NIA CFD Seminar, Season 1 (20112012)
[ These seminars were not webcast, but presentation files are available. ]

08282012, Christian Huettig
An Improved Formulation for the NavierStokes Equations with Variable Viscosity
08212012, Young Ju Lee
An Application of Multigrid Methods for the Simulation of NonNewtonian Fluid Flows
04242012, Travis Fisher
Entropy Stable High Order Finite Difference Schemes for Finite Domain Compressible Flows
04102012, Yi Liu
Rotorcraft Noise Prediction with Coupled Multidisciplinary Methods
03272012, Qiqi Wang
Computational Sensitivity Analysis of Chaotic Dynamical Systems
03132012, Balaji Shankar Venkatachari
The Spacetime Conservation Element and Solution Element (CESE) Numerical Framework
02282012, Mark H. Carpenter and Nail Yamaleev
Recent Advances for EnergyStable WENO Schemes
02142012, Wei Liao
Challenges in BoundaryLayer Stability Analysis Based On Unstructured Grid Solutions
01312012, Sriram K. Rallabhandi
Coupled CFD/Sonic Boom Adjoint Methodology and its Application to Aircraft Design
01172012, LiShi Luo
Kinetic Methods for CFD
12132011, Lian Duan
Direct Numerical Simulation and Large Eddy Simulation of Hypersonic Turbulent Flows
11292011, Elbert Jeyapaul
Turbulent Flow Separation in Threedimensional Asymmetric Diffusers
11152011, Christian Huettig
Finite Volume discretization on irregular Voronoi Grids
11012011, Hiro Nishikawa
Robust and Accurate Viscous Discretization by Hyperbolic Recipe
10182011, Boris Diskin
Mesh Effects on Accuracy of FiniteVolume Discretization Schemes
10042011, Hiro Nishikawa
FirstOrder Hyperbolic System Method

08282012
11:00am  noon
NIA Room 101
An Improved Formulation for the NavierStokes Equations with Variable Viscosity
We present a new formulation of the incompressible NavierStokes equations with variable viscosity. By utilizing the incompressibility constraint to remove the trace from the deviatoric stress tensor, we eliminate secondorder crossderivatives of the velocity field, simplifying and improving the accuracy of colocated discretization techniques on both structured and unstructured grids. This formulation improves the performance of SIMPLEtype algorithms that use sequential massmomentum
iterations to enforce incompressibility. A tracefree stress tensor also removes a typical source of netrotation for simulations employing freeslip boundary conditions in spherical geometry. We implement the new scheme as a modification of an existing Boussinesq convection code, which
we benchmark against analytical solutions of the Stokes problem in a spherical shell with both constant and radially dependent viscosity, and timedependent thermal convection at infinite Prandtl number with large viscosity contrasts.
Speaker Bio:

Dr. Christian Huettig received his Ph.D. in geophysics at the University of Muenster in 2010.
He earned his FHDiploma in Computer Science at the University of Applied Sciences, Mittweida,
and at the University of Applied Sciences, Zwickau. His area of expertise is finitevolume discretizations,
unstructured grids, image processing, high performance computing, and dynamic viscosities.
In March of 2011, he joined NIA and Hampton University's Atmospheric & Planetary Sciences department
working with Professor William B. Moore as a Postdoctoral Fellow.

Relevant Publications:

Christian Huettig, Nicola Tosic, William B. Moore,
An improved formulation for the incompressible NavierStokes equations with variable viscosity,
submitted to Physics of the Earth and Planetary Interiors.
[ preprint ]



08212012
11:00am  noon
NIA Room 101C
An Application of Multigrid Methods for the Simulation of NonNewtonian Fluid Flows
We shall present several applications of efficient and fast algorithms based on Multigrid Methods to simulate the nonNewtonian fluid flows. We discuss a novel numerical method designed by Xu and Lee (2004) and its improvement due to Li and Lee (2011) that can be used to handle the ratetype nonNewtonian equations in a unified and stable manner. We show how multigrid methods can be effectively used to solve the resulting discrete models. Various reallife applications as well as theoretical results will be presented. We shall present some enhancement of the methods developed using the parallel computing techniques as well jointly done with Leng Wei, Chensong Zhang.
Speaker Bio:

Dr. Young Ju Lee is Assistant Professor of
Department of Mathematics, Rutgers, the State University of New Jersey. He obtained PhD in Mathematics from the Pennsylvania State University in 2004. He worked as Assistant Researcher and Assistant Adjunct Professor in Mathematics Deptpartment at UCLA from 2004 to 2007. His research interests include
computational mathematics and numerical methods for partial differential equations, with a particular focus on
flow instabilities in complex fluids and material sciences.
[ Home Page ]

Relevant Publications:

Y.J. Lee, W. Leng, and C.S. Zhang, A SCALABLE AUXILIARY SPACE PRECONDITIONER FOR HIGHORDER FINITE ELEMENT METHODS, submitted, 2012.
[ pdf ]
Y.J. Lee, J. Xu, and C.S. Zhang, Stable Finite Element Discretizations for Viscoelastic Flow Models, Handbook of Numerical Analysis, Vol 16 (2011).
[ pdf ]



04242012
11:00am  noon
NIA Room 137
Entropy Stable High Order Finite Difference Schemes for Finite Domain Compressible Flows
High order methods often exhibit unstable behavior when simulating underresolved
gradients or shocks. Summationbyparts finite difference operators applied in
an energy stable fashion have been used to overcome some types of instability,
but the energy analysis relies on a linearization of the governing equations.
This type of analysis is not appropriate when discontinuities are admitted in
the solution. Using Burgers equation as a model, a nonlinear entropy analysis
has been used to construct entropy stable WENO finite difference operators
on bounded domains. These operators are provably stable even for
discontinuous solutions. This methodology is extended to the Euler and
Navier Stokes equations. New entropy stable WENO finite differences
have been constructed along with narrow stencil, high order entropy
stable viscous terms. The new schemes are applied to various
structured multiblock configurations and are shown effectively simulate
unsteady flows in moderately complex configurations that exhibit
significant vortical and/or shock structures. Additionally, for
smooth problems these methods do not exhibit a degraded order of accuracy
on generalized curvilinear grids.
Speaker Bio:

Mr. Fisher is a PhD candidate in the School of Mechanical Engineering
at Purdue University and works as a coop mechanical engineering in
the Computational AeroSciences Branch at NASA Langley Research Center.
He received his Master of Science in Mechanical Engineering from Purdue in 2009,
and his BSME with emphasis in computational engineering from Utah State University
in 2007. Mr. Fisher's primary research is Direct Numerical Simulations and
Implicit Larger Eddy Simulations of transitional and turbulent flows,
with a focus on stable and accurate high order numerical methods at all
compressible speed regimes. 


04102012
11:00am  noon
NIA Room 101C
Rotorcraft Noise Prediction with Coupled Multidisciplinary Methods
A physicsbased, systematically coupled, multidisciplinary prediction tool (MUTE) for rotorcraft noise is developed and validated with a wide range of flight configurations and conditions. MUTE is an aggregation of multidisciplinary computational tools that accurately and efficiently model the physics of the source of rotorcraft noise, and predict the noise at farfield observer locations. It uses systematic coupling approaches among multiple disciplines including Computational Fluid Dynamics (CFD), Computational Structural Dynamics (CSD), and highfidelity Acoustics. Within MUTE, advanced highorder CFD tools are used around the rotor blade to predict the transonic flow (shock wave) effects, which generate the highspeed impulsive noise. Predictions of the bladevortex interaction noise in low speed flight are also improved by using the Particle Vortex Transport Method (PVTM), which preserves the wake flow details required for blade/wake and fuselage/wake interactions. The accuracy of the source noise prediction is further improved by utilizing a coupling approach between CFD and CSD, so that the effects of key structural dynamics, elastic blade deformations, and trim solutions are correctly represented in the analysis. The blade loading information and/or the flow field parameters around the rotor blade predicted by the CFD/CSD coupling approach are used to get the acoustic signatures on the farfield observer locations with a highfidelity noise propagation code (PSUWOPWOP). The predicted results from the MUTE tool for rotor blade aerodynamic loadings and farfield acoustic signatures are compared and validated with a variation of experimental data sets, such as DNW test data, and HART II test data.
Speaker Bio:

Dr. Yi Liu is currently a senior research engineer at the
National Institute of Aerospace resident in NASA Langley Research Center. Dr. Liu obtained
his Ph.D in Aerospace Engineering from Georgia Institute of Technology at Atlanta in
May 2003. His current research projects are in the following areas: Rotorcraft
aerodynamic analysis and acoustic prediction; Microair vehicle and flapping
wing aerodynamics and numerical simulations ; Fixed wing aerodynamic analysis
and application of circulation control techniques , and Jet engine compressor
aerodynamic analysis and highfidelity blade design method.
[ Home Page ]



03272012
11:00am  noon
NIA Room 137
Computational Sensitivity Analysis of Chaotic Dynamical Systems
Computational sensitivity analysis has many applications, including
aerodynamic optimization, optimal control, inverse problems, data
assimilation, uncertainty quantification, and adaptive mesh
refinement. Popular methods for sensitivity analysis include the
tangent linear method and the adjoint method. In chaotic dynamical
systems, such as turbulent flows, aeroelastic oscillations, and the
weather system, many quantities of interest are time averages, a.k.a.
"climate" quantities. When computing sensitivity of these time average
output quantities, conventional methods, including tangent and adjoint
methods, suffer from a fundamental failure. The computed sensitivity
can be orders of magnitude larger than the true value.
This talk discusses the cause of the divergence of computed
sensitivity in chaotic dynamical systems, and present two new
computational algorithms for sensitivity analysis, designed to
overcome this challenge. The first algorithm uses the Lyapunov
spectrum decomposition; the second algorithm uses a constraint least
squares formulation for sensitivity analysis. Both algorithms are
computationally efficient, and produce good estimates of sensitivity
derivatives. We will present the computational result of these
algorithms for several chaotic dynamical systems. In addition to their
computational application, these algorithms also provide new
theoretical insights into the effect of perturbations in chaotic
dynamical systems, which could lead to answers to many practical
questions, such as "When LES is a reasonable approximation of DNS?".
Speaker Bio:

Dr. Qiqi Wang is Assistant Professor of Aeronautics and Astronautics
in Massachusetts Institute of Technology. His areas of expertise include design, optimization and
uncertainty quantification, unsteady flows, aeroelastics and aeromechanics, computational sensitivity analysis.
[ Home Page ]



03132012
11:00am  noon
NIA Room 137
The Spacetime Conservation Element and Solution Element (CESE) Numerical Framework
The spacetime conservation element and solution element (CESE) method is a novel highresolution, truly multidimensional numerical framework for solving the conservation laws, that has been developed by Dr. S.C. Chang and his coworkers at the NASA Glenn Research center. It is substantially different, in both concept and approach, from wellestablished methods such as the finitedifference, finitevolume methods etc. Its two main tenets are that (i) it treats space and time in a unified manner and thereby ensures conservation of flux, local as well as global, in both space and time; (ii) the core of the scheme is a nondissipative scheme, allowing for dissipative extensions to be built in a manner that can be justified mathematically without degrading the numerical accuracy. Its other features include the following: (i) use of a spacetime staggered stencil that allows for evaluation of fluxes at the cell interfaces without solving the Riemann problem; (ii) treating mesh values of the flow variables and their spatial derivatives as independent unknowns; (iii) for flows in multiple spatial dimensions, no directional splitting is employed, leading to a truly multidimensional scheme and (iv) naturally built for unstructured meshes (triangles and tetrahedrons). Since its inception, the CESE method has been successfully adapted to model various physical phenomena that include unsteady inviscid and viscous flows, CAA problems, traveling and interacting shocks, detonation waves, MHD vortex, hydraulic jump, crystal growth, chromatographic problems etc. The talk will mainly concern about all the foundational aspects of the framework, along with details on its error and stability analysis. The talk will also cover some of the newer developments in the framework such as higherorder schemes that shares the same stencil and stability constraints as the original scheme (2nd order accurate in space and time) and timeaccurate local timestepping procedures. Details on existing challenges and ongoing work will also be discussed.
Speaker Bio:

Dr. Balaji Shankar Venkatachari is currently a postdoctoral fellow at the University of Alabama at Birmingham and a resident at the NASA Langley Research Center in the Computational AeroSciences Branch. Dr. Venkatachari obtained his Ph.D. in Interdisciplinary Engineering from the University of Alabama at Birmingham in 2010 and received his Bachelors from Pondicherry University, India in 2001. His research interests include numerical algorithm development, Hypersonics, TPS modeling (continuum and multiscale modeling), and CAA.

