Prismatic Grid Research Articles

Cache blocking for flux reconstruction: Extension to Navier-Stokes equations and anti-aliasing

In this article, cache blocking is implemented for the Navier Stokes equations with anti-aliasing support on mixed grids in PyFR for CPUs. In particular, cache blocking is used as an alternative to kernel fusion to eliminate unnecessary data movements between kernels at the main memory level. Specifically, kernels that exchange data are grouped together, and these groups are then executed on small sub-regions of the domain that fit in per-core private data cache. Additionally, cache blocking is also used to efficiently implement a tensor product factorisation of the interpolation operators associated with anti-aliasing. By using cache blocking, the intermediate results between application of the sparse factors are stored in per-core private data cache, and a significant amount of data movement from main memory is avoided. In order to assess the performance gains a theoretical model is developed, and the implementation is benchmarked using a compressible 3D Taylor-Green vortex test case on both hexahedral and prismatic grids, with third-, fourth-, and fifth-order solution polynomials. The expected performance gains based on the theoretical model range from 1.99 to 2.83, and the speedups obtained in practice range from 1.51 to 3.91 compared to PyFR v1.11.0.

Influence of the spatial grid type on the result of calculating the neutron fields in the nuclear power plant shielding

The paper considers the influence of the spatial grid type on the result of solving the equation of neutron transport in the nuclear power plant (NPP) shielding. Neutron fields were calculated in a realistic model of a liquid metal cooled fast neutron tank reactor with an integral equipment layout. Structured cubic and unstructured hexahedral grids (pmsnsys and FRIGATE codes) and unstructured tetrahedral and prismatic grids (RADUGA T code) are used. Limiting values of the group fluxes averaged over the material zones for refined grids have been obtained. It has been shown that the calculation results depend on the type of approximation for the curvilinear inner boundaries between the material zones rather than on the grid cell type (cube, hexahedron, tetrahedron, prism). Using “toothed” approximations for curvilinear boundaries leads to an increase in the area of the boundaries, as well as to the neutron flux refraction condition arising on them. These effects lead to an upward bias in the transport equation solution, and for all energy groups. Conclusion. When solving an equation of neutron transport in the NPP shielding by a grid technique, it is necessary to use grids other than leading to “toothed” approximations of the inner boundaries. Tetrahedral or prismatic grids, or grids of arbitrary hexahedrons can be recommended, as well as composite grids in which cubic cells are located inside the material zone, and hexahedron cells are located near the zone boundary.

Fast 3D forward modeling of a potential field based on spherical symmetry of gravitational potential

A novel approach is developed to implement the forward modeling of a potential field caused by prismatic grids on gridded observations with higher efficiency and less memory. Based on the spherical symmetry of gravitational potential, we summarize the parity, symmetry, and interconversion relations from derivatives and higher derivatives of gravitational potential, which reveal that there are vast repetitive calculation and storage redundancies in conventional forward modeling of a potential field for prismatic grids, especially for cubic grids. These properties help to reduce not only the size of a single kernel matrix but also the number of necessary kernels in multicomponent forward modeling of a potential field, such as a gradient tensor field or joint inversion of a potential field. Several experiments on the synthetic and the realistic Bishop models are presented to illustrate how these properties are used in the forward modeling of gravity and magnetic gradient tensors. Based on the proposed properties, a 2D fast Fourier transform is performed to accelerate the discrete deconvolution of the kernel and the model parameters. With the new method, one single kernel can be reduced to half the number of model parameters, and the memory requirement and time cost of our method can be reduced by 1/8 and 1/2, respectively, compared with previous works. In forward modeling of six gravity gradient tensor components, only two kernels need to be computed and stored, which are 1/3 of the conventional method. These examples indicate that, with high precision, our method requires less memory and less time than conventional methods. It shows potential in the fast large-scale inversion of gravity, magnetic, and gradient tensors with limited hardware resources.

