*AeroAstro Magazine Highlight *

*The following article appears in the 2005–2006 issue of AeroAstro, the annual report/magazine of the MIT Aeronautics and Astronautics Department. © 2006 Massachusetts Institute of Technology. *

## Computational engineering is growing, and AeroAstro is in the thick of it

By David Darmofal, Jaume Peraire, Raul Radovitzky, and Karen Willcox

*Richard Whitcomb, one of the most influential aerodynamicists of the 20th century, was well known to design airfoil sections by hand. He would take a file into the wind tunnel at NASA Langley and modify an airfoil’s shape based on his understanding of aerodynamics and on the data he had just collected. Some 50 years later, airfoil design is now dominated by computational methods leading to the replacement of the wind tunnel with a laptop computer for this problem. In fact, the application of computational methods to engineering problems, that is, computational engineering, is a discipline with a much wider scope than airfoil design and sees application throughout all fields. There’re some particularly interesting research and educational activities happening in the Department of Aeronautics and Astronautics in this rapidly growing discipline. *

Intensive computation for simulation and optimization has become an essential activity in the design and operation of complex systems in engineering. Thus, while computational engineering is a discipline in itself, it advances all engineering. The recent National Research Council report “Research Directions in Computational Mechanics” points out that revenues from simulation and optimization software products are in the billions of dollars, and the overall economic impact of these products is in the trillions of dollars. Despite this considerable development, the same report predicts that the next decade will experience an explosive growth in the demand for accurate and reliable numerical simulation and optimization of complex systems.

Since the early days of computational mechanics, the aerospace community has been at the forefront of computational engineering. Not surprisingly, NASA has played a major role in the development of the early finite element codes for structural mechanics (e.g., NASTRAN) as well in the development of computational fluid dynamics. Traditionally, the aerospace industry has pioneered the use of the latest computational methods. In many cases aerospace companies have developed highly sophisticated in-house capabilities through alliances with universities and research institutions. The origin of the more recent paradigms on multidisciplinary design and optimization can also be traced to the same community. Within our department, computational methods are used in almost all research efforts. However, the advancement of computational methods for aerospace design is the focus of the MIT Aero-Astro Aerospace Computational Design Laboratory.

**Computational engineering challenges**

When airfoils are operating at, or near, their intended design conditions, computational fluid dynamics models can accurately approximate the aerodynamic flows in just a few seconds on a laptop computer. Thus, in much the same way that Whitcomb used his file and a wind tunnel to design airfoils, a modern aerodynamicist can use CFD methods to quickly try new airfoil design concepts. Aero-Astro Professor Mark Drela’s MSES software takes this modeling capability a step farther, and can automatically optimize airfoil shapes to achieve desired performance characteristics.

However, for problems that are more complex than airfoil design, computational methods are hindered by a combination of effects including:

**• Uncertainty:** Computational simulations begin with a set of model equations. These model equations (even if solved exactly) are only an approximate representation of reality. Furthermore, a computational model is typically constructed by discretizing these model equations. For example, to simulate the flow around an aircraft using a finite element method, the region around the body will be discretized into many small elements and the solution in each element will be assumed to be a polynomial. As the number of elements and/or the order of the polynomials in each element are increased, a well-constructed simulation will converge to the solution of the model equations. However, given that computational resources are finite, discretization errors will be present. Thus, modeling and discretization errors combine to create uncertainty in the validity of the computational simulation. As problems increase in complexity, these uncertainties typically increase as well.

**• Automation: **For complex, three-dimensional problems, in particular those with complicated geometry, the process of discretizing the problem can require significant human interaction. For example, the generation of meshes appropriate for simulation of flow around aircraft or in jet engines can require weeks of engineering effort. The main cause for this time requirement is that the process of generating meshes for complex geometries is far from robust and requires human intervention to circumvent problems. In fluid dynamic applications, the problem of meshing robustness is especially acute for flows with boundary layers that require thin elements near all surfaces. For comparison, once a mesh is generated, the simulation on these meshes typically can be completed in a day or two on a state-of-the-art computer. This lack of robustness leads to a lack of automation. Currently, it is not possible to go from engineering concept to computational simulation in a timely manner for complex problems.

**• Computational cost: **The cost of performing computational simulations is driven by the available computer speed and memory, and the choice of computational algorithm. As raw computer speed has continued to increase, so has the complexity of feasible simulations. In addition to speed gains for a single computer, state-of-the-art computational simulations are almost exclusively performed on clusters of interconnected computers. For example, the world’s fastest supercomputer is the BlueGene/L at the Department of Energy’s Lawrence Livermore National Laboratory. Manufactured by IBM, this computer has more than 100,000 processors, and is the only computer to achieve more than 100 teraflops on a standard linear algebra test case. (Flops is the number of FLoating point OPerations per Second, so a teraflop is a trillion floating point operations per second.) To use these clusters effectively, new computational algorithms are required that attempt to reduce the time spent communicating between each processor while increasing the time spent operating on the data within each processor. Interestingly, over the past 30 years, improvements in computational algorithms have contributed equally with improvements in computer hardware towards advances in simulation complexity.

**Computational engineering research **

**• Multiscale modeling for material design: **Material design has been largely based on empiricism. The main reason for this situation has been a lack of systematic strategies to design materials from a set of functional requirements: the connection between microstructure and performance is a priori unknown and has seldom been established. However, a critical societal need exists to develop new materials for a wide range of applications.

