontal tail. Furthermore, a cloud droplet impact test case starting from an unsteady flow around a 3D cylinder is performed to evaluate the code performances on unsteady problems.

Three-dimensional third-order gas-kinetic scheme on hybrid unstructured meshes for Euler and Navier–Stokes equations

In this paper, a third-order gas-kinetic scheme is developed on the three-dimensional hybrid unstructured meshes for the compressible inviscid and viscous flows. In the classical weighted essentially non-oscillatory (WENO) scheme, the high-order spatial accuracy is achieved by the non-linear combination of lower order polynomials. However, for the hybrid unstructured meshes, the procedures, including the selection of candidate stencils and calculation of linear weights, become extremely complicated, especially for three-dimensional problems. To overcome the drawbacks, a third-order WENO reconstruction is developed on the hybrid unstructured meshes, including tetrahedron, pyramid, prism and hexahedron. A general strategy is given for the selection of big stencil and sub-stencils for hybrid meshes, and the topologically independent linear weights are used in the spatial reconstruction. A unified interpolation is also used for the volume integral of different types of control volumes, as well as the flux integration over different cell interfaces. Incorporate with the two-stage fourth-order temporal discretization, the explicit high-order gas-kinetic schemes are developed for unsteady problems. With the lower–upper symmetric Gauss–Seidel (LU-SGS) methods and Jacobi iteration, the implicit high-order gas-kinetic schemes are developed for steady problems. To accelerate the computation, both explicit and implicit scheme is implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). Especially, for implicit parallel computation, Jacobi iteration is used. The speedup of GPU code suggests the potential of high-order gas-kinetic schemes for the large scale computation. A variety of numerical examples, from the subsonic to supersonic flows, are presented to validate the accuracy and robustness for both inviscid and viscous flows.

Hybrid unstructured mesh geometry model of the next-generation spallation neutron source at LANSCE

We have developed a hybrid Unstructured Mesh (UM)/Constructive Solid Geometry (CSG) model of the next-generation spallation neutron target-moderator-reflector-shield (TMRS) assembly Mark-IV at the Los Alamos Neutron Science Center (LANSCE) to perform MCNP neutronics calculations in support of the engineering design process. The hybrid model consists of an essential component of the new TMRS—the upper target—built as UM and the rest of the model that resembles the original TMRS Mark-III built as CSG. The UM model for the neutronics analysis as well as the model for the subsequent engineering analyses such as structural stress and fluid dynamics are automatically converted from the identical computer aided design (CAD) model. Such an automatic conversion is highly time-efficient and preserves a great level of detail of the original model. In addition, only a relatively small UM portion of our model (0.003 m3) is embedded into the surrounding CSG universe (314 m3), enabling a more efficient MCNP calculation due to the reduced requirements on computer memory and shorter computation time in comparison with a fully extended UM model. Our MCNP calculations focus on the neutronics performance and energy deposition in the upper target. They employ high-energy nuclear physics models, tabular data, and scattering kernels, use an 800 MeV proton beam as a source, tally secondary fast and thermal neutrons with point detectors, and apply mesh tallies and elemental edit outputs to score energy deposition from all particles, i.e., neutrons, photons, protons, and charged pions. Because the use of UM marks a major departure from our original method based entirely on the traditional CSG modeling with MCNPX 2.7.0, we validate the new hybrid UM/CSG model against the legacy CSG model. We found a good agreement between the two models, which demonstrates that MCNP6.2 with UM/CSG hybrids can solve complex neutronics problems at large accelerator facilities, including spallation neutron sources.

A new unstructured hybrid mesh generation method based on BP-ANN

The automation and intelligence of grid generation are still bottleneck problems in computational fluid dynamics. This problem can be solved by generating anisotropic quadrilateral by advancing layer method and isotropic triangular mesh by advancing front method. However, the advancing layer method needs to calculate the advancing direction, step size, a correction factor of the concave and convex area, so the automation level and efficiency of grid generation need to be improved. To solve the above problems, a hybrid grid generation method based on BP-ANN is proposed. The grid data generated by traditional methods are learned by a neural network, and the neural network can predict the above key parameters. Finally, a mesh generation example of 30P30N multi-element airfoil shows that the proposed algorithm can effectively improve the adaptability, efficiency and quality of hybrid mesh generation.

