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IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach

Results of a Collaborative Research Project Funded by the European Union, 2010 - 2014

herausgegeben von: Norbert Kroll, Charles Hirsch, Francesco Bassi, Craig Johnston, Koen Hillewaert

Verlag: Springer International Publishing

Buchreihe : Notes on Numerical Fluid Mechanics and Multidisciplinary Design

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

The book describes the main findings of the EU-funded project IDIHOM (Industrialization of High-Order Methods – A Top-Down Approach). The goal of this project was the improvement, utilization and demonstration of innovative higher-order simulation capabilities for large-scale aerodynamic application challenges in the aircraft industry. The IDIHOM consortium consisted of 21 organizations, including aircraft manufacturers, software vendors, as well as the major European research establishments and several universities, all of them with proven expertise in the field of computational fluid dynamics. After a general introduction to the project, the book reports on new approaches for curved boundary-grid generation, high-order solution methods and visualization techniques. It summarizes the achievements, weaknesses and perspectives of the new simulation capabilities developed by the project partners for various industrial applications, and includes internal- and external-aerodynamic as well as multidisciplinary test cases.

Inhaltsverzeichnis

Frontmatter

The IDIHOM Project

Frontmatter

The IDIHOM Project - Objectives, Project Structure and Research Activities

Abstract

In aeronautical industry numerical flow simulation has become a key element in the aerodynamic design process. However, in order to meet the ambitious goals for air traffic of the next decades, significant investment in enhancing the capabilities and tools of numerical simulations in various aspects is required. Within the 7^th European Research Framework Programme, the collaborative target research project IDIHOM was initiated. The overall objective of this project was to enhance and mature adaptive high-order simulation methods for large scale applications. Compared to its low-order counterparts, high-order methods have shown large potential to either increase the predictive accuracy related to the discretization error at given costs or to significantly reduce computational expenses for a prescribed accuracy. The IDIHOM project was driven by a top-down approach, in which dedicated enhancements and improvements of the complete high-order simulation framework, including grid generation, flow solver and visualization, were led by a suite of underlying and challenging test cases. The project gathered 21 partners from industry, research organizations and universities with well proven expertise in high-order methods. It started end October 2010 and finished March 2014.

N. Kroll

Research Activities

Frontmatter

The Generation of Valid Curvilinear Meshes

Abstract

It is now well-known that a curvilinear discretization of the geometry is most often required to benefit from the computational efficiency of high-order numerical schemes in simulations. In this article, we explain how appropriate curvilinear meshes can be generated. We pay particular attention to the problem of invalid (tangled) mesh parts created by curving the domain boundaries. An efficient technique that computes provable bounds on the element Jacobian determinant is used to characterize the mesh validity, and we describe fast and robust techniques to regularize the mesh. The methods presented in this article are thoroughly discussed in Ref. [1, 2], and implemented in the free mesh generation software Gmsh [4, 12].

C. Geuzaine, A. Johnen, J. Lambrechts, J. -F. Remacle, T. Toulorge

Curvilinear Mesh Generation for Boundary Layer Problems

Abstract

In this article, we give an overview of a new technique for unstructured curvilinear boundary layer grid generation, which uses the isoparametric mappings that define elements in an existing coarse prismatic grid to produce a refined mesh capable of resolving arbitrarily thin boundary layers. We demonstrate that the technique always produces valid grids given an initially valid coarse mesh, and additionally show how this can be extended to convert hybrid meshes to meshes containing only simplicial elements.

D. Moxey, M. Hazan, S. J. Sherwin, J. Peiro

Development of High-Order Meshing for Industrial Aerospace Configurations

Abstract

Within the IDIHOM project, ARA have worked to develop a high-order grid generation capability that allows the generation of meshes on three dimensional aircraft configurations typical of the complexity currently used in industrial finite volume simulations. Details of this capability are provided alongside examples of meshes generated using it and a discussion of its strengths and limitations. We conclude by considering the ways in which this existing capability may be further enhanced to provide a fully industrialised capability.

