Unstructured Grid Solver Research Articles

ExaWind: Open‐source CFD for hybrid‐RANS/LES geometry‐resolved wind turbine simulations in atmospheric flows

AbstractPredictive high‐fidelity modeling of wind turbines with computational fluid dynamics, wherein turbine geometry is resolved in an atmospheric boundary layer, is important to understanding complex flow accounting for design strategies and operational phenomena such as blade erosion, pitch‐control, stall/vortex‐induced vibrations, and aftermarket add‐ons. The biggest challenge with high‐fidelity modeling is the realization of numerical algorithms that can capture the relevant physics in detail through effective use of high‐performance computing. For modern supercomputers, that means relying on GPUs for acceleration. In this paper, we present ExaWind, a GPU‐enabled open‐source incompressible‐flow hybrid‐computational fluid dynamics framework, comprising the near‐body unstructured grid solver Nalu‐Wind, and the off‐body block‐structured‐grid solver AMR‐Wind, which are coupled using the Topology Independent Overset Grid Assembler. Turbine simulations employ either a pure Reynolds‐averaged Navier–Stokes turbulence model or hybrid turbulence modeling wherein Reynolds‐averaged Navier–Stokes is used for near‐body flow and large eddy simulation is used for off‐body flow. Being two‐way coupled through overset grids, the two solvers enable simulation of flows across a huge range of length scales, for example, 10 orders of magnitude going from O(μm) boundary layers along the blades to O(10 km) across a wind farm. In this paper, we describe the numerical algorithms for geometry‐resolved turbine simulations in atmospheric boundary layers using ExaWind. We present verification studies using canonical flow problems. Validation studies are presented using megawatt‐scale turbines established in literature. Additionally presented are demonstration simulations of a small wind farm under atmospheric inflow with different stability states.

A massively parallel implicit 3D unstructured grid solver for computing turbulent flows on latest distributed memory computational architectures

An implicit unstructured grid density-based solver–PRAVAHA based on a parallel variant of the lower upper symmetric Gauss-Seidel (LUSGS) method is developed to compute large-scale engineering problems. A four-layered parallel algorithm is designed to efficiently compute three-dimensional turbulent flows on massively parallel modern multiple instruction multiple data-stream (MIMD) computational hardware. This data parallel approach achieves multiple layers of parallelism including continuity of flow solution, transfer of solution gradients, and calculation of drag/lift/solution residuals, right up to the innermost implicit LUSGS solver sub-routine, which is relatively less explored in the literature. Domain decomposition is performed using the METIS software based on multi-level graph partitioning algorithms. Non-blocking message-passing interface library functions are used to manage inter-processor communication through explicit message passing, efficiently. Super-linear scalability of the parallel solver is established on the current state-of-the-art supercomputing facility, the 838 teraflops PARAM seva on up to 6144 cores. Linear or even super-linear speedup on problems of significant size is observed even on ad-hoc parallel computing platforms like workstations and multi-node clusters, for turbulent flow simulations.

Efficient spectral implementation of ODE wall model and the extension of integral wall model to unstructured LES solvers

While wall modeling has become an indispensable tool for scale-resolving simulation of high Reynolds numbers wall-bounded turbulent flows, discussion of efficient implementation of wall models in parallel unstructured-grid solvers is lacking. In this paper, we discuss physical and numerical improvements to two zonal wall models based on integral form of the boundary layer differential equations within an unstructured-grid cell-centered finite-volume LES solver. The first model is a novel implementation of the ODE equilibrium wall model, where the velocity profile is expressed in the integral form using the constant shear-stress layer assumption and the integral is evaluated using a spectral quadrature method, resulting in a local and algebraic (grid-free) formulation. The second model is the modified form of the integral wall model of Yang et al. (2015) [14], which is based on the vertically-integrated thin-boundary-layer PDE along with a prescribed composite velocity profile in the wall-modeled region. A modification to the inner layer velocity profile which fixes the coordinate invariance issue of the original model is proposed. Additionally, several numerical challenges unique to the implementation of these integral models in unstructured mesh environments, such as the exchange of wall quantities between wall faces and LES cells, and the computation of surface gradients, are identified and possible remedies are proposed. The computational performance of the wall models is assessed both in a priori and a posteriori settings against the traditional finite-volume based ODE equilibrium wall model, showing a comparable computational cost for the integral wall model, and superior cost scaling for the spectral implementation over the finite-volume based approach. Load imbalance among the processors in parallel simulations seems to severely degrade the parallel efficiency of finite-volume based ODE wall model, whereas the spectral implementation is remarkably agnostic to these effects. The integral wall model, however, is even more prone to parallel efficiency degradation than the finite-volume based ODE wall model due to communication overhead among processors in highly parallelized settings.

