Research : People : Publications : Seminars Publications of David Darmofal
E.M. Murman, T.M. Becker, D.L. Darmofal. Computational and visualization of leading edge vortex flows. Computing Systems in Engineering, Vol. 1, No. 2-4, 1990. D.L. Darmofal, R. Haimes. An analysis of 3-D particle path integration algorithms. Journal of Computational Physics, Vol. 123, No.1, 1996, pp. 182-195 (also, AIAA 95-1713). D.L. Darmofal. Comparisons of experimental and numerical results for axisymmetric vortex breakdown in pipes. Computers & Fluids, Vol. 25, No. 4, 1996, pp. 353-371. D.L. Darmofal, P.J. Schmid. The importance of eigenvectors for local preconditioning of the Euler equations. Journal of Computational Physics, Vol. 127, September 1996, pp. 346-362 (also, AIAA 95-1656). D.L. Darmofal, K. Siu. A robust, multigrid algorithm for the Euler equations with local preconditioning and semi-coarsening. Journal of Computational Physics, Vol. 151, No. 2, pp. 728-756, 1999, (also, AIAA 98-2428). D.L. Darmofal, P. Moinier, M.B. Giles. Eigenmode analysis of boundary conditions for the one-dimensional preconditioned Euler equations. Journal of Computational Physics, Vol. 160, No.1, pp. 369-384, 2000. D.A. Venditti, D.L. Darmofal. Adjoint error estimation and grid adaptation for functional outputs: Application to quasi-one-dimensional flow. Journal of Computational Physics, Vol. 164, No. 1, pp. 204-227, October 2000. J. Wong, D.L. Darmofal, J. Peraire. The Solution of the compressible Euler equations at low Mach numbers using a stabilized finite element algorithm. Computer Methods in Applied Mechanics and Engineering, Vol. 190, pp. 5719-5737, 2001. D.L. Darmofal, R.J. Khan, E.M. Greitzer, C. Tan. Vortex core behavior in confined and unconfined geometries: A Quasi-one-dimensional model. Journal of Fluid Mechanics, Vol. 449, pp. 61-84, 2001. D.A. Venditti, D.L. Darmofal. Grid adaptation for functional outputs: Application to 2-D inviscid, compressible flow. Journal of Computational Physics, Vol. 176, No. 1, pp. 40-69, 2002. J. Lu, D.L. Darmofal. A Quasi-Minimal Residual method for simultaneous primal-dual solutions and superconvergent functional estimates. SIAM Journal on Scientific Computing, Vol. 24, No. 5, pp. 1693-1709, 2003. D.A. Venditti, D.L. Darmofal. Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows. Journal of Computational Physics, Vol.187, No. 1, pp. 22-46, 2003. V.E. Garzon, D.L. Darmofal. Impact of geometric variability on axial compressor performance. ASME Journal of Turbomachinery, Vol. 125, No. 4, pp. 692-703, October 2003. Also, Proceedings of ASME Turbo Expo, Atlanta, Georgia, Paper No. 2003-GT-38130, June 2003. T.O. Okusanya, D.L. Darmofal, J. Peraire. Algebraic multigrid for stabilized finite element discretizations of the Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, Vol. 193, pp. 3667-3686, August 2004 E.J. Nielsen, J. Lu, M.A. Park, D.L. Darmofal. An Implicit, exact dual adjoint solution method for turbulent flows on unstructured grids, Computers & Fluids, Vol. 33, No. 9, pp. 1131-1155, November 2004. J. Lu, D. L. Darmofal. Higher-dimensional integration with Gaussian weight for applications in probabilistic design. SIAM Journal on Scientific Computing, Special Issue on Uncertainty Quantification, Vol. 26, No. 2, pp. 613-624, 2005. K.J. Fidkowski, T.A. Oliver, J. Lu, D.L. Darmofal. p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. Journal of Computational Physics, Vol. 207, pp. 92-113, 2005. V. Sidwell, D.L. Darmofal. The impact of blade-to-blade variability and assembly on turbine cooling performance. ASME