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Industrialisation of High-Order Methods – A Top-Down Approach

Final Report Summary - IDIHOM (Industrialisation of High-Order Methods – A Top-Down Approach)

Executive Summary:
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 7th 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 test case suite selected for the IDHOM project can be split into four application areas: external and internal aerodynamics, aero-elastics and aero-acoustics. Two different types of test cases were defined. So-called application challenges were mainly defined by industry and they are characterized by complex three-dimensional flows around complex geometries. A few underlying test cases were provided with moderate geometrical and/or flow complexity to speed-up the process of method enhancement. The test case suite was selected prior to project start. In the IDIHOM project significant progress in the development of high-order CFD methods and their application to cases which are of interest to the aerospace community was made. Dedicated research activities further enhanced the maturity of the methods and helped to enable a critical assessment of the potential and current limits of the novel high-order approaches for applications in aerospace industry.
Project Context and Objectives:
Introduction
The IDIHOM project started in October 2010 as a Specific Target Research Project of the 7th EU Framework Programme. The main goal of the project was to mature high-order adaptive CFD methods for industrial applications.
The project was originally scheduled for 36 months with a total budget of about 4.2 Million Euro. It has been extended by 6 months and was completed by 31 March 2014. The IDIHOM consortium was comprised of 21 organizations with well-proven expertise in higher-order methods or underlying technologies. The following partners from European aircraft manufactures, small and medium enterprises, major European research establishments and universities were involved: Dassault Aviation (France), Airbus Defense and Space (Germany), Cenaero (Belgium), NUMECA (Belgium), DLR (Germany), FOI (Sweden), INRIA (France), NLR (The Netherlands), ONERA (France), ARA (United Kingdom), TSAGI (Russia), VKI (Belgium), ARTS (France), Imperial College London (United Kingdom), University of Bergamo (Italy), University of Brescia (Italy), University of Stuttgart (Germany), Poznan University of Technology (Poland), Warsaw University of Technology (Poland), University of Linköping (Sweden), Université catholique de Louvain (Belgium). The project was coordinated by the German Aerospace Center (DLR).
Background, objectives, work description
Over the last two decades, computational fluid dynamics (CFD) has established itself to a point where it is widely accepted as an analysis and design tool complementary to theoretical considerations and experimental investigations. In aerospace, methods to solve the Navier-Stokes equations have matured from specialized research techniques to practical engineering tools being used on a routine basis in the industrial design process. Thus, numerical simulation has become one of the driving technologies for both, scientific discovery and industrial product development. Continuous development of physical models and numerical methods as well as the availability of increasingly powerful computers suggest using numerical simulation to a much greater extent than before, radically changing the way aircraft will be designed in the future.
On the other hand, despite the progress made, large aerodynamic simulations of viscous high Reynolds number flows around complex aircraft configurations are still by far too expensive in terms of turn-around time and computational resources. The requirement to achieve results at an engineering level of accuracy within wall-clock times that can be handled in the day-to-day procedure poses severe constraints on the application of CFD to aerodynamic design and data production. Improved flow physics modeling and the enormous increase in computer power is only one part of the solution. The other part is evidently dedicated to a necessary enhancement of the numerical methods themselves. The development of advanced CFD algorithms and their integration in an industrial environment to support multidisciplinary simulations and optimisation procedures and at the same time achieving high predictive accuracy will significantly reduce design cycle and cost and is therefore indispensable for industry.
The majority of the aerodynamic simulation tools currently used in the aeronautical industry for routine applications are mainly based on finite volume methods. Being bound in most of the cases to second order discretization of the underlying governing equations, real-life applications require tens or hundreds of million mesh points to enable accurate solutions and to provide deep insight into complex flow features. In recent years there has been worldwide an ever increasing effort in the development of high-order CFD methods because of their potential in delivering either improved predictive accuracy or reduced computational cost compared to their low-order counterparts. Many different strategies have been followed and their pros and cons have been evaluated for a diverse range of academic problems.