Computation of drag crisis of a circular cylinder using Hybrid RANS-LES and URANS models

Numerical simulation of flow past a circular cylinder across the “drag-crisis” region is extremely challenging for turbulence models because the boundary layer undergoes laminar–turbulent transition and variable-locus separation. We investigate the SA-DDES hybrid model along with two variants, namely, SA-kLES and SA-ILES, based on Spalart–Allmaras (SA) model, and include for comparison the SA-BCM transition and the SA-URANS models, for Re ranging from 50,000 to 5 million, using an in-house unstructured grid solver. All hybrid RANS-LES models produced clearly turbulent-like behavior, as evident from the Q-criterion, while the URANS models did not. A decline in the drag coefficient is noticed in all the turbulence models, but not the sharp decrease observed experimentally, with one exception: the SA-BCM transition model, which predicted the drag coefficients much closer to the experiments. The hybrid RANS-LES models outperformed the URANS SA-BCM model only in the fully turbulent trans-critical region and better represent the physics in the wake region for all Reynolds numbers studied. All the hybrid RANS-LES models produced similar results, suggesting comparatively equal performance in predicting separated flows. We believe that the performance of a hybrid model for mid-range Reynolds numbers will be greatly enhanced if the model is equipped to handle the laminar–turbulent transition.

Analytical formulas for verification of aerodynamic force and moment computations

In this paper, we derive analytical formulas for the drag, lift, and moment coefficients of a circular cylinder exposed to a fictitious flow defined by analytical functions in two and three dimensions, and demonstrate that these formulas serve as a useful tool for quickly verifying the implementation of force and moment computation algorithms in computational fluid dynamics solvers. Focusing on a typical second-order unstructured-grid solver, we will show that the lift and drag coefficients consist of second-order accurate pressure and first-order accurate viscous force coefficients, and thus it is not always possible to uniquely determine their orders of accuracy although all will be first-order accurate on fine enough grids. For the circular cylinder geometry, the pitching moment coefficient depends only on the viscous stresses and is therefore first-order accurate. In three dimensions, rolling and yaw moments have both pressure and viscous contributions, and therefore they are asymptotically first-order accurate. Viscous contributions to the force and moment coefficients are first-order accurate even for regular grids because the gradient stencil is not symmetric typically at a boundary and any linearly-exact gradient algorithm can be first-order accurate at best; hence, the velocity gradients used to compute the viscous stresses at a wall are first-order accurate. For verification, therefore, it is necessary to verify the pressure and viscous contributions separately; it can be performed rigorously with the analytical formulas presented in this paper.

Impact of ionization rate on the transmission of electromagnetic wave in realistic plasma

A self-consistent calculation model of hypersonic fluid and electromagnetic wave (EM) propagation around a vehicle was used for radio frequency (RF) blackout prediction. First, the plasma flow around the RAMC-II vehicle at an altitude of 61 km was calculated using the finite-volume method with a newly developed unstructured grid solver. The electron number density around the RAMC-II vehicle shows good agreement with the flight test data and NASA data. Then, the effect of chemical reaction ionization rate on the plasma flow is studied, which shows that the electron number density decreases with the decrease in the chemical reaction ionization rate. Finally, based on the influence of the chemical reaction ionization rate on plasma flow, the transmission properties of the electromagnetic wave in realistic plasma at different chemical reaction ionization rates were investigated. The numerical results show that the signal loss of EM waves decreases with the decrease in the ionization rate. The ionization rate is reduced by 25 times, and the electromagnetic wave signal loss is reduced by approximately 30 dB. Based on the study, a scheme to reduce the electron number density around the vehicle by reducing the ionization rate of the chemical reaction, thereby reducing the signal loss of the electromagnetic wave, can be considered to mitigate the RF blackout.