A p-multigrid compact gas-kinetic scheme for steady-state acceleration

In this paper, the high-order compact gas-kinetic scheme (CGKS) on three-dimensional hybrid unstructured mesh is further developed with the p-multigrid technique for steady-state solution acceleration. The p-multigrid strategy is a two-level algorithm. On the high-order level, the CGKS with high-order compact initial reconstruction is used to evolve both cell-averaged conservative flow variables and their gradients at the beginning of next time step. On the low-order level, starting from the high-order level solution the cell-averaged conservative flow variables is evolved by a first-order scheme, where implicit backward Euler smoother is adopted for accelerating the convergence of steady-state solution. The final iterative updating scheme becomes numerically simple and computationally efficient. The effectiveness of the p-multigrid method is validated in both subsonic and supersonic flow simulations in two- and three-dimensional space with hybrid unstructured mesh. One order of magnitude speedup in the convergence rate has been achieved by the approach in comparison with the explicit counterpart.

An efficient edge based data structure for the compressible Reynolds‐averaged Navier–Stokes equations on hybrid unstructured meshes

AbstractAn efficient edge based data structure has been developed in order to implement an unstructured vertex based finite volume algorithm for the Reynolds‐averaged Navier–Stokes equations on hybrid meshes. In the present approach, the data structure is tailored to meet the requirements of the vertex based algorithm by considering data access patterns and cache efficiency. The required data are packed and allocated in a way that they are close to each other in the physical memory. Therefore, the proposed data structure increases cache performance and improves computation time. As a result, the explicit flow solver indicates a significant speed up compared to other open‐source solvers in terms of CPU time. A fully implicit version has also been implemented based on the PETSc library in order to improve the robustness of the algorithm. The resulting algebraic equations due to the compressible Navier–Stokes and the one equation Spalart–Allmaras turbulence equations are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the FGMRES Krylov subspace algorithm. In order to further improve the computational accuracy, the multiscale metric based anisotropic mesh refinement library PyAMG is used for mesh adaptation. The numerical algorithm is validated for the classical benchmark problems such as the transonic turbulent flow around a supercritical RAE2822 airfoil and DLR‐F6 wing‐body‐nacelle‐pylon configuration. The efficiency of the data structure is demonstrated by achieving up to an order of magnitude speed up in CPU times.

High-order gas-kinetic scheme on three-dimensional unstructured meshes for compressible flows

In this paper, a high-order gas-kinetic scheme is developed on three-dimensional unstructured meshes for compressible Euler and Navier–Stokes equations. To achieve the high-order spatial accuracy, the three-dimensional weighted essentially non-oscillatory (WENO) reconstruction is extended to the unstructured tetrahedral and hexahedral meshes. A simple strategy is adopted for the selection of candidate stencils, and the topologically independent linear weights are used for the spatial reconstruction. The efficiency and robustness of the classical WENO reconstruction are improved. In addition to the two-stage fourth-order temporal discretization and lower–upper symmetric Gauss–Seidel method, the explicit and implicit high-order gas-kinetic schemes are developed for unsteady and steady problems. Accuracy tests on hexahedral and tetrahedral grids validate the third-order of accuracy, and various three-dimensional incompressible and compressible numerical experiments are also presented. The results validate the accuracy and robustness of the proposed scheme for both inviscid and viscous flows. In the future, the current scheme will be extended to the hybrid unstructured meshes and Reynolds-averaged Navier–Stokes simulation with high Reynolds numbers.

A Gradient Compression-Based Compact High-Order Gas-Kinetic Scheme on 3D Hybrid Unstructured Meshes

In this paper, a compact gas-kinetic scheme (CGKS) for compressible flow is constructed on hybrid unstructured mesh. Based on high-order gas evolution model at cell interfaces both cell-averaged flow variables and their gradients can be updated in CGKS and used in a compact third-order multi-resolution WENO reconstruction. In the precious CGKS, the flow variables at a cell interface are assumed to be continuous in space in the update of cell-averaged slopes. In order to improve the robustness of the scheme in discontinuous region in three-dimensional space, a compression factor for the cell-averaged gradients is proposed to take into account the possible discontinuity at cell interfaces. The accuracy of the scheme doesn't deteriorate with the implementation of the compression factor. Numerical tests from incompressible to hypersonic flow are presented to validate the high-order CGKS and demonstrate the effectiveness of the gradient compression factor for three-dimensional flow simulation on unstructured mesh.