C. Johnston, S. Barnes

High-Order 3D Anisotropic Hybrid Mesh Generation for High-Reynolds Number Flows

Abstract

This paper considers a problem of generation of high-order anisotropic hybrid grids to be used for simulation of high-Reynolds number compressible turbulent flows around 3D geometries. The algorithm relies on generating a curvilinear structural grid in the boundary layer region, separately from the usual low-order unstructured grid in the rest of the computational domain. A grid deformator based on an elastic analogy is used in order to curved unstructured elements. The whole process is driven by the global spacing described in a form of a metric field. The presented method is verified for the OneraM6 wing and the L1T2 high lift testcases.

P. Szałtys, J. Majewski, S. Gepner, J. Rokicki

Anisotropic Adaptation for Simulation of High-Reynolds Number Flows Past Complex 3D Geometries

Abstract

The paper presents the anisotropic adaptation algorithm applied to simulations of high-Reynolds turbulent compressible flows past complex 3D geometries. The adaptive algorithm relies on anisotropic grid-cell spacing definition provided by the error estimator in a form of a metric field. The error estimator is based on the Hessian of the solution with additional terms used to improve the grid spacing in the regions of high viscous shear forces. The adaptive algorithm is used for the two testcases the Onera M6 wing and the High Lift Prediction Workshop 1 trap wing.

J. Majewski, P. Szałtys, J. Rokicki

Deformation of Curvilinear Meshes for Aeroelastic Analysis

Abstract

The article presents elastic analogy approach of deformation curvilinear meshes applied in aeroelastic simulations. The details of algorithm used in developed software with the new metrics designated for high-order mesh quality assessment are presented. The article ends the example of LANN wing deformed by featured tool. Presented software allows conducting the aeroelastic simulation based on CFD discontinuous Galerkin High Order solver.

K. Kotecki, H. Hausa, M. Nowak, W. Stankiewicz, R. Roszak, M. Morzyński

Mesh Curving Techniques for High Order Discontinuous Galerkin Simulations

Abstract

In the development of the next generation of numerical methods for CFD, Discontinuous Galerkin methods are promising a substantial increase in efficiency and accuracy. While the particular high order methods can be very distinct, they have in common that they must rely on a high-order approximation of curved geometries to maintain their high-order of accuracy. The generation of curved meshes is thus a topic whose importance cannot be overstated, if one truly wants to apply DG methods to problems with industrial relevance. Especially aerospace applications heavily rely on complex geometries and pose high requirements to the quality of geometry representation. In this work we present several techniques to produce high order meshes, relying on linear meshes, which can be generated by standard commercial mesh generation tools. We describe the generation of the curved surface meshes and curved volume meshes, which can be particularly difficult for curved boundary layers.

F. Hindenlang, T. Bolemann, C. -D. Munz

Multigrid Solver Algorithms for DG Methods and Applications to Aerodynamic Flows

Abstract

In this chapter we collect results obtained within the IDIHOM project on the development of Discontinuous Galerkin (DG) methods and their application to aerodynamic flows. In particular, we present an application of multigrid algorithms to a higher order DG discretization of the Reynolds-averaged Navier-Stokes (RANS) equations in combination with the Spalart-Allmaras as well as the Wilcox-kω turbulence model. Based on either lower order discretizations or agglomerated coarse meshes the resulting solver algorithms are characterized as p- or h-multigrid, respectively. Linear and nonlinear multigrid algorithms are applied to IDIHOM test cases, namely theL1T2 high lift configuration and the deltawing of the second Vortex Flow Experiment (VFE-2) with rounded leading edge. All presented algorithms are compared to a strongly implicit single grid solver in terms of number of nonlinear iterations and computing time. Furthermore, higher order DG methods are combined with adaptive mesh refinement, in particular, with residual-based and adjoint-based mesh refinement. These adaptive methods are applied to a subsonic and transonic flow around the VFE-2 delta wing.