Grid-independent large-eddy simulation of turbulent wake flow using explicit differential filters

Large-eddy simulations (LES) using explicit filtering are performed to obtain grid-independent solutions of turbulent wake flow behind a circular cylinder at ReD = 3900 on non-Cartesian type grids. A differential elliptic equation where the filter kernel is implicitly defined is discretized in an unstructured-grid solver to enable explicit filtering on non-Cartesian grids. The separation of filtering procedure from discretization is known to produce an LES solution of which error is mainly attributed to the capability of a sub-filter scale (SFS) model. Equipped with the differential filter and the Vreman SFS model, explicitly filtered LES on unstructured grids is shown to produce nearly grid-independent solutions for flow over a circular cylinder at a critical Reynolds number.

Unstructured continuum–kinetic solver with fluid–particle interaction for in-space propulsion contaminant dispersal

A new parallel generalized unstructured grid solver for prediction of rarefied gas dynamics is presented. The method is based on the direct numerical solution of the semi-classical Boltzmann equation using a discrete velocity method (DVM) and supports accurate prediction of non-continuum flows in near-vacuum rarefied flow regimes. For in-space propulsion applications which involve mixed continuum–rarefied environments, the flow regimes are solved separately through the use of DVM and hybrid RANS/LES solution procedures, respectively, on the same computational domain while interacting with one another. The solver also supports coupled Lagrangian particle transport and coalescence/breakup modeling to enable prediction of plume flow impingement and contaminant dispersal through mixed continuum–rarefied environments around spacecraft. Such simulation capabilities are essential for the prediction of spacecraft environments concerning plume impingement pressure, heating, and contamination on spacecraft components such as solar panels and sensitive instruments. Example applications include venting and plume flow environments from spacecraft main engines and attitude control thrusters firing in near-vacuum conditions. The framework upon which the solvers are developed is introduced along with a detailed description of the direct Boltzmann solution and collision integral evaluation procedures. The accuracy of standalone kinetic and coupled continuum–kinetic predictions is validated by comparison against experimental data for shock structure using various different intermolecular interaction models. Results are presented to demonstrate the merits of the capability for prediction of high-speed gas–particle interaction through complex moving shock systems, and thruster plume flow impingement with liquid droplet tracking in near-vacuum conditions.

Advanced validation of CFD-FDTD combined method using highly applicable solver for reentry blackout prediction

An analysis model of plasma flow and electromagnetic waves around a reentry vehicle for radio frequency blackout prediction during aerodynamic heating was developed in this study. The model was validated based on experimental results from the radio attenuation measurement program. The plasma flow properties, such as electron number density, in the shock layer and wake region were obtained using a newly developed unstructured grid solver that incorporated real gas effect models and could treat thermochemically non-equilibrium flow. To predict the electromagnetic waves in plasma, a frequency-dependent finite-difference time-domain method was used. Moreover, the complicated behaviour of electromagnetic waves in the plasma layer during atmospheric reentry was clarified at several altitudes. The prediction performance of the combined model was evaluated with profiles and peak values of the electron number density in the plasma layer. In addition, to validate the models, the signal losses measured during communication with the reentry vehicle were directly compared with the predicted results. Based on the study, it was suggested that the present analysis model accurately predicts the radio frequency blackout and plasma attenuation of electromagnetic waves in plasma in communication.