In Europe, the specific target research project ADIGMA (Adaptive Higher-Order Variational Methods for Aerodynamic Applications in Industry) was initiated within the 6th European Research Framework Programme, in order to add a major step towards the development of next generation CFD tools with significant improvements in accuracy and efficiency for turbulent aerodynamic flows. The main objective of the ADIGMA project (2006-2009) was the development of innovative high-order methods for the compressible flow equations in combination with reliable adaptive solution strategies, enabling mesh independent numerical simulations for aerodynamic applications. The project concentrated on technologies showing the highest potential for efficient high-order discretization on unstructured meshes, namely the Discontinuous Galerkin (DG) methods and the Continuous Residual Distribution (CRD) schemes. Although significant progress has been made in ADIGMA, it was finally concluded that many of the achievements in high-order simulation methods are still far away from industrial maturity. In general, the high-order methods investigated within ADIGMA demonstrated the potential for reducing the size of the discrete system by a factor of about 5-10 for most of the considered aerodynamic test cases, however, the gain could not fully transferred to increased runtime performance as limited attention has been paid to efficient solvers for large scale applications. On a given mesh, high-order discretization involves more floating point operations than do their low-order counterparts. Strong, memory-efficient solution algorithms are required to outperform well-tuned low-order methods. Furthermore, the ability of generating coarse unstructured meshes suitable for high-order methods has been identified as a major bottleneck for industrial type applications. At the end of the ADIGMA research project it was recommended that further dedicated research effort is required to fully exploit the high-order methods for routine applications in aerospace industry.
In 2011 the follow-on project IDIHOM (Industrialization of High-Order Methods) was initiated within the 7th European Research Framework Programme. It was motivated by the increasing demand of the European aerospace industries to improve their CFD-aided design procedure and analysis by using accurate and fast numerical methods. IDIHOM follows a top-down approach. A comprehensive suite of challenging application cases proposed by industry was set up prior to the project to direct dedicated development and improvement of high-order solvers at hand. The test case suite includes turbulent steady and unsteady aerodynamic flows, covering external and internal aerodynamics as well as aero-elastic and aero-acoustic applications. The complete process chain of the high-order flow simulation capability was addressed, with focus on flow solver efficiency and mesh generation capabilities, but including also visualisation and coupling of CFD to other disciplines for multidisciplinary analysis. The challenging application cases defined by the industry formed the basis for the demonstration and assessment of the current status of high-order methods as a workhorse for industrial applications. IDIHOM was assigned to help to close the gap between current expectations of what high-order methods are capable of and their strongly required use for industrial real-world applications - reaching out for improved, more accurate and time-saving design processes.
The main objectives to be achieved by gathering expertise from European experts in the field of numerical analysis in aerodynamic and multidisciplinary design are summarized as follows:
• Advance the maturity of current high-order methods, in particular Discontinuous Galerkin and Continuous Residual-Based approaches, and apply them to complex flows which are of particular interest for the aeronautical industry.
• Demonstrate the capabilities of high-order methods in solving industrially relevant, challenging applications and achieving synergy effects by combining requirements from external and internal aerodynamic flows.
• Investigate the capability of high-order methods to multidisciplinary topics as aero-acoustics & aero-elastics.
• Extend high-order methods to advanced turbulence models.
• For the adaptive high-order methods employed, advance the Software Technology Readiness Level from about 3 (status at the end of the ADIGMA project) to 5.
• Facilitate co-operation between European industries, research establishments and universities and foster co-operation between different industries as there are airframe, turbo-engines, helicopters, and ground transportation.
Reaching these objectives shall enable industry to use high-order methods in their daily work. Improved accuracy coupled with a reduction of computation and hence turn-around time is a pre-requisite for a routine employment of novel methods in future aircraft design cycles.
The IDIHOM consortium was comprised of 21 organisations with well-proven expertise in higher-order methods or underlying technologies. Partners from European aircraft manufactures, small and medium enterprises, major European research establishments and universities were involved. The project was coordinated by the German Aerospace Center (DLR).
As mentioned already, the IDIHOM project followed a top-down approach to enhance the maturity of current high-order methods for routine use in aeronautical industry. Enhancement and improvement activities were identified which enable a robust, efficient and accurate computation of the comprehensive set of application challenges. The advancement of the complete set of the high-order environment was addressed to fulfil the industrial requirements, including mesh generation and adaptation, solver robustness and convergence acceleration, parallelization strategies for advanced computer hardware as well as flow visualisation.