Edge-Based Finite Element Formulation of Magnetohydrodynamics at High Mach Numbers

In the context of the development of HALO3D (High Altitude Low Orbit 3D), an edge-based Finite Element Method multidisciplinary solver for hypersonic flows, this paper presents the simulation of flows with an imposed magnetic field. Applying the low-magnetic Reynolds number approximation, a current-continuity equation replaces Maxwell's equations with the Hall effect introduced through an electrical conductivity tensor. The approach is validated via the simulation of ionized flow through singly-paired segmented electrodes. Viscous, ionized flow simulations over a hemisphere at Mach 21.38 and over the OREX (Orbital Re-entry Experiment) capsule at Mach 17.61 are also presented. The 3D unstructured hybrid meshes used for these cases are optimized with a highly anisotropic methodology based on the Hessians of the solution, combining multi-physics adaptation criteria such as density, pressure, temperature, velocity, turbulent viscosity and electric potential. Unlike uniform mesh refinement or gradient-based mesh enrichment, this approach greatly improves accuracy without increasing mesh size.

A meshless geometric multigrid method based on a node-coarsening algorithm for the linear finite element discretization

A meshless geometric multigrid (GMG) method based on a node-coarsening algorithm is proposed in the context of finite element method (FEM) with unstructured grids consisting of linear elements. Unlike the existing GMG methods, the present method does not require the generation of a sequence of coarse grids so that all the problems related to coarse-grid generation can be eliminated. Instead, only the sets of nodes in coarse levels are constructed for multigrid computation from the finest grid by using the node-coarsening algorithm that can be employed for any kind of a 2D/3D unstructured grid as well as a hybrid grid on the finest level. The implementation of the present coarsening algorithm is simple in the sense that the boundary information of the finest grid is not required. A searching algorithm to calculate the area/volume-shape function of the finite element method is also proposed to derive an operator for linear interpolation of multigrid computation. We have successfully validated the proposed method for various 2D/3D benchmark problems by showing that the elapsed time of the present GMG method is linearly proportional to the number of unknowns of a linear system of equations. We have also confirmed that the proposed method is nearly as efficient as the grid-based MG method based on a sequence of coarse grids in terms of CPU time. Lastly, we have successfully validated the meshless GMG method by solving an elliptic equation formulated by the finite volume method on a complicated 3D geometry filled with a hybrid unstructured mesh.

Adaptive Mesh Refinement Simulations of Gas Dynamic Flows on Hybrid Meshes

An adaptive mesh refinement algorithm for simulations of the Navier–Stokes equations on unstructured hybrid meshes is presented. Numerical results for compressible supersonic flow around a sphere are given.

Influence of inlet and outlet placement on the hydrodynamics of culture tanks for Atlantic salmon

The salmon farming industry has recently shifted to larger culture tanks with greater water flows to optimize the land-based production, but tanks approaching 1000 m3 in volume create challenging hydrodynamics. This paper presents a computational study of four combinations of inlet and outlet designs of a commercial land-based aquaculture tank. Windows-based OpenFOAM solvers are used to solve the conservation equations for tank hydrodynamics with an implicit unsteady second-order Eulerian (finite volume) technique on unstructured hybrid meshes. The model is validated by the velocity measurements at discrete locations in the tank using acoustic doppler velocimetry. To understand the dispersion of biosolids in the tank, 500 particles with a uniform size of 200 µm are tracked in the Lagrangian frame. While the tank's Reynolds number varies between 2E6 - 3.5E6 depending on the flow exchange rate, the local Reynolds number at the inlet pipe is about 2E5 which discovers the drag-crisis phenomenon. The effect of inlet and outlet placement on the velocity, vorticity and turbulence is addressed. The existing tank design could be improved using the bottom-drain and corner-inlet options, which strengthens rotational flow with better uniformity. Such design change is also proved to provide better particle removal and thus ensure the improved self-cleaning ability of the tank.

Solution of cavitating compressible flows using Discontinuous Galerkin discretisation

A methodology for modelling cavitating flows using a high-order Adaptive Mesh Refinement (AMR) approach based on the Discontinuous Galerkin method (DG) is presented. The AMR implementation used features on-the-fly adaptive mesh refinement for unstructured hybrid meshes. The specific implementation has been developed for the resolution of complex multi-scale phenomena where high accuracy p-adaptive discretisations are combined with an h-adaptive data structure. This approach accommodates the fine spatial resolution for the interface discontinuities and the shock waves observed in compressible cavitating flows. The Tait equation of state is used for the modelling of the liquid phase while an isentropic path is assumed for the liquid/vapour mixture. Second order spatial and a third order non-oscillatory temporal discretisation are used for the integration of the mass and momentum conservation equations, in order to resolve the flow structures responsible for the formation of cavitation bubbles and the resulting compression waves. Assessment of the developed methodology is performed for the one-dimensional advancement of a compressible liquid-vapour interface and the symmetric collapse of a spherical vapour bubble.Following, results obtained with the developed multi-scale modelling AMR approach has revealed a complex bubble collapse mechanism near a rigid wall, providing evidence of processes that have been unknown before due to reduced resolution and dissipative nature of past simulations. The impinging jet accompanying the collapse of a bubble near a wall, was found to induce vortical structures, which result to the formation of a secondary cavitation of a wall-attached bubble at the vicinity of the impingement jet shear layer. At the final stages of the initial bubble collapse, the impinging jet was found to penetrate the centre-line of the wall bubble inducing its partial collapse. This secondary collapse results to a rich spatial structure of shock waves, interacting with the secondary bubbles. Moreover, the calculated pressure level are found to be much higher than those reported from previous methodologies.