A flux correction for finite-volume discretizations: Achieving second-order accuracy on arbitrary polyhedral grids

In this paper, we propose a flux correction technique generally applicable to practical finite-volume discretizations of a single flux evaluation per face for achieving second-order accuracy on arbitrary polyhedral grids involving non-planar faces. The proposed technique is derived from the k-exact finite-volume discretization approach originally introduced by Brenner. We take it as a general methodology for constructing a second-order discretization on arbitrary polyhedral grids, and identify a term considered as missing in other practical finite-volume discretizations; it is thus considered as a reason for the loss of second-order accuracy in many of such methods: e.g., a cell-centered discretization loses second-order accuracy on grids with non-planar faces as typical in polyhedral grids. In particular, we write the term as a vector involving flux gradients and show that it can be easily implemented as a correction to a numerical flux at each face. Also, we will show that a consistent definition of a control volume is critically important for achieving second-order accuracy on general polyhedral grids. We then discuss its general applicability and impact on accuracy and efficiency with simple but illustrative examples: the edge-based solver is made to achieve faster iterative convergence on irregular tetrahedral grids with adjustable centroids while preserving second-order accuracy; both the edge-based and cell-centered discretizations are made second-order accurate on irregular prismatic grids having non-planar faces.

有翼大気圏再突入機の空力特性予測に適したプリズム格子生成法

This study proposes a computational grid generation method to generate prismatic grids suitable for shock adaptation around a winged re-entry vehicle. The grid generation method proposed here is based on an existing method (Takanashi, S., Computers & Fluids, 19 (1991), pp. 393--399), which uses the theory of electric force lines to determine the computational grid lines. In order to control the distortion of the prismatic grids, the proposed method introduces three modifications to the existing method: 1) the grid generation process is divided into two stages, 2) the height of the prism layers is adjusted by considering the curvature of geometries, and 3) the cell width is optimized using the spring analogy. Both the proposed and existing methods are applied to generation of computational grids for a winged re-entry vehicle, HYFLEX. It is found that the existing method gives a computational grid containing cells not suitable for flow computations. On the other hand, the proposed method successfully gives a computational grid with which the flow computation is stably performed. By applying an adaptive refinement of prismatic layers to the detached shock wave, a smooth flow field is obtained behind the sharply resolved shock wave.

Solving EM Scattering From Complex Thin Dielectric/PEC Composite Targets by a VSIE-Based Method

A nonconformal and nonoverlapping domain decomposition method (DDM) based on hybrid volume and surface integral equation (VSIE) is presented for modeling complex thin dielectric/perfect electric conductor (PEC) composite targets. To reduce the unknown amount of the conventional volume integral equation (VIE) for thin dielectric bulks, the improved simplified prism vector (ISPV) basis function is developed. By using the basis function, the volume integrals can be simplified into surface integrals or line integrals, which significantly reduce the simulation time. Prism grids can also avoid the overmeshing problem for thin dielectrics. Moreover, they can be perfectly matched to the triangular meshes widely used in surface integral equation (SIE) hence assures a simple and robust VSIE implementation. Next, in order to increase the flexibility of geometrical modeling and accelerate the convergence of the presented VSIE system for electrically large and multiscale composite targets, a DDM is further developed. In this DDM scheme, discontinuous Galerkin approaches are, respectively, employed for VIE and SIE, accounting for conformal/nonconformal volume grids and surface grids between adjacent subdomains. In addition, an interior penalty term is introduced to stabilize the DDM solution. Finally, some numerical results are considered and analyzed to show the validity, efficiency, and applicability of the presented scheme.

A mathematical model based on unstructured mesh for ice accretion

This paper proposes a three-dimensional model to simulate ice accretion on the surface of an aircraft. The model is developed using a prism grid cell, which enables iterations with an unstructured mesh. The model assumes that the impinged water droplets on the surface can form a thin water film, and ice accretion is caused by the flow and solidification of the film. The model is developed by analyzing the conservations of mass, momentum, and energy for the thin water film on the surface. The mass and energy conservation equations of the water film are discretized on the prism grid cell, while the momentum conservation equation, which is simplified using lubrication theory, is integrated along the surface normal direction to obtain an analytical solution for the film velocity. The thicknesses of the water film and ice layer are calculated by iterating the discretized mass and energy conservation equations with the analytical solution of the film velocity. The model is verified by comparing its results with published experimental and numerical data. The results show that the model provides accurate predictions of ice accretion under different conditions, even when using an unstructured grid.