As mentioned already, the IDIHOM project followed a top-down approach to enhance the maturity of current high-order methods for routine use in aeronautical industry. Enhancement and improvement activities were identified which enable a robust, efficient and accurate computation of the comprehensive set of application challenges. The advancement of the complete set of the high-order environment was addressed to fulfil the industrial requirements, including mesh generation and adaptation, solver robustness and convergence acceleration, parallelization strategies for advanced computer hardware as well as flow visualisation.
The technical work in IDIHOM was structured in three main work packages (WP), all of them split into specific work tasks. WP2 was the key driver of the project, as it demonstrated and steered the top-down approach of IDIHOM. In a first task the pre-selected test cases were further specified in terms of geometry, flow and boundary conditions. Reference solutions using second-order finite volume methods and baseline solutions employing high-order methods available at project start were computed. These results were then used in a second task for detailed comparisons with solutions obtained with the improved high-order methodologies available at the end of the project. Common test case templates were defined, ensuring that reference, baseline and final results are properly compared, allowing a thorough assessment of the achievements and advances gained through the IDIHOM project. Work package WP3 addressed the improvement of high-order solvers with regard to the IDIHOM application challenges and the underlying test cases. After successful completion of the precursor project ADIGMA, focus was not put on the general development of high-order approaches, but more on the maturity of the implementation of codes at hand, thus extending the available capabilities of the solvers with respect to physical modeling, the applicability to large-scale application cases and the treatment of time accurate simulations. In work package WP4 the enhancement of underlying technologies of high-order methods were addressed. Basically three aspects are of concern, in which high-order methods have special requirements. These are mesh generation, mesh adaptation and flow visualisation. Therefore, specific development actions were carried out to tackle the test cases considered in the project.
The test case suite selected for the IDHOM project can be split into four application areas: external and internal aerodynamics, aero-elastics and aero-acoustics. Two different types of test cases were defined. So-called application challenges were mainly defined by industry and they are characterized by complex three-dimensional flows around complex geometries. A few underlying test cases were provided with moderate geometrical and/or flow complexity to speed-up the process of method enhancement. The test case suite was selected prior to project start. During the course of the project, some modifications and adaptations were made due to lack of reference results and detailed geometry definitions.

Project Results:
Work performed and results achieved within the project
IDIHOM focused on two aspects, the implementation of advanced turbulence models and the efficiency improvement of solution algorithms for the nonlinear discrete systems for both steady and time-accurate applications.
In terms of advanced physical modeling Explicit Algebraic Reynolds Stress Models (EARSM) up to cubic terms of the anisotropy tensor coupled with the two-equation turbulence model was implemented in the frame of high-order Discontinuous Galerkin solvers. Reynolds stress turbulence models proved to be more reliable when being used for a wide range of applications compared to the classical one- or two-equation turbulence models. EARSM was selected because of the good compromise between improved modeling of turbulence and moderate associated cost. The advanced turbulence model was successfully applied to various underlying and challenging test cases. For some problems improved physical modeling was demonstrated resulting in a very small computational overhead compared to standard 2-equation turbulence models. However, it has been observed that for more complex applications often the EARSM approach was difficult to converge to a steady state solution.
Another area of research was the extension and adapation of high-order methods to scale resolving simulations. High-order methods are well suited since these simulations require high resolution in both space and time. Different approaches were followed within IDIHOM. In the frame of hybrid RANS/LES (DES), the X-LES approach was employed in a high-order block-structured code in combination with local block-wise grid refinement as well as in a high-order DG code. Impressive results were obtained for quite a number of test cases. Furthermore, high-order Discontinuous Galerkin and Residual Based Compact schemes were further developed and validated for LES and DNS. In particular, the quality of the implicit LES (ILES) approach in the frame of the DG discretization was demonstrated. The absence of tuning parameters and the robustness of DG methods with respect to mesh quality indicated industrial viability. For scale resolving simulations significant progress was made compared to start of the project.