Improving Reliability of Supercomputer CFD Codes on Unstructured Meshes

The paper describes a particular technical solution targeted at improving reliability and quality of a highly-parallel computational fluid dynamics code written in C++. The code considered is based on rather complex high-accuracy numerical methods and models for simulation of turbulent flows on unstructured hybrid meshes. The cost of software errors is very high in largescale supercomputer simulations. Reproducing and localizing errors, especially “magic” unstable bugs related with wrong memory access, are extremely problematic due to the large amount of computing resources involved. In order to prevent, or at least notably filter out memory bugs, an approach of increased reliability is proposed for representing mesh data and organizing memory access. A set of containers is proposed, which causes no overhead in the release configuration compared to plain arrays. At the same time, it provides throughout access control in the safe mode configuration and additional compile-time protection from programming errors. Furthermore, it is fully compatible with heterogeneous computing within the OpenCL standard. The proposed approach provides internal debugging capabilities that allow us to localize problems directly in a supercomputer simulation.

Numerical investigation on combustion instability modeling in a lean premixed gas turbine combustor combining finite element analysis with local flame transfer function

The present work suggests a numerical approach using an FEM (finite element method) code for the eigenvalue calculation of the thermoacoustic combustion instabilities coupling with the local flame transfer function in a generic lean premixed combustor. The URANS (unsteady Reynolds average Navier-Stokes) simulation shows a good agreement in capturing steady and unsteady flame geometries with the measurement in the literature. Also, global and local parameters of flame responses to acoustic velocity fluctuations undergo quantitatively similar changes in prediction and in the experiment. The numerically determined flame transfer function and gas properties are incorporated in an in-house Helmholtz solver to compute eigenvalues of the target combustor. In the solver, the Helmholtz equation is discretized with a Galerkin FEM on a multi-dimensional hybrid unstructured mesh. The nonlinearity related with the heat release source term is treated with an iterative methodology, and the large scale eigenvalue calculation is performed using the shift-invert approach available in the ARPACK (ARnoldi PACKage) library. The predictive capabilities of the current modeling approach are validated against the measured mode frequency and instability growth rate. In addition, the prediction results show the effect of spatially-distributed heat release on the thermoacoustic model accuracy.

A rezoning-free CESE scheme for solving the compressible Euler equations on moving unstructured meshes

We construct a space-time conservation element and solution element (CESE) scheme for solving the compressible Euler equations on moving meshes (CESE-MM) which allow an arbitrary motion for each of the mesh points. The scheme is a direct extension of a purely Eulerian CESE scheme that was previously implemented on hybrid unstructured meshes (Shen et al. (2015) [43]). It adopts a staggered mesh in space and time such that the physical variables are continuous across the interfaces of the adjacent space-time control volumes and, therefore, a Riemann solver is not required to calculate interface fluxes or the node velocities. Moreover, the staggered mesh can significantly alleviate mesh tangles so that the time step can be kept at an acceptable level without using any rezoning operation. The discretization of the integral space-time conservation law is completely based on the physical space-time control volume, thereby satisfying the physical and geometrical conservation laws. Plenty of numerical examples are carried out to validate the accuracy and robustness of the CESE-MM scheme.

JAXA’s and KHI’s Contribution to the Third High Lift Prediction Workshop

This paper is based on results presented at the Third High Lift Prediction Workshop. The Japan Aerospace Exploration Agency provided computer-aided design models and experimental results of the Japan Aerospace Exploration Agency Standard Model to the workshop as a test case. An unstructured hybrid mesh generator, MEGG3D, was applied to the Japan Aerospace Exploration Agency Standard Model wing-body and wing-body-nacelle-pylon configurations to generate grids, which were provided for the use of workshop participants by the committee. This paper presents details of experimental results and the method for deforming the computer-aided design models and volume grids based on the experiment. The Japan Aerospace Exploration Agency and Kawasaki Heavy Industries, Ltd., performed computational fluid dynamics simulations of the test case as workshop participants. Kawasaki Heavy Industries also generated custom participant-generated grids. Their computational results using the TAS code and Cflow are discussed.