Journal of Turbomachinery, Vol. 127, No. 4, pp. 763-770, October 2005. K.J. Fidkowski, D.L. Darmofal. A triangular cut-cell adaptive method for high-order discretizations of the compressible Navier-Stokes equations. Journal of Computational Physics, Vol. 225, pp. 1653-1672, 2007. T.A. Oliver, D.L. Darmofal. Analysis of dual consistency for discontinuous Galerkin discretizations of source terms. SIAM Journal of Numerical Analysis, Vol. 47, Issue 5, pp. 3507-3525, 2009. L.T. Diosady, D.L. Darmofal. Preconditioning methods for discontinuous Galerkin solutions of the Navier-Stokes equation. Journal of Computational Physics, Vol. 228, No. 11, pp. 3917-3935, 2009. G.E. Barter, D.L. Darmofal. Shock capturing with PDE-based artificial viscosity for DGFEM: Part 1, Formulation. Journal of Computational Physics, Vol. 229, No. 5, pp. 1810-1827, 2010. M.A. Park, D.L. Darmofal. Validation of an output-adaptive, tetrahedral cut-cell method for sonic boom prediction. AIAA Journal, Vol. 48, No. 9, 2010. M. Yano, D.L. Darmofal. BDDC Preconditioning for high-order Galerkin Least Squares methods using inexact solvers. Computer Methods in Applied Mechanics and Engineering, Vol. 199, No. 45-48, 2010. J. Krakos, D.L. Darmofal. Effect of small-scale output unsteadiness on adjoint-based output sensitivity. AIAA Journal, Vol. 48, No. 11, pp.2611-2623, 2010. K.J. Fidkowski, D.L. Darmofal. Review of output-based error estimation and mesh adaptation in computational fluid dynamics. AIAA Journal, Vol. 49, No. 4, pp.673-694, 2011. H. Sun, D.L. Darmofal, R. Haimes. On the impact of triangle shapes for boundary layer problems using high-order finite element discretization. Journal of Computational Physics, Vol. 231, No. 2, pp. 541-557. J. Krakos, Q. Wang, S.R. Hall, D.L. Darmofal. Sensitivity analysis of limit cycle oscillations. Journal of Computational Physics, 2012 (to appear).
D.L. Darmofal, R. Haimes. Visual feature identification for 3-D data sets. 1991 AIAA CFD Conference, AIAA Paper 91-1583. R. Haimes, D.L. Darmofal. Visualization in computational fluid dynamics: a case study. In IEEE Visualization Conference Proceedings, 1991. D.L. Darmofal, R. Haimes. Visualization of 3-D vector fields: variations on a stream. AIAA Aerospace Sciences Conference, 1992, AIAA Paper 92-0074. D.L. Darmofal. The role of vorticity dynamics in vortex breakdown. AIAA 24th Fluid Dynamics Conference, 1993, AIAA 93-3036. D.L. Darmofal, E.M. Murman. On the trapped wave nature of vortex breakdown. AIAA 25th Fluid Dynamics Conference, 1994, AIAA 94-2318. D.L. Darmofal, A.W. Cary, K.G. Powell. Wave propagation and stability characteristics of vortical flows in varying-area pipes. AIAA 1995 Fluid Dynamics conference, AIAA 95-2307. S. Galls, O. Rediniotis, D.L. Darmofal. Development of an interactive, real-time, multimedia flow-diagnostics laboratory. AIAA 1996 Aerospace Sciences Meeting, AIAA 96-0158. D.L. Darmofal. Analysis of a conservation law model for axisymmetric vortices in pressure gradients with applications to vortex breakdown. AIAA 1996 Aerospace Sciences Meeting, AIAA 96-0800. D.L. Darmofal, R. Haimes. Preliminary development of a visual environment for multidisciplinary optimization. AIAA 1996 Fluid Dynamics Conference, AIAA 96-1942. A.W. Cary, D.L. Darmofal, K.G. Powell. Onset of the spiral mode of vortex breakdown. 1997 AIAA Aerospace Sciences Meeting, AIAA 97-0439. A.W. Cary, D.L. Darmofal, K.G. Powell. Evolution of asymmetries in vortex breakdown. 1998 AIAA Aerospace Sciences Meeting, AIAA 98-2904. A.de la Garza, D.L. Darmofal. An All-at-Once approach for multidisciplinary design optimization. 