Fast and accurate forward modelling of gravity field using prismatic grids

Fast and accurate forward modelling of gravity field using prismatic grids

Generalized prism grid: a pillar-based unstructured grid for simulation of reservoirs with complicated geological geometries

Grid generation is critical to numerical reservoir simulations. High-quality grids guarantee the fidelity of a reservoir model and keep the flow calculations simple. In this study, we propose a 3D unstructured grid, the generalized prism grid (GPG), to model reservoirs with complicated geological geometries, including horizons, pinch-outs, faults, fractures, and bore holes. GPG is a layered, pillar-based grid. The location of a face node is specified by its elevation, and the pillar to which it is attached. Compared with the hexahedral corner point grid (CPG), GPG is a polygon prism and therefore more flexible; whereas, compared with the 2.5D perpendicular bisection (PEBI) grid, GPG allows polygons morphing through the stratum. We built a gridding algorithm to fulfil the features of GPG. The algorithm first constructs a 2D triangular mesh for one layer by setting up control points and grid densities for geological objects, such as fractures, faults, and wells, distributing triangular grid points with the “advancing front method,” and performing Delaunay optimization to the points. The polygon mesh is the dual grid of the triangular mesh. Taking the polygon mesh as a reference, the mesh for each layer of the strata is a morphing of it, with edges being stretched and points being assigned with heights. We also designed a compact file format to store GPG data and implemented the flux calculation method for GPG in a reservoir simulator. The attractive features of GPG are demonstrated through four examples. The conciseness and flexibility of GPG make it a potential new standard grid format replacing CPG.

RANSE-based simulation and analysis of scale effects on open-water performance of the PPTC-II benchmark propeller

This paper presents our numerical study of the scale effects on a tip-rake propeller, the PPTC-II, based on the RANS simulations using software FLUENT 6.3. The low Re option in SST k–ω model is adopted at model scale, together with fine prism grids to resolve the viscous sub-layer. At full scale, standard wall function is adopted. The scale-effect corrections yielded by our RANS simulations are compared with those obtained from the ITTC method. To explain the CFD results, an analysis of sectional forces is performed. To investigate how the tip rake influences propeller scale effects, the geometry of PPTC-II is modified by removing the tip rake only, and the RANS-predicted scale effects for the modified propeller, PPTC-II-m, are compared with those for the PPTC-II. The study indicates that the scale effect on propeller thrust can be as important as that on the torque; somehow the RANS- and ITTC-based predictions for full-scale efficiency agree quite well; the tip-rake reduces tip loading and tip vortex strength, and brings about large differences in the scale effects as compared with the propeller without tip-rake.

On representing complex configurations as asymptotic geometry

Treating geometry as an asymptotic representation is a novel approach that allows the geometry to become a function of mesh resolution. Small-scale features are filtered and smoothed out based on the grid resolution. Increasing the mesh refinement allows the geometry to asymptote towards its exact shape. Treating geometry with an asymptotic representation allows for improvements in prismatic grid generation in computational fluid dynamics, specifically by smoothing poor visibility regions, and by smoothing away small-scale features that have a negligible effect on the overall flow solution. The level set method, coupled with min/max flow, is used to filter out small-scale features based on the grid discretization size, thus smoothing the geometry. Detailed verification studies are employed in this work, showing that the method represents smooth surfaces with an order of accuracy of 2. Validation studies of the approach show asymptotic behavior of the surface area as the grid is refined. Further examples of the approach are presented, including examples of targeted filtering, where certain areas of interest are smoothed further while retaining the small-scale features in others.

2D adaptivity for 3D problems: Parallel SPE10 reservoir simulation on dynamically adaptive prism grids

We present an approach for parallel adaptive mesh refinement for 3D applications on triangular prism grids. Subsurface, oceanic or atmospheric flow problems in geosciences often have small vertical extent or anisotropic input data. Key solution features, such as shock waves, mostly emerge in horizontal directions and require little vertical capturing, such that 2D adaptivity is an attractive option. We extended sam(oa)2, a 2D code with fully dynamically adaptive refinement based on Sierpinski space-filling curves, by adding support for 2.5D grids: retaining fully adaptive horizontal refinement and load balancing, but introducing uniformly refined columns of vertical grid layers. We evaluate the potential of this approach on the SPE10 benchmark, a particularly hard two-phase flow problem in reservoir simulation. SPE10 investigates oil exploration by water injection in heterogeneous porous media. Performance of sam(oa)2 is memory-bound for this scenario with up to 70% throughput of the STREAM benchmark and parallel efficiency of approx. 91% for weak scaling on up to 8192 cores.