Japan Aerospace Exploration Agency Studies for the Second High-Lift Prediction Workshop

This paper summarizes Japan Aerospace Exploration Agency studies using a structured grid solver UPACS and an unstructured grid solver TAS-code for the second AIAA CFD High-Lift Prediction Workshop test cases and follow-on problems. Computations are performed for the grid convergence study using the configuration without any slat tracks and flap track fairings on a series of multi-block structured grids and a series of unstructured grids provided by the High Lift Prediction Workshop committee. In this paper, the following are mainly discussed: 1) grid convergence verification study of the turbulence models using a two-dimensional bump case, 2) grid convergence studies for Spalart–Allmaras and shear stress transport turbulence models using UPACS, 3) change of grid convergence and predicted flow fields with and without a nonlinear quadratic constitutive relation model for Spalart–Allmaras and shear stress transport turbulence models using UPACS including evaluation at higher angles of attack, and 4) comparison studies using different solvers UPACS and TAS on different grid systems with and without the quadratic constitutive relation model for the Spalart–Allmaras model.

Japan Aerospace Exploration Agency Studies for the Fifth AIAA Drag Prediction Workshop

This paper summarizes studies using the multiblock structured grid solver UPACS and an unstructured grid solver FaSTAR by the Japan Aerospace Exploration Agency for the fifth AIAA Computational Fluid Dynamics Drag Prediction Workshop test cases and follow-on problems. Computations are performed on a series of multiblock structured grids provided by the Workshop committee. For FaSTAR, the grids are treated as unstructured hexahedral grids. Other sets of multiblock structured grids and unstructured grids generated at the Japan Aerospace Exploration Agency are also used for computations. The following is mainly discussed: 1) grid-convergence studies for Spalart–Allmaras and shear-stress transport turbulence models using UPACS and far-field drag analyses using postprocessing software called TEBUNCO, cooperatively developed at the Japan Aerospace Exploration Agency and the University of Naples “Federico II”; 2) investigation of side-of-body flow-separation behavior at high angles of attack using UPACS with the Spalart–Allmaras or shear-stress transport model, and the change with and without a nonlinear quadratic constitutive relation model; and 3) validation of FaSTAR with the automatic hexahedral grid generator HexaGrid.

Node-pair finite volume/finite element schemes for the Euler equation in cylindrical and spherical coordinates

A numerical scheme is presented for the solution of the compressible Euler equations in both cylindrical and spherical coordinates. The unstructured grid solver is based on a mixed finite volume/finite element approach. Equivalence conditions linking the node-centered finite volume and the linear Lagrangian finite element scheme over unstructured grids are reported and used to devise a common framework for solving the discrete Euler equations in both the cylindrical and the spherical reference systems. Numerical simulations are presented for the explosion and implosion problems with spherical symmetry, which are solved in both the axial–radial cylindrical coordinates and the radial–azimuthal spherical coordinates. Numerical results are found to be in good agreement with one-dimensional simulations over a fine mesh.

G618 Immersed Boundary Methodを用いた表面の振動を伴う翼まわりの数値解析(GS6-4 数値計算,一般セッション)

Characteristics of a flow field around a wing with surface oscillation are investigated using an immersed boundary method. The immersed boundary method is to represent the effect of an immersed body in a flow by a virtual volume force. In this study, the method is successfully adapted to an unstructured-grid solver "FrontFlow/red" based on the Finite Volume scheme. Low Reynolds number flows, such as flows around Micro Aerial Vehicles and Unmanned Aerial Vehicles, are likely to cause early separation. A possible way to restrict this separation is to apply an oscillatory morphing wing shape. Comparisons between static and actuated simulations indicate that the actuation does significantly reduce separation for low Reynolds number cases.

Running unstructured grid‐based CFD solvers on modern graphics hardware

AbstractTechniques used to implement an unstructured grid solver on modern graphics hardware are described. The three‐dimensional Euler equations for inviscid, compressible flow are considered. Effective memory bandwidth is improved by reducing total global memory access and overlapping redundant computation, as well as using an appropriate numbering scheme and data layout. The applicability of per‐block shared memory is also considered. The performance of the solver is demonstrated on two benchmark cases: a NACA0012 wing and a missile. For a variety of mesh sizes, an average speed‐up factor of roughly 9.5 × is observed over the equivalent parallelized OpenMP code running on a quad‐core CPU, and roughly 33 × over the equivalent code running in serial. Copyright © 2010 John Wiley & Sons, Ltd.

Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids

An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of time-integration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.