As mentioned earlier, the construction of a robust and memory-efficient solver is a pre-requisite of efficient high-order methods. For steady state computations or unsteady phenomena which allow for rather large physical time steps, implicit formulations are generally preferred due to the fact that viscous terms, stretched meshes with very small mesh size in at least one direction and the high-order formulation all contribute to severe time step restrictions. Therefore, the research within IDIHOM concentrated on implicit solution methods. Due to the fact that additional, independent degrees of freedom are introduced to describe the high-order content of the solution, it is very difficult if not impossible to base the implicit treatment on just a lower-order approximation, as typically done for finite volume schemes. If the high-order content is not treated implicitly, the overall scheme becomes explicit. As a consequence, most implicit treatments make use of the full high-order Jacobian, resulting in considerable memory requirements. Although it is not possible to completely replace the implicit operator or preconditioner by a low-order approximation, an attractive alternative are so-called p-multigrid methods, variants of which were proposed by several partners. In spite of the name, these approaches approximate the numerical solution on single mesh, but with different order methods. While improvements over single-level computations were shown for a number of cases, there is still room for improvement. If for example, relatively fine meshes are used due to mesh generation restrictions, the effectivity of this approach might be rather limited. Therefore, alternative multigrid strategies based on agglomeration of meshes (h-multigrid) were developed and investigated. In the frame of DG methods, the corresponding discretizations require the use of non-parametric basis functions. The resulting hierarchy of levels can be exploited to use the nonlinear FAS multigrid approach or, alternatively, to formulate linear multigrid method to be used an effective preconditioner within a Krylov solver. The combination of both multigrid strategies proved to be the most robust and efficient approach for a wide range of applications. For the Residual Distribution methods a non-linear LU-SGS method was developed and successfully applied to 2D and 3D test cases. In addition, improvements of implicit methods for time-accurate computations were made.
Adaptive refinement techniques are essential for high-order methods to be competitive with standard finite-volume solvers. In the previous project ADIGMA substantial effort was devoted to the development of local refinement approaches related to both, mesh and discretization order refinement. Based on this work, limited activities were carried out within IDIHOM to further improve and mature the local refinement techniques for more complex applications.
High-order grid generation and visualisation
To fully exploit the capabilities of high-order methods, higher-order representation of the boundaries is required. Furthermore, for stretched elements often encountered close to the solid wall boundaries in aerospace applications, the volume mesh needs to be considered as curvilinear as well, at least close to the curved surfaces. Such high-order meshes are typically not readily available and the support in commercial grid generation software is not available. Based on the experience gained in ADIGMA, dedicated research activities were devoted to further development and enhancement of high-order mesh generation techniques. Focus was put on generation of coarse unstructured meshes for geometries of industrial interest. Different technologies were investigated and further enhanced including mesh adaptation techniques. Although some good progress towards this overall objective was made, the generation of usable grids for the most complex test cases considered in IDIHOM proved to be more difficult than anticipated when planning the project. In general difficulties were caused by problems in generating an initial coarse linear volume grid upon which most of the high-order grid generation algorithms depend. Usable capabilities were made available for 2D and simple 3D test cases. The use of mesh adaptation was successfully demonstrated for some of the IDIHOM 3D test cases.
With respect to visualisation limited effort was spent to investigate and further enhance existing open software tools following the super-sampling technique. This technique relies on a visualisation sub-mesh for each element in the underlying computational mesh, thereby approximating nonlinear data per element via a subdivision into several linear segments. Appropriate interfaces to the open source visualization tools were developed and integrated. In addition an alternative approach was investigated, in which the polynomial data are visualised directly.
