
Spectral Difference Method for Incompressible Viscous Flow
:
Patrice Castonguay

Aerodynamics of hard disk drives and
Vortex suppression of flow past bluff bodies
:
Andre Chan

Geometry Parameterization and Automation for CFD
:
Edmond Chiu

Airfoil optimization and genetic algorithm
:
Matt Culbreth

Supersonic Biplane Design via Adjoint Method
:
Rui Hu
In developing the next generation supersonic transport airplane, two major
challenges must be resolved. The fuel efficiency must be significantly
improved, and the sonic boom propagating to the ground must be dramatically
reduced. Both of these objectives can be achieved by reducing the shockwaves
formed in supersonic flight. The Busemann biplane is famous for using
favorable shockwave interaction to achieve nearly shockfree supersonic flight
at its design Mach number. Its performance at offdesign Mach numbers,
however, can be very poor.
We study the performance of supersonic biplane airfoils at design and
offdesign conditions. The choked flow and flowhysteresis phenomena
of these biplanes are studied. These effects are due to finite thickness
of the airfoils and nonuniqueness of the solution to the Euler equations,
creating over an order of magnitude more wave drag than
that predicted by supersonic thin airfoil theory. As a result, the offdesign
performance is the major barrier to the practical use of supersonic biplanes.
We improve the offdesign performance of supersonic biplanes using adjoint
based aerodynamic optimization technique. The Busemann biplane is used as
the baseline design, and we alter its shape to achieve optimal wave drags
in series of Mach numbers ranging from 1.1 to 1.7, during both acceleration
and deceleration conditions. The optimized biplane airfoils dramatically
reduces the effects of the choked flow and flowhysteresis phenomena, while
maintaining a certain degree of favorable shockwave interaction effects at the
design Mach number. Compared to a diamond shaped single airfoil of the same
total thickness, the wave drag of our optimized biplane is lower at almost all
Mach numbers, and is significantly lower at the design Mach number. In
addition, by performing a NavierStokes solution for the optimized airfoil,
we find that the optimized biplane improves the total drag,
including the wave drag and the viscous drag, compared to a single diamond
airfoil.

Adjoint method and Modelling of Turbulent Flow Transition
:
JenDer Lee

Threedimensional Spectral Difference Highorder Accurate Unstructured
Compressible Viscous Solver with Shock Capturing Ability and Large Eddy
Simulation:
Chunlei Liang
The Spectral Difference (SD) method combines the salient feautures of
structured and unstructured grid methods to achieve high computational
efficiency and geometric flexibility. Similar to the discontinuous Galerkin
(DG) and spectral volume (SV) methods, the SD scheme achieves highorder
accuracy by locally approximating the solutions as a high degree polynomial
inside each cell. Onedimensional Riemann solvers are employed to deal with the
levels of interface jumps. Most importantly, being based on the differential
form of the equations, SD formulation is simpler than that of the DG and SV
methods as no test function or surface integral is involved. Conservation
properties are still maintained by a judicious placement of the nodes at
quadrature points of the chosen unstructured simplex.
SD method is also being applied to study a few classical turbulent flow
simulation testing cases.

Edgebased Meshless Methods for Compressible Flow Simulations
:
Aaron Katz

Development of a highorder spectral difference method for fluidstructure interaction and computational flapping wing aerodynamics:
Kui Ou

Implicit and pmultigrid method for the spectral difference unstructured
compressible viscous solver:
Sachin Premasuthan
The convergence of Spectral Difference method for viscous NavierStokes
equations can be accelerated using both implicit LowerUpper Symmetric
GaussSeidl (LUSGS) relaxation method and pmultigrid approach. Blending
implicit and pmultigrid approaches, the speedup is achieved in the order of 10
to 100.

Time Spectral Method for Rotorcraft Flow with Vorticity
Confinement:
Nawee Butsuntorn
By utilizing the periodic nature of the rotorcraft flow field, the Fourier
based Time Spectral method lends itself to rotorcraft simulation and
significantly increases the rate of convergence compared to traditional
implicit time integration schemes such as the second order backward difference
formula (BDF). Simulation of helicopter flows can adhere to engineering
accuracy without the need of massive computing resources or long turnaround
time by choosing an alternative framework for rotorcraft simulation. The method
works in both hovering and forward flight regimes and has shown to be more
computationally efficient and sufficiently accurate.
A Vorticity Confinement method is under investigation and has been shown to
work well in subsonic and transonic simulations. Vortical structure can be
maintained after long distances without resorting to the traditional mesh
refinement technique.