Propeller Effect on 3D Flow at the Stern Hull of a LNG Carrier Using Finite Volume Method

Numerical study and RANS simulations have been applied to investigate the incompressible free surface flow around the stern hull of Liquefied Natural Gas (LNG) ship affected by working propeller behind of her. Experimental works are carried out using LNG ship model in Marine Teknologi Center (MTC) of Univrsiti Teknologi Malaysia (UTM) to verify the computational fluid dynamic (CFD) results. Ansys-CFX 14.0 based on viscous flow finite volume code using the two-phase Eulerian–Eulerian fluid approach and shear stress transport (SST) turbulence model have been used in this study. A tetrahedral unstructured combined with prism grid were used with the viscous flow code for meshing the computational domain of water surface around it. CFD simulation has been verified using available experimental results. Finally, the flow structure, streamlines, velocity and pressure distribution around stern hull and propeller zone are discussed and analysed.

Numerical Simulation of Steady and Unsteady Motion for an AUV with Complex Geometry

Abstract This article simulates steady and unsteady motion of a complex geometry AUV (Autonomous Underwater Vehicle) pumped by four stern tubes. The model is similar to actual body without any simplification in order to get high resolution result, meshed by hybrid grids with prismatic grids near body while unstructured grids filling the left domain. Integrating to RNG k-e equation by cell centered finite volume scheme, the steady resistance is got and compared with that of experiment. Dealing with this analytical data we correct the experiment data, within 1.7 percent difference. During unsteady motion, added moment source is added to moment equation, while implicit dual time is applied to discretize the time dependent conserved variables, the complex pump-propelled AUV moving from stationary to a constant velocity (steady velocity) is simulated, with acceleration dicreasing in exponential with time. Its drag and corresponding velocity vector are obtained at each time step. The drag at constant velocity is validated compared with that of steady motion.

Fluid structure interaction for circulation valve of hydraulic shock absorber

Based on the working principle and the damping characteristic of hydraulic shock absorber, a fluid structure interaction method was presented, which was used to analyze the microcosmic and high-frequency processing mechanism of fluid structure interaction between circulation valve and liquid of hydraulic shock absorber. The fluid mesh distortion was controlled by the CEL language, and the fluid structure interaction mathematical model was established. The finite element model was established by ANSYS CFX software and was analyzed by dynamic mesh technique. The local sensitive computational area was meshed by prismatic grid, which could reduce the negative volume problem during the simulation. The circulation valve and liquid of hydraulic shock absorber were simulated and analyzed under the condition of sinusoidal inlet velocity loads. Flow characteristic and dynamics characteristic were obtained. The pressure distribution and the displacement of circulation value were obtained, and the acceleration curve of circulation valve was simulated and analyzed. The conformity of the final simulation results with the experimental datum indicates that this method is accurate and reliable to analyze the dynamics characteristic between circulation valve and liquid of hydraulic shock absorber, which can provide a theoretical foundation for optimizing hydraulic shock absorber in the future.

Numerical study on human model shape and grid dependency for indoor thermal comfort evaluation

Various computer-simulated person (CSP) models have been used to represent occupants in indoor airflow simulations using computational fluid dynamics (CFD). Despite the capability of CFD to predict temperature and velocity fields in an automotive cabin or a room in a building, it is more difficult to evaluate the degree of thermal comfort considered by the CSP models. Up to now, the shapes of CSP models and their grid characteristics have not been studied for the evaluation of indoor thermal comfort. In this paper, the effects of the human model’s shape and the physical characteristics of the grids are studied. The FLUENT code is used for analysis, and the predicted mean vote (PMV), predicted percentage dissatisfied (PPD), and equivalent homogeneous temperature (EHT) values are used for the evaluation and comparison of thermal comfort. The computational results show that the CSP shape and grid features do not affect the global flow fields or the evaluations of PMV and PPD. However, more precise results are obtained from the evaluation of thermal comfort by EHT when detailed human models with a prism grid are used.