Multiscale materials modeling combined with high-performance simulation provides a rational approach for material design. Led by Professor Raul Radovitzky, the department’s computational solid modeling group is successfully applying this modeling paradigm to a variety of problems including the description of anomalous plastic deformation in nanocrystalline metals, dynamic response of polycrystalline metals, nanoscale plasticity in biomimetic materials with extreme fracture toughness, and high-rate response of soft biological tissue and human organs to blast loads. By way of example, the following figure shows our efforts to describe blast effects on the human brain using our coupled blast-structure interaction capability, tissue models and realistic geometries from 3D magnetic resonance imaging. The figure shows two snapshots at t = 1.13ms and t = 1.74ms of a simulation of the interaction of a blast wave produced by the explosion of 1.5Kg of TNT at a stand-off distance of 1.5 m on a human cranium. The blast delivers a pressure wave with an overpressure of approximately 5 atm at the point of impact with the cranium. Stress wave propagation and multiple reverberations inside the skull lead to peak strain energy densities in excess of 750 J m−3.

**• Model reduction for real-time simulation and optimization**: While the use of high fidelity computational models such as CFD is widespread for analysis and design, an emerging challenge is real-time simulation and optimization. The need for real-time simulation is critical for many applications, including emergency response to natural disasters, industrial accidents, and terrorist attacks, control of dynamical processes and adaptive systems, and interactive design of complex systems. The challenge is to develop models of sufficient accuracy than can be used in real-time decision making.

One approach to developing an accurate, real-time modeling capability is known as model reduction. In general terms, model reduction entails the systematic generation of computationally-efficient representations of large-scale systems that result, for example, from high fidelity discretization of partial differential equations. More specifically, a reduced-order model can be obtained by using the structure of the governing equations and mathematical techniques to identify key elements of the system input/output behavior. In the past decade, reduction methodology has been developed and applied for many different disciplines, including controls, fluid dynamics, structural dynamics, circuit design, and weather prediction. Model reduction research in ACDL, led by Professor Karen Willcox, has focused on the development and application of model reduction methodology for aerospace problems that include compressor blade aeroelasticity, supersonic inlet flow dynamics, and active flow controller design. Our current projects include development of a new methodology that creates reduced-order models for inverse problems. We are applying this methodology to a data-driven framework for real-time reconstruction of hazardous events from sparse measurements.

**• Next-generation CFD algorithms:** A major ACDL research area within the Aerospace Computational Design Laboratory is the development of next-generation algorithms for computational fluid dynamics. Led by Professor Dave Darmofal, Bob Haimes, and Professor Jaime Peraire, and supported by the Air Force, NASA, Boeing, and Ford, the goal of this research is to improve the aerothermal design process for complex configurations by significantly reducing the time from geometry-to-solution at engineering-required accuracy. A key ingredient in our approach is the use of adaptive methods to automatically control the discretization error. The basic premise of an adaptive CFD method is to simulate the flow on an initial mesh, estimate the error contributed by each element within the mesh, and refine the mesh in elements that most contribute to the estimated error. A novel aspect of our adaptive method is that it seeks to control the impact of discretization error on outputs of engineering importance such as lift, drag, or moments. Thus, engineering decisions can be made with increased confidence that key outputs have been accurately estimated. For certain classes of problems, we have moved beyond error estimates and can bound the output error.

**Teaching Computational Engineering**

Computational engineering is a multidisciplinary field requiring knowledge of mathematics, computer science, and engineering. At the undergraduate level, we have developed 16.901 Computational Methods in Aerospace Engineering. The learning objectives for this subject are for the students to attain:

**• ** a conceptual understanding of computational methods commonly used for analysis and design of aerospace systems

**• ** a working knowledge of computational methods including experience implementing them for model problems drawn from aerospace engineering applications

**• ** a basic foundation in theoretical techniques to analyze the behavior of computational methods

This subject’s enrollment has grown in size each year. In the spring of 2006, more than 40 students were enrolled. During the semester, students gain hands-on experience with computational methods by implementing them to solve various aerospace-derived problems; for example, in 2005, students developed a finite volume method to approximate the supersonic flow over a circular cylinder.

At the graduate education level, a new interdepartmental Master of Science program in Computation for Design and Optimization has been created. The CDO interdisciplinary program provides a strong foundation in computational approaches to the design and operation of complex engineering and scientific systems. Furthermore, the program provides a focal point for the large computational engineering research community at MIT. The current program has more than 20 affiliated faculty members from the schools of Engineering, Science, and Sloan. Aero-Astro is well represented: the program co-director is Jaume Peraire; and Dave Darmofal, Olivier de Weck, Raul Radovitzky, and Karen Willcox are affiliates. The department offers several graduate subjects in computational engineering, all of which are also a part of the CDO program. These include:

- 16.225J: Computational Mechanics of Materials
- 16.888J: Multidisciplinary System Design Optimization
- 16.910J: Introduction to Numerical Simulation
- 16.920J: Numerical Methods for Partial Differential Equations
- 16.930: Advanced Numerical Methods for Partial Differential Equations

Computational engineering has changed the way aerospace design is conducted. As the use of computational engineering spreads, new challenges will continue to arise. We look forward to addressing these challenges.

*David Darmofal is an Associate Professor of Aeronautics and Astronautics and a MacVicar Fellow. Jaume Peraire is a Professor of Aeronautics and Astronautics, director of the Aerospace Computational Design Laboratory, and co-director of the Program in Computation for Design and Optimization. Raul Radovitzky is the Charles Stark Draper Associate Professor of Aeronautics and Astronautics. Karen Willcox is an Associate Professor of Aeronautics and Astronautics. Lead author Darmofal may be reached at darmofal@mit.edu.*