Multidisciplinary Design Optimization (MDO) of Supersonic Business Jet
using Approximation Models:
Hyoung S. Chung
The recent growth of MDO concept to exploit the synergism of mutually
interacting phenomena among different disciplines increases the computational
burden and complexity of the design process. To solve these problems, an
alternative using approximation models to the actual highfidelity analysis
code is getting increased attention as a necessity of MDO process. Currently,
the advantages and disadvantages of various approximation models such as
Response Surface and Kriging methods are being investigated. Research focuses
on improving those methods so that they can be effectively incorporated in MDO
process for aircraft design.

Parallel Unstructured AMR Scheme in Quiet Supersonic Platform
Configuration:
Seongim Choi
Adaptive mesh refinement (AMR) is an advanced numerical technique gaining
popularity in the scientific and engineering computing community for solving
largescale computing problems. The use of AMR techniques can significantly
improve computational efficiency, and computer memory efficiency, by devoting
finite computing resources (CPU time, memory) to the computational regions
where they are most needed, making it possible to compute an accurate numerical
solution with much less computing resources comparted to the use of a global
fine mesh.

Computational Aeroelasticity in Turbomachinery:
Hirofumi Doi
Dynamic aeroelastic phenomenon such as flutter in Turbomachinery will be
simulated by performing fluid/structural coupled computations. Combination of
an unsteady flow solver for turbomachinery called TFLO and a finite element
structural solver has been developed through transformation of loads and
energy, deformation tracking mesh system, high order synchronization between
the two solvers, etc.

The OneEquation SpalartAllmaras Turbulence Model:
Kaveh Hosseini
The SpalartAllmaras model is an eddy viscosity model. The eddy viscosity is
directly solved from a transport equation rather than solving the kinetic
energy of turbulence k, or any other quantity proportional to k, and defining
eddy viscosity from it. Research focuses on a robust implementation of the
OneEquation SpalartAllmaras Turbulence Model in the 2D NavierStokes flow
solver FLO103. The main difficulty is that this turbulence model's convergence
is very sensitive especially in the case of explicit flow solvers.

An ImplicitExplicit Hybrid Scheme for Calculating Complex Unsteady Flows:
John Hsu
In current practice, unsteady flow simulations for turbomachinery are performed
using a dualtimestepping scheme. This work is motivated by the need to solve
the timeaccurate NavierStokes equations with greatly decreased computational
cost. The purpose of this research is to investigate the introduction of an
initial ADI step, guaranteeing second order accuracy in time, followed by a
small number of cycles of the dualtimestepping scheme augmented by multigrid.
The O(delta t^2) accuracy in time should be retained without the need for large
numbers of inner iterations required for convergence of typical iterative
methods. The details of this new scheme are presented in this research while
examples are given to demonstrate the second order accuracy and the convergence
properties of the scheme.

Design Optimization of HighLift configurations Using a Viscous
AdjointBased Method:
Sangho Kim
Current research focuses on twodimensional highlift aerodynamic optimization
using a continuous adjoint method. The adjoint method is extremely efficient
since the computational expense incurred in the calculation of the complete
gradient with respect to an arbitrary number of design variables is effectively
independent of the number of design variables. Aerodynamic design using the
Reynolds Averaged NavierStokes equations as the flow model has recently been
performed for a single element airfoil and the accuracy of the gradient
information from this method has also been proved.

NonLinear Frequency Domain Method in 3D:
Ki Hwan Lee
The main focus of this work is to apply Frequency Domain Method (FDM) to the
nonlinear unsteady flow solver in 3D. The ability to calculate rough
approximations in 3D, comparable to the accuracy of experimental data, would
allow us the initial data that are theoretically solid and at the same time,
render faster convergence to steady state.

Reduced Order Modeling:
Patrick LeGresley
Research focuses on the development of reduced order models for use in design
and optimization. To be computationally feasible the order of some systems,
such as an aeroelastic system with millions of degrees of freedom, may need to
be reduced. I am currently investigating the use of Proper Orthogonal
Decomposition (POD) as a means to construct linear based models, with the
ultimate goal of applying these models to Aerodynamic Shape Optimization (ASO)
and Multidisciplinary Design Optimization (MDO) problems.