M. Wallraff, R. Hartmann, T. Leicht

Time Integration in the Discontinuous Galerkin Code MIGALE - Steady Problems

Abstract

This chapter presents the high-order Discontinuous Galerkin (DG) solver named MIGALE for the steady solution of the RANS and k − ω turbulence model equations. During the IDIHOM project theMIGALE features have been enhanced both in terms of the prediction capability and solver efficiency, due to the implementation of an Explicit Algebraic Reynolds Stress Model (EARSM) and of the h- and p-multigrid (MG), respectively. algorithm. Several high-order DG results of 2D and 3D subsonic/ transonic turbulent test cases, proposed within the IDIHOM EU project, demonstrated the capability of the method.

F. Bassi, L. Botti, A. Colombo, A. Crivellini, C. De Bartolo, N. Franchina, A. Ghidoni, S. Rebay

Time Integration in the Discontinuous Galerkin Code MIGALE - Unsteady Problems

Abstract

This chapter presents recent developments of a high-order Discontinuous Galerkin (DG) method to deal with unsteady simulation of turbulent flows by using high-order implicit time integration schemes. The approaches considered during the IDIHOM project were the Implicit Large Eddy Simulation (ILES), where no explicit subgrid-scale (SGS) model is included and the DG discretization itself acts like a SGS model, and two hybrid approaches between Reynolds-averaged Navier- Stokes (RANS) and Large Eddy Simulation (LES) models, namely the Spalart-Allmaras Detached Eddy Simulation (SA-DES) and the eXtra- Large Eddy Simulation (X-LES). Accurate time integration is based on high-order linearly implicit Rosenbrock-type Runge-Kutta schemes, implemented in the DG code MIGALE up to sixth-order accuracy. Several high-order DG results of both incompressible and compressible 3D turbulent test cases proposed within the IDIHOM project demonstrate the capability of the method.

F. Bassi, L. Botti, A. Colombo, A. Crivellini, A. Ghidoni, A. Nigro, S. Rebay

High-Order, Linear and Non-linear Residual Distribution Schemes for Steady Compressible RANS Equations

Abstract

Linear and non-linear Residual Distribution schemes for the discretization of the RANS equations are presented. Non-linear schemes are particularly suited for the discretization of transonic flows due to their capacity to give a monotone approximation of discontinuous solutions without the necessity to add artificial viscosity. A non-linear LUSGS solver is considered to construct a robust implicit solver for the discretization of two and three-dimensional problems.

R. Abgrall, D. De Santis

Development and Validation of a Massively Parallel High-Order Solver for DNS and LES of Industrial Flows

Abstract

This work is part of the development of a new generation CFD solver, Argo, based on the discontinuous Galerkin Method (DGM), specifically targeted towards accurate, adaptive, reliable and fast DNS and LES of industrial aerodynamic flows. Several aspects were investigated in IDIHOM. A first activity was the optimisation of the parallellisation strategy, resulting in highly efficient scaling, demonstrated on some of the largest computers in Europe. A second activity concerned the assessment and validation on several academic benchmark problems of the capability of DGM to perform direct numerical simulation (DNS) and (implicit) Large Eddy Simulation (iLES). Two moderately complex flows are treated, namely the ILES of the transitional flow in the low pressure turbine cascade T106C and the isothermal jet issueing from the JEAN nozzle.

C. C. de Wiart, K. Hillewaert

A High-Order Finite-Volume Method with Block-Structured Local Grid Refinement

Abstract

Time-dependent vortex-dominated flows are computed accurately with a high-order finite-volume method on structured grids. In order to attain the required grid resolution in the vortex region, block wise local grid refinement is employed. A new topology-based block refinement algorithm allows the efficient generation of such block-wise refined meshes. The high-order finite-volume method is extended with high-order interpolation to deal with the partially continuous grids at block interfaces that result from the refinement. Results are presented for three applications: one time-accurate RANS computation of a helicopter flow case and two hybrid RANS-LES computations of strongly separated flows.