A 3D hybrid grid generation technique and a multigrid/parallel algorithm based on anisotropic agglomeration approach

A hybrid grid generation technique and a multigrid/parallel algorithm are presented in this paper for turbulence flow simulations over three-dimensional (3D) complex geometries. The hybrid grid generation technique is based on an agglomeration method of anisotropic tetrahedrons. Firstly, the complex computational domain is covered by pure tetrahedral grids, in which anisotropic tetrahedrons are adopted to discrete the boundary layer and isotropic tetrahedrons in the outer field. Then, the anisotropic tetrahedrons in the boundary layer are agglomerated to generate prismatic grids. The agglomeration method can improve the grid quality in boundary layer and reduce the grid quantity to enhance the numerical accuracy and efficiency. In order to accelerate the convergence history, a multigrid/parallel algorithm is developed also based on anisotropic agglomeration approach. The numerical results demonstrate the excellent accelerating capability of this multigrid method.

Large-Eddy Simulation of Heat Transfer Around a Square Cylinder Using Unstructured Grids

This paper presents a method of large-eddy simulation on unstructured grids designed to predict the wall heat transfer in typical aeronautical applications featuring turbulent flows and complex geometries. Two types of wall treatments are considered: a wall-function model using a full tetrahedral grid and a wall-resolved method computed on a hybrid tetrahedral–prismatic grid. These two approaches are tested against the square-cylinder case at moderate Reynolds number (), in which many reference data are available for flow dynamics and heat transfer. Both predict accurately the unsteady flow around the cylinder and in its near wake, but only the wall-resolved approach reproduces the Nusselt-number global value and its spatial distribution around the cylinder wall. This latter method is used to investigate the coupling between periodic vortex shedding and wall heat transfer using a phase-averaged analysis.

Grid Generation and Airwake Simulation on Ship

Dynamic characteristics of flow field on the ship deck are complex. CFD(Computational Fluid Dynamics) results of LHA ship were verified the accuracy of numerical simulation through compared with the experimental data. Three different grids were generated to discuss and analyze the influence of the prismatic layer grid. The results show that, the presence of prismatic layer grid does not affect the results. With calculating the full-size aircraft carrier ship, the mechanical evolution of vortices in the ship deck airwake field was found. The results can provide an important reference for engineering calculation of the fluid dynamics and establish best design method early in a ship's planning stage.

A novel approximation method for multivariate data partitioning

PurposeThe plain High Dimensional Model Representation (HDMR) method needs Dirac delta type weights to partition the given multivariate data set for modelling an interpolation problem. Dirac delta type weight imposes a different importance level to each node of this set during the partitioning procedure which directly effects the performance of HDMR. The purpose of this paper is to develop a new method by using fluctuation free integration and HDMR methods to obtain optimized weight factors needed for identifying these importance levels for the multivariate data partitioning and modelling procedure.Design/methodology/approachA common problem in multivariate interpolation problems where the sought function values are given at the nodes of a rectangular prismatic grid is to determine an analytical structure for the function under consideration. As the multivariance of an interpolation problem increases, incompletenesses appear in standard numerical methods and memory limitations in computer‐based applications. To overcome the multivariance problems, it is better to deal with less‐variate structures. HDMR methods which are based on divide‐and‐conquer philosophy can be used for this purpose. This corresponds to multivariate data partitioning in which at most univariate components of the Plain HDMR are taken into consideration. To obtain these components there exist a number of integrals to be evaluated and the Fluctuation Free Integration method is used to obtain the results of these integrals. This new form of HDMR integrated with Fluctuation Free Integration also allows the Dirac delta type weight usage in multivariate data partitioning to be discarded and to optimize the weight factors corresponding to the importance level of each node of the given set.FindingsThe method developed in this study is applied to the six numerical examples in which there exist different structures and very encouraging results were obtained. In addition, the new method is compared with the other methods which include Dirac delta type weight function and the obtained results are given in the numerical implementations section.Originality/valueThe authors' new method allows an optimized weight structure in modelling to be determined in the given problem, instead of imposing the use of a certain weight function such as Dirac delta type weight. This allows the HDMR philosophy to have the chance of a flexible weight utilization in multivariate data modelling problems.