Relevant Publications:

Link to CESE Home page
Link to an opensource code based on CESE
1. Chang, S. C., The Method of SolutionTime Conservation Element and Solution Element  A New Approach for Solving the NavierStokes and Euler Equations, Journal of Computational physics, 119, 295324, 1995.
2. Wang, X. Y. and Chang, S. C., A 2D NonSplitting Unstructured Triangular Mesh Euler Solver Based on the
SpaceTime Conservation Element and Solution Element Method, Computational Fluid Dynamics Journal, vol.8 no.2,
July 1999.
3. Zhang, Z.C., Yu, S. T. J., and Chang, S. C., A SpaceTime Conservation Element and Solution Element Method for Solving the Euler Equations Using Quadrilateral and Hexahedral Meshes, Journal of Computational Physics, 175, 168199, 2002.
4. Chang, S. C., Himansu, A., Loh, C. Y., Wang, X. Y., Yu, S. T., and Jorgenson, P., Robust and Simple NonReflecting Boundary Conditions for the SpaceTime Conservation Element and Solution Element Method, Technical Paper 2077
(AIAA Press, Washington, DC 1997).
5. Venkatachari, B., Cheng, G. C., Soni, B. K., and Cang, S. C., Validation and VErification of Courant Number
Insensitive CE/SE Method for Transient Viscous FLow Simulations, Mathematics and Computeres in SImulation,
Vol. 78, Issue 56, September 2008, pp 653670
6. Chang, C.L., ThreeDimensional NavierStokes Calculations Using the Modified SpaceTime CESE Method, AIAA 20075818.
7. Yen, Joseph C., Duell, Edward G., and Martindale, William, CAA Using 3D CESE Method with a Simplified Courant Number Insensitive Scheme, AIAA 20062417.
8. Chang, S.C., A New Approach for Constructing Highly Stable High Order CESE Schemes, AIAA 2010543.
9. Bilyeu, D.L., Chen,Y.Y., and Yu, S.T.J., Highorder CESE Methods for the Euler Equations, AIAA 20110298.
10. Chang, S.C., Wu, Y., Yang, V., and Wang, X.Y., Local TimeStepping Procedures for the SpaceTime Conservation
Element and Solution Element Method, Inter. J. of Comput. Fluid Dyn., Vol. 19, No. 5, pp. 359380, July 2005.
11. Yen. Joseph C., " Demonstration of a MultiDimensional TimeAccurate Local TimeStepping CESE Method," AIAA 20112755.



02282012
11:00am  noon
NIA Room 137
Recent Advances for EnergyStable WENO Schemes
Weighted Essentially NonOscillatory (WENO) schemes are routinely used to perform high resolution simulations of canonical problems containing discontinuities. Because conventional WENO formulations rely on structured meshes, extension to complex geometries is problematic. Herein, we demonstrate a general multiblock WENO capability, based on uniformly accurate fourthorder and sixthorder, finitedomain, Energy Stable WENO (ESWENO) operators. The new ESWENO operators feature boundary closures that maintain design accuracy, conservation and L2 stability, while accommodating full WENO stencil biasing. Test cases are presented that demonstrate the efficacy of the new approach.
[ presentation file (pdf) ] 
Mark H. Carpenter Nail Yamaleev 
Speaker Bio:

Dr. Mark H. Carpenter is a Senior Research Scientist at Computational Aerosciences Branch of NASA Langley Research Center. His areas of expertise include highorder methods in CFD, stability of numerical schemes, and unsteady flow computations.
Dr. Nail K. Yamaleev is an Associate Professor of Mathematics at North Carolina A&T State University. He is an expert in adjointbased methods for timedependent optimization problems, grid adaptation methods, highorder schemes for the NavierStokes equations, and reducedorder modeling.