Scope of applications
The external and internal aerodynamic test cases computed in the project served to illustrate the capabilities of current higher-order schemes, but also the challenges facing the approaches. A large variety of underlying and application test cases covering high geometrical and flow complexity as well as coupling to other disciplines were successfully computed. In general, it can be said that many flows of industrial interest can now be computed in a routine manner using higher-order schemes, although in some cases problems are still reported regarding flow features such as shocks. Even though there are indications of favorable aspects of the new approaches, it was proven whether for typical RANS-type application problems the approaches evaluated have the potential of improving the overall efficiency of the industrial codes in current use. A major problem for the project was the lack of appropriate higher-order meshes made available, reducing the amount of quantitative data produced. Nevertheless, the IDIHOM project provided strong indications that higher-order methods have the potential to reduce the discrete system size required for mesh convergence within industrial accuracy for many cases. For smooth flow fields this reduction typically seems to reach around one order of magnitude. However, despite the significant improvements achieved related to flow solver technologies, for most cases the reduction in problem size did not translate to significantly reduced overall computational time. Adaptive strategies were found to be an important ingredient to reduce the overall problem size and thus alleviate the high computational cost per degree of freedom associated to high-order methods. Moreover, the project indicates that future computer hardware developments may increase the attractiveness of higher-order methods since the data locality support extreme parallelization for large scale applications. This might be in particular pay-off for unsteady scale-resolving simulations in which high resolution is required in both space and time. The high potential of high-order methods for scale-resolving simulations has been clearly demonstrated in IDIHOM. In particular, the unstructured high-order methods are of great interest for industry. Similar to highly specialist academic high-order codes used for fundamental research, they offer low-dissipative, low-dispersive schemes on unstructured grids allowing scale resolving simulations (hybrid RANS/LES, LES/DNS) for applications which are of industrial interest.
Finally, high-order multidisciplinary simulations were successfully demonstrated in the IDIHOM project including aero-elastic and aero-acoustic problems.
General conclusions and recommendations
In the IDIHOM project significant progress in the development of high-order CFD methods and their application to cases which are of interest to the aerospace community was made. Dedicated research activities further enhanced the maturity of the methods and helped to enable a critical assessment of the potential and current limits of the novel high-order approaches for applications in aerospace industry.
Despite the progress, the current status of the technology seems to prohibit an immediate incorporation of these tools into routine industrial processes. Even though a large range of simulation scenarios were covered within the project, no single existing implementation is capable of covering the whole spectrum of applications which is offered by established lower order codes. Certainly, the time frame for development of high-order methods is much shorter than was invested into classical approaches, e. g. 2nd order finite volume schemes. However, additional reasons for a slowdown of the progress can also be observed. High-order methods are, in general, less forgiving than low-order approaches. If any ingredient in the overall process is done slightly incorrect, the order can easily be destroyed and the overall efficiency of the approach is significantly reduced. In contrast to that, for state-of-the-art second-order methods, there is a certain tolerance for simplified treatments allowing a relatively easy extension of the methods to a large variety of applications covering e.g. complex geometries, flow fields with strong shock waves, bodies in relative motions and coupling of CFD with other disciplines.
In the short term, there is a high potential for high-order methods in the area of scale-resolving simulations as demonstrated in the project. In these scenarios resolution requirements are particularly high, which yields a large benefit for high-order approaches. Due to resolution requirements in time, explicit time integration is often a viable choice. This greatly simplifies solution algorithms and increases robustness of the methods. Furthermore, massively parallel implementations are almost trivial for explicit time integration schemes. In the frame of fundamental research, high order methods are already in use for scale-resolving simulations. However, they are often dedicated to structured grids and are therefore limited to problems with simple to moderately complex geometries. Recent developments of high-order finite element approaches allow the construction of low-dissipative, low-dispersive methods on unstructured grids enabling scale-resolving simulations for more complex geometries. This type of simulation scenarios is of increasing interest to aerospace industry as it greatly reduces (or even overcomes) the issues of physical modeling in certain applications.
Currently, high-order meshing for complex geometries seems to be the most severe restriction in the overall simulation technology tool chain, in particular if considering meshes with high aspect ratio stretched elements as typically used in RANS or DES-type applications in aerospace. Undeniably, progress has been achieved through IDIHOM and other research projects over the last years. The generation of 2D unstructured high-order meshes might be considered as manageable. However, for 3D cases it is already very difficult to generate appropriately coarse meshes at all, and the modification to high-order is expensive and error-prone. Many difficulties might be related to technical issues with the implementation rather than fundamental problems. However, in the long run, considerable progress will have to be made in this area if high-order methods shall ever be available for general purpose aerospace applications. Until then, simplified procedures based on local surface reconstructions or the exploitation of structured mesh blocks can be used to further exploit the potential of the underlying CFD methods.