1998 AIAA Applied Aerodynamics Meeting, AIAA 98-2515. D.L. Darmofal. Eigenmode analysis of boundary conditions for the one-dimensional preconditioned Euler equations. NACA/CR-1998-208741, ICASE Report No. 98-51 (also AIAA 99-3352). O. Rediniotis, G. Webb, D.L. Darmofal. Reduced-order transition control via optimal projection. 1999 SPIE Annual International Symposium on Smart Structures and Materials, SPIE Paper No. 3667-74. D.A. Venditti, D.L. Darmofal. A Multilevel error estimation and grid adaptive strategy for improving the accuracy of integral outputs. 1999 AIAA Computational Fluid Dynamics Conference, AIAA Paper No. 99-3292. J. Wong, D.L. Darmofal, J. Peraire. A Galerkin Least Squares algorithm in entropy variables for low Mach number flows. Finite Element in Fluids 2000 Conference, Austin, TX, May 2000. D.A. Venditti, D.L. Darmofal. Grid adaptation for functional outputs of 2-D compressible flow simulations. 2000 AIAA Fluid Dynamics Conference, AIAA Paper No. 2000-2244, Denver, Co, July 2000. D.L. Darmofal, E.M. Murman, M. Love. Re-engineering aerodynamics education. 2001 AIAA Aerospace Sciences Meeting, Reno, NV, January 2001, AIAA Paper No. 2001-0870. A.W. Cary, D.L. Darmofal. Onset of axisymmetric and non-axisymmetric vortex breakdown. AGARD Applied Vehicle Technology Panel (AVT) Symposium on Advanced Flow Management, Loen, Norway, May 2001. D.A. Venditti, D.L. Darmofal. A grid adaptive methodology for functional outputs of compressible flow simulations. 2001 AIAA Computational Fluid Dynamics Conference, AIAA Paper No. 01-2659. D.L. Darmofal, D.H. Soderholm, D.R. Brodeur. Using concept maps and concept questions to enhance conceptual understanding. Proceedings of the 2002 American Society for Engineering Education Annual Conference & Exposition, Montreal, June 2002. Also to appear in 32nd ASEE/IEEE Frontiers in Education Conference, Boston, MA, November 6 - 9, 2002. D.L. Darmofal, D.A. Venditti. A grid adaptive strategy for functional outputs in aerodynamic applications. Fifth World Congress on Computational Mechanics, Vienna, Austria, July 2002. E.J. Nielsen, J. Lu, M.A. Park, D.L. Darmofal. An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids, AIAA-03-0272, January 2003. V. Sidwell, D.L. Darmofal. Probabilistic analysis of a turbine cooling air supply system: the effect on airfoil oxidation life. Proceedings of ASME Turbo Expo, Atlanta, Georgia, Paper No. 2003-GT-38119, June 2003. K.J. Fidkowski, D.L. Darmofal. Development of a higher-order solver for aerodynamic applications. 42nd AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2004-0436, January 2004. J. Lu, D.L. Darmofal. Adaptive precision methodology for flow optimization via output error control. 42nd AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2004-1096, January 2004. V.E. Garzon, D.L. Darmofal. On the aerodynamic design of compressor airfoils for robustness under geometric uncertainty. Proceedings of 2004 ASME Turbo Expo, Vienna Austria, Paper No. 2004-53581. C.M. Lamb, D.L. Darmofal. Performance-based geometric tolerancing of compressor blades. Proceedings of 2004 ASME Turbo Expo, Vienna Austria, Paper No. 2004-53592. V. Sidwell, D.L. Darmofal. A Selective assembly method to reduce the impact of blade flow variability on turbine life. Proceedings of 2004 ASME Turbo Expo, Vienna, Austria, Paper No. 2004-53930. T. Oliver, K.J. Fidkowski, D.L. Darmofal. Multigrid solution of higher-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. International Conference on Computational Fluid Dynamics, Toronto, July 2004. (This paper won the Best Student Paper Award for this conference). D.L. Darmofal, R. Haimes. Towards the next generation in computational fluid dynamics. 