Unstructured Cartesian Grid Methodology for Inviscid Nonequilibrium Hypersonic Flows

In this work, a solution-adaptive unstructured Cartesian grid solver for thermochemical nonequilibrium hypersonic flows with a two-temperature model is developed. The Cartesian grid methodology offers the convenience of automatic grid generation over three-dimensional complex geometries with minimum user intervention. At the same time, an accurate higher-order flux calculation over unstructured-grid topologies is provided. To avoid convergence problems in the explicit flow solver, a point-implicit method is adopted to discretize the source terms. The AUSMPW+ numerical scheme with MUSCL data reconstruction is used, preventing nonphysical oscillations and carbuncle phenomena. The accuracy of the present methodology was verified against DPLR (NASA Ames Research Center's structured-grid nonequilibrium flow solver), showing a good agreement between the two codes. As expected, the AUSMPW+ scheme effectively resolved the large gradients of the flow properties at the shock waves. In parallel, the point-implicit technique used for the source terms allows the original Courant-Friedrichs- Lewy constraints of the explicit solver to be maintained.

Towards Verification of Unstructured-Grid Solvers

New methodology for verification of finite-volume computational methods using unstructured grids is presented. The discretization order properties are studied in computational windows, easily constructed within a collection of grids or a single grid. Tests are performed within each window and address a combination of problem-, solution-, and discretization/grid-related features affecting discretization error convergence. The windows can be adjusted to isolate particular elements of the computational scheme, such as the interior discretization, the boundary discretization, or singularities. Studies can use traditional grid-refinement computations within a fixed window or downscaling, a recently-introduced technique in which computations are made within windows contracting toward a focal point of interest. Grids within the windows are constrained to be consistently refined, allowing a meaningful assessment of asymptotic error convergence on unstructured grids. Demonstrations of the method are shown, including a comparative accuracy assessment of commonly-used schemes on general mixed grids and the identification of local accuracy deterioration at boundary intersections. Recommendations to enable attainment of design-order discretization errors for large-scale computational simulations are given.

Structured and Unstructured Navier-Stokes Solvers for the Third Drag Prediction Workshop

Drag predictions of the DLR-F6 wing body, with and without the FX2B fairing, are demonstrated using both structured and unstructured grid solvers. The ability to accurately predict incremental drag is key to drag-based design and optimization. The focus of this study was to demonstrate drag and grid convergence on the two configurations. Analyses of the F6 configurations were based on the structured Navier-Stokes code, CFL3D, and on two unstructured Navier-Stokes codes, BCFD and CFD + +. Drag and grid convergence characteristics, drag polars, and pressure distribution for the configurations are presented. Results illustrate the use of a mature, structured-grid generator and solver compared to the use of two new-technology, unstructured grid generators and solvers.

Comparison Study of Drag Prediction by Structured and Unstructured Mesh Method

Comparison study of computations for the Third AIAA Computational Fluid Dynamics Drag Prediction Workshop is performed on the DLR-F6 wing-body configurations with and without the wing-body fairing using the structured grid solver UPACS and unstructured grid solver TAS code. Grid convergence study at a fixed C L using a family of three difference density grids and the results by a sweep are discussed. The self-made multiblock structured grids and mixed-element unstructured grids are employed. Another participant's grid is also compared. Comparisons between the two codes are conducted using the same turbulence model. Moreover, the detailed comparisons are conducted on the grid topology at the comer of the wing-body junction, the turbulence models, and the thin-layer approximation in viscous terms using the multiblock structured grids. The reconstruction schemes to realize the second-order spatial accuracy are also compared on unstructured grids. By comparing the results, the sensitivity of drag prediction to these factors is discussed.

Adaptive embedded and immersed unstructured grid techniques

Embedded mesh, immersed body or fictitious domain techniques have been used for many years as a way to discretize geometrically complex domains with structured grids. The use of such techniques within adaptive, unstructured grid solvers is relatively recent. The combination of body-fitted functionality for some portion of the domain, together with embedded mesh or immersed body functionality for another portion of the domain offers great advantages, which are increasingly being exploited. The present paper reviews the methodologies pursued so far, addresses implementational issues and shows the possibilities such techniques offer.