Aerodynamic Shape Optimization of Wings including Planform Variations:
Kasidit Leoviriyakit
Current reseach focuses on the formulation of optimization techniques based on
control theory for aerodynamic shape design in inviscid compressible flow
modeled by the Euler equations. The design methodology has been extended to
include wing planform optimization. A model for the structure weight has been
included in the design cost function to provide a meaningful design. A
practical method to combine the structural weight into the design cost function
has been studied. Results of optimizing a wingfuselage of a commercial
transport aircraft show a successful trade of planform design, leading to
meaningful designs. The ongoing results also support the necessity of
including the structure weight in the cost function.

Multidisciplinary Optimization:
Joaquim Martins
Research is in the area of multidisciplinary optimization applied to aircraft
design. The focus is on the use of highfidelity models in aerodynamic and
structural analysis and on the coupling of these two disciplines. Efficient
calculation of sensitivities in these analyses is also part of this research.

Computational Methods for Analysis and Design of Aircraft:
Georg May
Research focuses on computational methods for the design of aircraft, such as
aerodynamic shape optimization via control theory, using the adjoint method,
and advanced techniques in computational fluid dynamics. It involves topics
related to multigrid methods in an unstructured mesh environment. In particular an efficient algorithm for the automatic generation of a sequence of coarse
meshes from a given fine mesh, which at the same time allows a control of the
quality of the meshes, has been developed, implemented and tested. This
algorithm is based on the edge collapsing technique, which uses repeated
deletion of edges and update of the data structure for a given mesh to achieve
a well controlled coarsening. It also investigate techniques for mesh
optimization.

Unsteady NavierStokes Computations:
Matt McMullen
Research focuses on the efficient computation of solutions to the unsteady
NavierStokes equations. Current focus is on the application of harmonic
balance techniques to steady state solvers. Efficiency comparisons will
be generated between frequency and time domain computations. The research
will generate a new class of solvers which will be validated on low Reynolds
number flows.

Aerodynamic Shape Optimization Techniques Based on Control Theory:
Siva Nadarajah
Research focuses on the following three topics. First, the study of the
tradeoff between the complexity of the discretization of the adjoint equation
for both the continuous and discrete approach, the accuracy of the resulting
estimate of the gradient, and its impact on the computational cost to approach
an optimum solution. Second, the development of the unsteady adjoint equation.
Optimal control of time dependent trajectories require the solution of the
adjoint equation in reverse time from a final boundary condition. The research
will produce unsteady adjoint algorithms for the optimization of a blade shape
for a helicopter rotor to minimize the average drag over a complete revolution.
Similar techniques can also be used to reduce radiated noise from aircraft
engines. Third, the development of an adjoint method for the calculation of
noncollocated sensitivities in supersonic flow. The goal is to develop a set
of discrete adjoint equations and their corresponding boundary conditions in
order to quantify the influence of geometry modifications on the pressure
distribution at an arbitrary location within the domain of interest.

Surf the NonLinear Wave:
Sriram Shankaran
Develop a numerical wind tunnel facility to predict the physics of tightly
coupled aerodynamic and flexible membranes. Using this tool as a "sensor" in a
design loop, "shape" changes to the membrane are estimated, thereby achieving
desired performance goals. The eventual aim of this research is to develop a
robust design methodology for flexible membranelikestructures under the
influence of aerodynamic forces, with possible applications to the design of
sails for shortboards or yachts.

Aeroelasticity, Viscous Simulations, and Automatic Mesh Generation:
Ryan Vartanian
Research investigates methods for automatic mesh generation around arbitrary
shape configurations. Complex configurations (such as high lift systems,
automobiles, etc.) currently present immense difficulties to researchers in
computational aerodynamics due to mesh generation problems. Programs like
CART3D allow for solution of these configurations for the Euler equations.
However, solutions for the NavierStokes equations require fine mesh resolution
near the boundary, and cartesian methods often require a prohibitive number of
cells to accurately resolve boundary layer effects. This research is in the
process of developing a solution to this problem by generating bodyfitted
unstructured meshes that have desirable orthogonality, smoothness, and cell
volume properties. This algorithm is currently in its early stages, but the
current methods look promising.