For many routine use cases in aerospace industry, e. g. steady-state RANS computations for cruise conditions, state-of-the-art second order methods are very mature and thus fairly competitive, in particular as the absolute accuracy requirements might not be too demanding. Thus, the potential for improvement with high-order methods is limited in this area. The benefit will be larger for unsteady simulations in which spatial errors can accumulate over time, such that spatial accuracy is more important than for steady state simulations. In this class of problems, the benefit might be particularly large for interaction phenomena, typically including the resolution of vortices over long distances. Another example might be the simulation of local effects for (active) flow control. The latter scenario has the additional advantage that the simulation of basic effects is typically associated to relatively simple geometries, which eases the meshing.
As it seems unlikely even in the long run that all numerical simulations in industry will be performed with high-order approaches, it might be wise to develop a common code framework based on unstructured methods that can handle low- and high-order approaches and features a close integration of both. Good candidates are general implementations of continuous or discontinuous finite element methods since these approaches coincide with the highest flexibility concerning solution algorithms and offer a large amount of intensive experience. As demonstrated in the IDIHOM project, an important ingredient is adaptivity, in particular for high-order methods. The additional availability of reliable error estimators is an essential aspect for the management of uncertainties, which is of increasing importance in industrial applications. With these ingredients, a successful incorporation of high-order numerical methods into aerospace CFD codes for industrial use seems possible. In the long run, the method of choice can then be selected case by case based on the application and simulation intent. In order to achieve this goal, a continuation of the current efforts is required. The European research project IDIHOM focused development on the applicability of high-order approaches to industrially relevant simulations and the required supporting technologies. Even though this work was successful, there is need for further progress in order to transfer the current demonstration of applicability to a status, where the associated tools can be used on a routine basis with a minimal amount of user interaction.

Potential Impact:
Dissemination and exploitation
The knowledge gained in the IDIHOM project, the computational methods developed and the particular results generated were disseminated in various forms. Important means are publications in journals, technical papers and presentations at national and international conferences. In particular, the dedicated mini-symposia held at various international CFD conferences, the VKI Lecture Series course on high-order methods and the final IDIHOM report being published as a dedicated book in the Springer Series “Notes on Numerical Fluid Mechanics and Multidisciplinary Design” are seen as important channels to disseminate the project results. Within the project a comprehensive data base for the evaluation of higher-order methods was created. The data base includes specification of test cases, computational grids, solutions of higher-order obtained with various approaches as well as reference solutions of standard industrial second-order methods. This test case suite is of high interest to the CFD community to promote the further development and application of high-order CFD tools. As a consequence, the IDIHOM consortium was heavily involved in the organisation of the 1st and 2nd International Workshop on High-Order CFD Methods held in 2011 (US) and in 2013 (Germany).
The IDIHOM objectives enabled a strong cooperation between universities, research establishments and aircraft industry as well as software vendors. According to their role the organisations will apply different dissemination and exploitation strategies. The universities taking part in IDIHOM will directly exploit the project findings for teaching and training students and researchers in advanced high-order methods. The close cooperation with research organisations and industry will lead to the training of qualified personnel with knowledge of the industrial requirements, thereby increasing the potential of graduates for employment within industry. The project outcome will allow universities to pursue their goals in the field of applied mathematics and computational fluid dynamics, both in research and education. The research organisations participating in IDIHOM will directly exploit the knowledge gained in the project by improving their numerical tools for complex aeronautical applications. Bases on results of the comprehensive test case suite, the potential and limits of these methods for tackling challenging applications were highlighted and future research directions were identified. The aircraft industry was directly involved in the transfer process. With the help of the research establishments as central providers of highly sophisticated CFD methods, aircraft industry will further explore the most promising methods for selected applications for aerodynamic and multidisciplinary design work

List of Websites:
website: www.idihom.de
contact: Dr. Norbert Kroll, DLR, norbert.kroll@dlr.de