J. Kok, H. van der Ven

Aghora: A High-Order DG Solver for Turbulent Flow Simulations

Abstract

This paper presents details of the solver Aghora for the simulation of unsteady compressible turbulent flows. Different modelling levels are used: Reynolds averaged Navier-Stokes equations coupled with turbulence transport equations, variational multi-scale formulation of large-eddy simulation, and direct numerical simulation. The space discretization is based on a high-order discontinuous Galerkin method with representation of curved boundaries. High-order explicit and implicit Runge-Kutta methods are used for the time integration. The performance of the solver will be assessed in various examples of compressible turbulent flow numerical simulation in three space dimensions.

F. Renac, M. de la Llave Plata, E. Martin, J. -B. Chapelier, V. Couaillier

Implementation of High-Order Discontinuous Galerkin Method for Solution of Practical Tasks in External Aerodynamics and Aeroacoustics

Abstract

For solution of 3D stationary RANS equations, closed by EARSM turbulence model, high order Discontinuous Galerkin method (degree of basic polynomials K = 2, 3 with 1st order implicit smoother is proposed. Modifications, which were introduced in the method to achieve stability and fast convergence, are described. The method is enhanced by the use of improved Gauss quadrature rules and by the use of improved Gauss quadrature rules and of h − p multigrid multigrid acceleration and is implemented into NUMECA FINE^TM/Hexa code in version for massive parallel calculations. For solution of 3D nonstationary Isentropic Linearized Euler Equations within the perturbation approach in aeroacoustics, explicit high order Discontinuous Galerkin method is implemented. Calculations of various tests, including U3, U2 and A14, demonstrate the efficiency of developed methods.

I. S. Bosnyakov, S. V. Mikhaylov, A. N. Morozov, V. Y. Podaruev, A. I. Troshin, V. V. Vlasenko, A. V. Wolkov, A. Garcia-Uceda, C. Hirsch

High-Order Residual Distribution and Error Estimation for Steady and Unsteady Compressible Flow

Abstract

In the first part, an extension of upwind residual distribution schemes for high-order accurate solution of hyperbolic problems is introduced, based on the use of spatially varying distribution matrices. Following this, the application to adjoint-based error estimation for steady compressible flow is presented. Finally the resolution of acoustic wave propagation by a space-time residual distribution is discussed. The accuracy of the methodology is demonstrated on several test cases.

M. Vymazal, L. Koloszar, S. D’Angelo, N. Villedieu, M. Ricchiuto, H. Deconinck

Recent Progress in High-Order Residual-Based Compact Schemes for Compressible Flow Simulations: Toward Scale-Resolving Simulations and Complex Geometries

Abstract

Recent developments about the extension of high-order Residual-Based Compact schemes to unsteady flows and complex configurations are discussed, with application to scale-resolving simulations and complex turbomachinery flows.

P. Cinnella, C. Content, K. Grimich, A. Lerat, P. Y. Outtier

A High-Order Discontinuous Galerkin Chimera Method for the Euler and Navier-Stokes Equations

Abstract

In this article a non-conservative Chimera method for the Euler and Navier-Stokes equations is introduced. The CFD solver for the Chimera method is based on a high-order Discontinuous Galerkin formulation and employs modal basis functions. As the method features at least two different grids, interpolation operators have to be defined between the two grids which is achieved by a discrete projection. A detailed description of the adaption of the temporal integration schemes is given and their implementation is validated for the explicit and implicit schemes against results using only a single grid.