43rd AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2005-0087, January 2005. G.Barter, D. Darmofal. Shock capturing with higher-order, PDE-based artificial viscosity. 18th AIAA CFD Conference, Miami, FL, AIAA-2007-3823, June 2007. (This paper won first place in the Best Student Paper competition at this conference.) T.Oliver, D. Darmofal. An unsteady adaptation algorithm for discontinuous Galerkin discretizations of the RANS equations. 18th AIAA CFD Conference, Miami, FL, AIAA-2007-3940, June 2007. K. Fidkowski , D. Darmofal. An adaptive simplex cut-cell method for discontinuous Galerkin discretizations of the Navier-Stokes equations. 18th AIAA CFD Conference, Miami, FL, AIAA-2007-3941, June 2007. (This paper won second place in the Best Student Paper competition at this conference.) L. Diosady , D. Darmofal. Discontinuous Galerkin solutions of the Navier-Stokes equations using linear multigrid preconditioning. 18th AIAA CFD Conference, Miami, FL, AIAA-2007-3942, June 2007. C.W. Moeckel, D.L. Darmofal, T.R. Kingston, R.J.G. Norton. Toleranced designs of cooled turbine blades through probabilistic thermal analysis of manufacturing variability. Proceedings of 2007 ASME Turbo Expo, Montreal, Canada, Paper No. GT2007-28009. M. Park, D. Darmofal. Parallel anisotropic tetrahedral adaptation. 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA-2008-917, January 2008. J. Modisette, D. Darmofal. An output-based adaptive and higher-order method for a rotor in hover. AIAA Applied Aerodynamics Meeting, Honolulu, Hawaii, AIAA-2008-7343, August 2008. M. Park , D. Darmofal. Output adaptive tetrahedral cut-cell validation for sonic boom prediction. AIAA Applied Aerodynamics Meeting, Honolulu, Hawaii, AIAA-2008-6594, August 2008. J. Krakos, D. Darmofal. Effect of small-scale unsteadiness on adjoint-based output sensitivity. 19th AIAA CFD Conference, San Antonio, TX, AIAA-2009-4274, June 2009. H. Sun, D. Darmofal, R. Haimes. On the impact of triangle shapes for boundary layer problems using high-order finite element discretization. 48th AIAA Aerospace Sciences Meeting, Orlando, FL, AAIA-2010-542, January 2010. J.M. Modisette, D. Darmofal. Toward a robust, higher-order cut-cell method for viscous flows. 48th AIAA Aerospace Sciences Meeting, Orlando, FL, AIAA-2010-721, January 2010. L.T. Diosady, D.L. Darmofal. Domain decomposition preconditioners for higher-order hybridizable discontinuous Galerkin discretizations. 16th International Conference on Finite Elements in Flow Problems, Munich, Germany, March 2011. M. Yano, D.L. Darmofal. An Optimization-based Framwork for Controlling Discretization Error through Anisotropic h-Adaptation. 16th International Conference on Finite Elements in Flow Problems, Munich, Germany, March 2011. J. Krakos, Q.Wang, S.R. Hall, D.L. Darmofal. Sensitivity analysis of limit cycle oscillations. 20th AIAA CFD Conference, Honolulu, HI, AIAA-2011-3553, June 2011. M. Yano, J.M. Modisette, D.L. Darmofal. The Importance of mesh adaptation for higher-order discretizations of aerodynamics flows. 20th AIAA CFD Conference, Honolulu, HI, AIAA-2011-3852, June 2011 (This paper won second place in the Student Paper competition at the conference). M. Yano, D.L. Darmofal. An Optimization framework for anisotropic simplex mesh adaptation: Application to aerodynamic flows. 50th AIAA Aerospace Sciences Meeting, Nashville, TN, January 2012.