Relevant Publications:

T. Fisher, M.H. Carpenter, N. K. Yamaleev, S. Frankel, Boundary closures for 4thorder Energy Stable WENO finite difference schemes,
J. of Computational Physics, Vol. 230, No. 10, pp. 37273752, 2011.
[ online ]
N. K. Yamaleev and M. H. Carpenter, A systematic methodology for constructing highorder energy stable WENO schemes, J. of Computational Physics, Vol. 228, No. 11, 2009.
[ online ]
N. K. Yamaleev and M. H. Carpenter, Thirdorder energy stable WENO scheme, J. of Computational Physics, Vol. 228, No. 8, pp. 30253047, 2009.
[ online ]



02142012
11:00am  noon
NIA Room 137
Challenges in BoundaryLayer Stability Analysis Based On Unstructured Grid Solutions
The reduction of vehicle drag can directly result in the decrease of the aircraft fuel burn. Since the laminar skin friction is generally much lower than its turbulent counterpart, reducing drag by controlling the amount of laminar flow over a wing surface offers potential improvements in fuel efficiency, range and payload. Crossflow instability of threedimensional boundary layers is a common cause of flow transition in sweptwing flows. Since the air turns due to wing sweep and pressure gradient, it is challenging to maintain laminar flows over a swept wing because of the crossflow effect. Discrete Roughness Elements (DRE) technology has been shown to work effectively for controlling the crossflowinduced transition at relativelty low Reynolds numbers. Tests and applications of a laminar flow wing with the feature of microscale roughness are being carried out for higher Reynolds nubmbers under real transonic flight conditions, which are based on a modified Gulfstream III (G3) aircraft with a gloved wing.
In the present research, the fully unstructured NavierStokes solver FUN3D is used for threedimensional computational fluid dynamics (CFD) analysis of the G3 aircraft with the gloved wing. A direct extraction of boundarylayer profiles, which are required for mean flow input to stability analysis, from unstructured CFD solutions is not a trivial task. The objectives of the current effort include: 1) Develop a flow stability analysis procedure based on the unstructured grid strategy and implement it to the NASA inhouse code, FUN3D, and LASTRAC; 2) Couple it with the adjoint capability of FUN3D for laminar flow control, design and optimization of lowdrag aircraft wings under realistic flight conditions; 3) Apply the developed tools to evaluate the effectiveness of the DRE technology at high Reynolds numbers of relevance to transport aircraft. With some interesting results shown here, the challenges in the extraction of "stabilityquality" mean flows from unstructured grid solutions will also be discussed.
Speaker Bio:

Dr. Wei Liao is currently a research scientist at the National Institute of
Aerospace resident in NASA
Langley Research Center. Dr. Liao obtained his Ph.D. in Mechanical Engineering from National University of Singapore
in Oct. 2004. His research interest include the following general areas:
Flow instability and transition, turbulence modeling and simulation, thermochemical nonequilibrium flows,
bioinspired flows, large scale scientific computation, aerodynamic optimization design,
and the following specific areas: kinetic methods,
multigrid algorithms, overset grid strategy and adjoint equation method.



01312012
11:00am  noon
NIA Room 137
Coupled CFD/Sonic Boom Adjoint Methodology and its Application to Aircraft Design
It is generally realized that optimization using adjoint methodology is a game changing process in the geometry shape
optimization discipline. Within the supersonics community, sonic boom mitigation has been and is a major obstacle.
Previous work on using adjoints to mitigate sonic boom included meeting pressure distribution objectives that were in
the nearfield i.e. closer to the aircraft. This meant that the optimization did not account for sonic boom where it
mattered most  at the ground level. In addition, specification of a target pressure nearfield is problematic for two reasons.
Firstly, one has to make sure that the target is reachable through deformation of the baseline OML; this could take
several trial and error iterations. Secondly, there is no guarantee that the optimizer can find the desired target.
In fact, since adjoints depend on gradient based optimizers, and since there are several local minima in the chosen
objective functions, premature convergence is a known and documented phenomena. Because of the nature of boom
propagation, premature convergence of not reaching the prescribed target can have a negative impact on the sonic
boom at the ground level. This presentation talks about the ongoing work that overcomes these issues by using
objectives based on the sonic boom signature targets or using sonic boom loudness metrics at the ground level.
This not only alleviates the designer of the difficult task of specifying a target nearfield, but also guarantees
that the sonic boom loudness is lesser than the baseline, even under premature convergence conditions.
This is the first work in literature where the a) boom adjoint based on advanced boom propagation is developed, b)
boom adjoint is coupled with CFD adjoint, and c) aircraft outer mold line shaping is performed based on the desired
groundbased metric. This opens the door for various analysis and design possibilities. Some design results and
several interesting extensions will be discussed.
Speaker Bio:

Dr. Sriram Rallabhandi is currently a senior research engineer at the National Institute of Aerospace. He received his Bachelors from Indian Institute of Technology (IIT), Kanpur, India in May 2000, MS and Ph.D. from Georgia Tech in May 2002 and May 2005 respectively, all in Aerospace Engineering. He was the Hampton Roads AIAA Young Engineer of the Year (2010), AIAA Laurence J. Bement Best Paper Award winner (2010) and part of the team that received the NASA Superior Accomplishment Award (2011). His research interests include Aircraft Design, Sonic Boom Reduction, Multidisciplinary Design Optimization (MDO), and Model Order Reduction.

Relevant Publications:

Rallabhandi, S. K., Sonic Boom Adjoint Methodology and its Applications, AIAA20113497
[ First Page ]
Rallabhandi, S. K., Advanced Sonic Boom Prediction Using Augmented Burger's Equation, AIAA20111278
[ First Page ]
Nielsen, E. J., Diskin, B., and Yamaleev, N. K., Discrete AdjointBased Design Optimization of Unsteady Turbulent Flows on
Dynamic Unstructured Grids, AIAA Journal, Vol. 48, No.6, 2010, pp. 11951206. [ pdf available ]



01172012
11:00am  noon
NIA Room 137
Kinetic Methods for CFD
Computational fluid dynamics (CFD) is based on direct discretizations
of the NavierStokes equations. The traditional approach of CFD is
now being challenged as new multiscale and multiphysics problems
have begun to emerge in many fields  in nanoscale systems, the scale
separation assumption does not hold; macroscopic theory is therefore
inadequate, yet microscopic theory may be impractical because it
requires computational capabilities far beyond our present reach.
Methods based on mesoscopic theories, which connect the microscopic
and macroscopic descriptions of the dynamics, provide a promising
approach. Besides their connection to miscroscopic physics, kinetic
methods also have certain numerical advantages due to the linearity of
the advection term in the Boltzmann equation. We will discuss two
mesoscopic methods: the lattice Boltzmann equation and the gaskinetic
scheme, their mathematical theory and their applications to simulate
various complex flows.
Speaker Bio:

Dr. LiShi Luo is the Richard F. Barry Distinguished Professor of
Mathematics and Statistics at Old Dominion University. His research interests include kinetic theory
and nonequilibrium statistical mechanics, lattice Boltzmann equation and CFD, complex fluids.



12132011
11:00am  noon
NIA Room 137
Direct Numerical Simulation and Large Eddy Simulation of Hypersonic Turbulent Flows
The development of predictive CFD tools is critical for the design of next generation highspeed vehicles for routine and affordable rapid global transport and space exploration. So far, we have only limited understanding of the intricate interaction between turbulence and many important flow processes typical of highspeed flows, such as shock wave turbulent boundary layer interaction and flowsurface interaction. In turn, the lack of physicsbased turbulence models results in excessive skepticism and unrefined, costly engineering designs. Highfidelity simulations like direct numerical simulations (DNS) and largeeddy simulations (LES) provide a vast amount of accurate and detailed turbulence data that can be used to study critical fundamental phenomena and to develop physicsbased models.
In this talk, newly developed DNS and LES methodologies are introduced for highspeed turbulent flows. These numerical tools are capable of capturing flow features across a wide range of length and time scales, thus robust for a broad range of turbulent flow conditions, including flows containing shock waves, chemical reactions, radiation, and surface interactions. The talk will focus on applying these multiscale, multiphysics tools to investigate the interaction of riblet surface with the overlying turbulent flow which reduces drag and surface heating. If time permits, other flow features explored using these tools will also be covered.
Speaker Bio:

Dr. Lian Duan is currently a research scientist at the National Institute of Aerospace based in NASA Langley Research Center. He received his Ph.D. in Mechanical and Aerospace Engineering (MAE) from Princeton University in May 2011. He was the recipient of Princeton Graduate Fellowship (2005 2006) and Princeton MAE Crocco Award for Teaching Excellence (Fall, 2008). His research interests include highspeed transitional and turbulent flows, airbreathing propulsion, laminar and turbulent flow control, and high performance computing. 