M. Wurst, M. Kessler, E. Krämer

High-Order Discontinuous Galerkin Schemes for Large-Eddy Simulations of Moderate Reynolds Number Flows

Abstract

In this article, we describe the capabilities of high order discontinuous Galerkin methods at the Institute for Aerodynamics and Gasdynamics for the Large-Eddy Simulation of wall-bounded flows at moderate Reynolds numbers. In these scenarios, the prediction of laminar regions, flow transition and developed turbulence poses a great challenge to the numerical scheme, as overprediction of numerical dissipation can significantly influence the accuracy of the integral quantities. While this increases the burden on the numerical scheme and the LES subgrid model, the moderate Reynolds numbers prevent the occurrence of thin wall boundary layers and allows the resolution of the boundary layer without the need for wall modelling strategies. We take full advantage of the low numerical errors and associated superior scale resolving capabilities of high order spectral approximations by using high order ansatz functions up to 12th order, which allows us to resolve the significant features of these flows at a very low number of degrees of freedom. Without the need for any additional filtering, explicit or implicit modelling or artificial dissipation, the high order scheme capture the turbulent flow at the considered Reynolds number range very well.

We apply our approach to standard benchmark test cases for transitional and turbulent flows in internal and external aerodynamics: A well investigated square duct channel at Re _τ = 395, a closed channel configuration with streamwise periodic hills at Re _h = 10,595, a circular cylinder flow at Re _D = 3900 and a transitional airfoil test case at Re = 60,000. We focus on a comparison with established schemes of lower order with explicitly or implicitly added subgrid scale models, while using fewer or approximately the same number of degrees of freedom. We demonstrate that for all computations, we achieve an equal or better match to Direct Numerical Simulation and experimental results, while retaining perfect parallel scaling and achieving very low computing times.

T. Bolemann, A. Beck, D. Flad, H. Frank, V. Mayer, C. -D. Munz

Aeroelastic System for Large Scale Computations with High Order Discontinuous Galerkin Flow Solver

Abstract

Article presents the development process of aeroelastic system basing on finite volume CFD solver for higher order methods. The main aspect is interpolation tools which allows application of Discontinuous Galerkin solution of CFD solver. There is also described the elastic analogy deformation tool for curvilinear mesh. To summarize, the two testcases of wing and wing-body configuration aircraft are presented.

K. Kotecki, H. Hausa, M. Nowak, W. Stankiewicz, R. Roszak, M. Morzyński

New Developments for Increased Performance of the SBP-SAT Finite Difference Technique

Abstract

In this article, recent developments for increased performance of the high order and stable SBP-SAT finite difference technique is described. In particularwe discuss the use ofweak boundary conditions and dual consistent formulations.The use ofweak boundary conditions focus on increased convergence to steady state, and hence efficiency.Dual consistent schemes produces superconvergent functionals and increases accuracy.

J. Nordström, P. Eliasson

Higher-Order RANS and DES in an Industrial Stabilized Finite Element Code

Abstract

This chapter describes the contribution of Dassault Aviation to the IDIHOM Project. It focuses on the extension of its stabilized finite element Navier-Stokes code to higher-order elements and more specifically on industrial RANS and DES applications.

F. Chalot, F. Dagrau, M. Mallet, P. E. Normand, P. Yser

High-Order Visualization with ElVis

Abstract

Accurate visualization of high-order meshes and flow fields is a fundamental tool for the verification, validation, analysis and interpretation of high-order flow simulations. Standard visualization tools based on piecewise linear approximations can be used for the display of highorder fields but their accuracy is restricted by computer memory and processing time. More often than not, the accurate visualization of complex flows using this strategy requires computational resources beyond the reach of most users. This chapter describes ElVis, a truly high-order and interactive visualization system created for the accurate and interactive visualization of scalar fields produced by high-order spectral/hp finite element simulations. We show some examples that motivate the need for such a visualization system and illustrate some of its features for the display and analysis of simulation data.

J. Peiro, D. Moxey, B. Jordi, S. J. Sherwin, B. W. Nelson, R. M. Kirby, R. Haimes

Direct Visualization of Piecewise Polynomial Data

Abstract

High order methods are regarded as a primary means to significantly improve the efficiency of numerical techniques. While the particular high order methods can be very distinct, most have in common that their solution is represented by piecewise polynomials. However, since high order methods evolved only recently, most of the present visualization techniques are not suited for the needs of resulting simulation data; they are predominantly based on tensor product linear interpolation and applying them to high order data is nowadays accomplished by static resampling, involving prohibitive storage and computation costs, and providing at most sufficient results. In this paper, we describe two of our existing visualization approaches and discuss some of the involved problems and concepts, and exemplify them using different high order simulation results.