11292011
11:00am  noon
NIA Room 137
Turbulent Flow Separation in Threedimensional Asymmetric Diffusers
Threedimensional flow separation in asymmetric diffusers has been a challenge to predict by Linear EddyViscosity Turbulence Models (LEVM), as they are qualitatively incorrect. The work is motivated by
the need for a detailed study of 3D separation in asymmetric diffusers, to understand the separation phenomenon, assess the predictability of existing RANS models, and propose modeling refinements.
Timeresolving simulations show several mean streamwise vortices that originate from singular wall stress locations and interact downstream. Explicit Algebraic Reynolds Stress Model (EARSM) predicts the separation adequately as they resolve the turbulence anisotropy; however improvements are required to predict the Reynolds stresses accurately. The sensitivity of LEVM and EARSM to transverse effects is studied by generating a series of diffusers having the same streamwise pressure gradient and parameterized by diffuser inlet aspect ratio. Analyzing the secondary flow field and comparing with LES results has helped identify inadequacies and propose modeling refinements to EARSM, thus accurately predicting the pressure recovery
and mean flow field.
Speaker Bio:

Dr. Elbert Jeyapaul is a NASA postdoctoral fellow at Langley research center.
He earned his PhD in Aerospace engineering from Iowa state university in August 2011.
His area of expertise is in Flow separation, Singlepoint turbulence modeling and LES.

Relevant Publications:

E. Jeyapaul and P Durbin, Threedimensional turbulent flow separation in diffusers, AIAA2010918, 48th AIAA Aerospace sciences meeting, January 2010, Orlando.
E. Jeyapaul and P Durbin, Separation in a family of 3D asymmetric diffusers, Flow, Turbulence and Combustion Journal, submitted.



11152011
11:00am  noon
NIA Room 137
Finite Volume discretization on irregular Voronoi Grids
This talk focuses on a formulation to discretize the NavierStokes equations with a FiniteVolume method (FVM) on Voronoi grids. These grids provide some unique geometrical properties that suit the FVM and are straight forward to implement, other properties require special care. The code developed upon this method is used to model mantle convection in a spherical shell in 3D. The challenge for these models is the viscosity variation that can reach several orders of magnitude. Another aspect of this talk will be efficient parallelization of spherical grids and whether we can use pressure decoupling methods like SIMPLE* as carefree as literature suggests.
Speaker Bio:

Dr. Christian Huettig is a Postdoctoral Associate at NIA.
His area of expertise is finitevolume discretizations, unstructured grids, and dynamic
viscosities.

Relevant Publications:

Huettig, C., Stemmer, K., Finite volume discretization for dynamic viscosities on Voronoi grids, Physics of the Earth and Planetary Interiors (2007) [ online ]
Huettig, C., Stemmer, K., The spiral grid: A new approach to discretize the sphere and its application to mantle convection, Geochem. Geophys. Geosyst., 9, Q02018, 2008
[ online ]
Huettig, C., Breuer, D., Regime classification and planform scaling for internally heated mantle convection, Physics of the Earth and Planetary Interiors, Volume 186, Issues 34, June 2011, Pages 111124



11012011
11:00am  noon
NIA Room 137
Robust and Accurate Viscous Discretization by Hyperbolic Recipe
This talk will discuss robust and accurate viscous discretizations for unstructured grids.
It is proposed that robust and accurate viscous schemes consist of two terms: consistent and damping terms.
The former is responsible for approximating the viscous term consistently.
The latter is required for the highfrequency error damping, which is critical to robustness and accuracy on
unstructured grids. A simple recipe for constructing viscous schemes equipped with effective
damping terms will be presented. The recipe is to derive a viscous scheme from an inviscid scheme (e.g., upwind) applied to
an equivalent hyperbolic system for the viscous term.
Numerical results will be presented to demonstrate the significant impact
of the damping term on highlyskewed irregular grids.
Speaker Bio:

Dr. Hiro Nishikawa is a senior research scientist at NIA. He earned Ph.D. in Aerospace Engineering and
Scientific Computing at University of Michigan in 2001. He joined NIA in 2007, and has been working
on the agglomeration multigrid method for unstructured 3D RANS solvers. His area of expertise is the fundamental algorithm
development for CFD, currently focusing on multigrid and viscous discretization methods.
[ Home Page ]



10182011
11:00am  noon
NIA Room 137
Mesh Effects on Accuracy of FiniteVolume Discretization Schemes
This study considers the effects of mesh irregularities on accuracy of unstructured nodecentered finitevolume discretization schemes. Three classes of meshes are considered: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancinglayer grids. The mesh quality within the classes ranges from high for regular meshes to extremely low for irregular meshes including random perturbation of mesh nodes. For inviscid fluxes, the considered novel efficient edgebased finitevolume discretization scheme uses a leastsquares gradient reconstruction with a quadratic fit and is nominally third order on general triangular meshes. A common secondorder GreenGauss scheme is considered for viscous fluxes. The effects of mesh irregularity on gradient accuracy, truncation errors, and discretization errors are separately studied. The study will be presented at the session "Grid Quality Metrics Related to Solution Accuracy" at 50th AIAA Aerospace Sciences Meeting, Nashville, TN, January 2012.
Speaker Bio:

Dr. Boris Diskin is an Associate Research Fellow at NIA. He earned Ph.D. in Applied Mathematics at The Weizmann Institute of Science, Israel in 1998. He was a Senior Research Scientist at ICASE and joined NIA from its inception in 2003. His area of expertise is adjointbased optimization and grid adaptation methods, finitevolume discretizations, and multigrid methods. [ Home Page ]

Relevant Publications:

Diskin B. and Thomas J. L., Comparison of nodecentered and cellcentered unstructured finitevolume discretizations: inviscid fluxes, AIAA Journal, 2011, 49(4), pp. 836854
[ pdf ]
Katz A. and Sankaran V., Mesh quality effects on the accuracy of CFD solutions on unstructured meshes, AIAA2011652.
Diskin B., Thomas J. L., Nielsen E. J., Nishikawa H., and White J. A., Comparison of nodecentered and cellcentered unstructured finitevolume discretizations: viscous fluxes, AIAA Journal (2010), 48(7), pp. 13261338.
[ pdf ]
Thomas J. L., Diskin B., and Ramsey C. L., Towards Verification of UnstructuredGrid Solvers, AIAA Journal(2008), 46(12), pp. 30703079
[ pdf ]
Diskin B. and Thomas J. L., Accuracy of Gradient Reconstruction on Grids with High Aspect Ratio, NIA Report 200812.
[ pdf ]
Diskin B. and Thomas J. L., Accuracy Analysis for MixedElement FiniteVolume Discretization Schemes, NIA Report 200708.
[ pdf ]



10042011
11:00am  noon
NIA Room 137
FirstOrder Hyperbolic System Method
This is a story about an idea of numerically solving, ultimately, all partialdifferential equations as hyperbolic systems.
Hyperbolic systems will be presented for the diffusion, the advectiondiffusion, and the compressible NavierStokes
equations. These systems can then be discretized by methods for hyperbolic systems alone. Whatever the discretization
method is, the resulting code will be ordersofmagnitude faster than conventional codes and it will be capable of
computing the diffusive/viscous/heat fluxes to the same order of accuracy as that of the main variables on irregular grids.
This talk will explain how it can be true, present numerical results, and discuss future developments.
Speaker Bio:

Dr. Hiro Nishikawa is a senior research scientist at NIA. He earned Ph.D. in Aerospace Engineering and
Scientific Computing at University of Michigan in 2001. He joined NIA in 2007, and has been working
on the agglomeration multigrid method for unstructured 3D RANS solvers. His area of expertise is the fundamental algorithm
development for CFD, currently focusing on multigrid and viscous discretization methods.
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09202011
11:00am  noon
NIA Room 137
First Organizational Meeting
Boris Diskin