T. Bolemann, M. Üffinger, F. Sadlo, T. Ertl, C. -D. Munz

Assessment of High-Order

Frontmatter

External Aerodynamic Test Cases

Abstract

In this chapter the testcases in the IDIHOM project treating external aerodynamic flow are subjected to an industrial assessment. The chapter serves to illustrate the level of complexity that can be presently handled using higher order discretization methods. In addition, a discussion on the efficiency and robustness of the codes compared with the current state of the art is included.

K. A. Sørensen, C. Johnston, T. Leicht, F. Chalot, P. Eliasson, F. Bassi, V. Couaillier, M. Kessler

Internal Aerodynamic Test Cases

Abstract

This section gathers the descriptions of all test cases concerning internal flows, as well as the most important results obtained by the participants in the IDIHOM project. The test cases comprise a transonic compressor (NASA Rotor 37), a subsonic nozzle (JEAN), low pressure turbine cascades in turbulent (T106A) and transitional conditions (T106C) and finally 2 validation cases, namely a bump flow from the DESIDER project, and the periodic flow over a 2D hill from the ERCOFTAC QNET CFD database. Depending on the test case, RANS, LES and even DNS computations were performed.

K. Hillewaert, A. Garcia-Uceda, C. Hirsch, J. Kok, M. de la Llave Plata, F. Renac

Aeroelastic Testcases in IDIHOM Project

Abstract

In the IDIHOM Project three aeroelastic testcases have been calculated. Two of them - LANN Wing and DLR-F6 wing-body configuration - have been conducted by PUT. The last one, the HART II rotor has been prepared by NLR. Each partner has used different technology and software tools, hence each of the testcases describes the results of the simulation and technology which has been used.

K. Kotecki, H. van der Ven, J. Kok, H. Hausa, M. Nowak, W. Stankiewicz, R. Roszak, M. Morzyński

Aeroacoustic Test Cases

Abstract

In this article, the results of aeroacoustic cases obtained by high-order methods are presented. One internal and one external case are considered. The internal case is a transonic cavity. It has been computed by three parters, namely FOI-LiU (Linköping University), University of Stuttgart (USTUTT) and Dassault Aviation (DASSAV). FOI-LiU has computed with their higher order accurate finite difference solver using a block structured grid. Comparisons are made to reference calculations using an unstructured grid with Edge. USTUTT uses a high order discontinuous Galerkin spectral element code for the final high-order computations and a mixed modal/nodal DG code for the baseline computations. Dassault Aviation uses their in-house stabilized finite element code Aether, both for the reference and the higher-order computations. In both instances unstructured tetrehedral grids are used. The external case is a quasi-two dimensional generic wing and flap configuration defined in the VALIANT FP7 project. Two institutions were involved in the high-order simulation of this low-Mach number test case, M = 0.15, Central Institute of Aero- and Hydrodynamics, TsAGI, and the von Karman Institute, VKI. In the following, the acoustic predictions corresponding to the two test cases will be described.

L. Koloszar, N. Villedieu, H. Deconinck, I. S. Bosnyakov, S. V. Mikhaylov, A. N. Morozov, V. Y. Podaruev, A. I. Troshin, V. V. Vlasenko, A. V. Wolkov, P. Eliasson, T. Bolemann, F. Chalot

Backmatter

Titel: IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach
herausgegeben von: Norbert Kroll
Charles Hirsch
Francesco Bassi
Craig Johnston
Koen Hillewaert
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-12886-3
Print ISBN: 978-3-319-12885-6
DOI: https://doi.org/10.1007/978-3-319-12886-3

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