R. Haimes, M. Giles, D.L. Darmofal. Visual3 - a software environment for flow visualization. Von Karman Institute Lecture Series on Computer Graphics and Flow Visualization in CFD, 1991. D.L. Darmofal, B. van Leer. Local preconditioning: Manipulating Mother Nature to fool Father Time. Computing the Future II: Computational Fluid Dynamics and Transonic Flow. Editors: D. Caughey and M. Hafez. John Wiley & Sons, 1998. D.L. Darmofal. Towards a robust multigrid algorithm with Mach number and grid independent convergence. Fourth ECCOMAS Computational Fluid Dynamics Conference Proceedings. John Wiley & Sons, 1998. D.L. Darmofal, B. Van Leer. Characteristic time-stepping or local preconditioning of the Euler equations. 30th Von Karman Institute Computational Fluid Dynamics Lecture Series, 1999. D.L. Darmofal, B. Van Leer. Multigrid acceleration of the preconditioned Euler and Navier-Stokes equations. 30th Von Karman Institute Computational Fluid Dynamics Lecture Series, 1999. B. Van Leer, D.L. Darmofal. Steady Euler solutions in O(N) operations. Proceedings of Sixth European Multigrid Conference, September 27-30, 2000, Gent, Belgium, Editors: E. Dick and K. Riemslagh, Springer-Verlag, Heidelberg. D.L. Darmofal. Educating the future: the impact of pedagogical reform in aerodynamics. Computing the Future IV. Editors: D. Caughey and M. Hafez. World Scientific Publishing cool, 2005. D.L. Darmofal. Enhancing conceptual understanding in aerodynamics. 42nd AIAA Aerospace Sciences Meeting and Exhibit, January 2004 (presentation only). K.J. Fidkowski, D.L. Darmofal. Output error estimation and adaptation in Computational Fluid Dynamics: Overview and recent results. 47th AIAA Aerospace Sciences Meeting, Orlando, FL, AIAA-2009-1303, January 2009. L.T. Diosady, D.L. Darmofal. Massively parallel solution techniques for higher-order finite-element discretizations in CFD. Adaptive High-order Methods in Computational Fluid Dynamics. Editor Z.J. Wang. World Scientific Publishing Co., 2011.
Internal Memoranda and Progress Reports D.L. Darmofal. Enhancing Conceptual Understanding. MIT Faculty Newsletter, TeachTalk column, Vol. XV, No. 2, November 2002. D.L. Darmofal. Changing Pedagogy: What Students Say. Aero/Astro Annual, 2005. T.A. Oliver, D.L. Darmofal. Analysis of dual consistency for discontinuous Galerkin discretizations of source terms. ACDL Technical Report TR-06-1, Aerospace Computational Design Laboratory, Dept. of Aeronautics & Astronautics, MIT, September 2006. K.J. Fidkowski, D.L. Darmofal. Output-based adaptive meshing using triangular cut cells. ACDL Technical Report TR-06-2, Aerospace Computational Design Lab, Dept. of Aeronautics & Astronautics, MIT, October 2006. M. Yano, D.L. Darmofal. On dual-weighted residual error estimates for p-dependent discretizations. ACDL Technical Report TR-11-1, Aerospace Computational Design Lab, Dept. of Aeronautics & Astronautics, MIT, September 2011.
Barrett McCann, Texas A&M University, Master's Thesis. Evaluation of Local Preconditioners for Multigrid Solutions of the Compressible Euler Equations. November 1996. Andrew Cary, University of Michigan, Doctoral Thesis. Non-axisymmetric Effects in Vortex Breakdown. May 1997 (co-supervised with Ken Powell). Karan Deep Singh, Texas A&M University, Master's Thesis. Software Development for an Improved Particle Image Velocimetry. March 1998. Kyu-sup Kim, Texas A&M University, Master's Thesis. An Adaptive Mesh Method for the Simulation of Blade Vortex Interaction. April 1998. Srikanth Raghunathan, Texas A&M University, Master's Thesis. An Adaptive Cycling Multigrid Algorithm for Two-dimensional Convection-dominated Flows. June 1998. Kwun-ki Siu, Texas A&M University, Master's Thesis. A Robust, Locally Preconditioned Multigrid Algorithm for the Euler Equations. June 1998. Antonio de la Garza, Texas A&M University, Master's Thesis, An All-at-Once Approach for Multidisciplinary Preliminary Aircraft Design. August 1998. Vinod Srinivasan, Texas A&M University, Master's Thesis. Multidiscipinary Simulation of a Flexible Hydrofoil. December 1998. Michael Cain, Texas A&M University, Master's Thesis. A Robust, Locally Preconditioned Multigrid Algorithm for the Navier-Stokes Equations. May 1999. James Lu, M.I.T., Master's Thesis. Krylov Subspace Methods for Simultaneous Primal-Dual Solutions and Superconvergent Functional Estimates. July 2002. Sean Bradshaw, M.I.T., Master's Thesis. Physics-based, Reduced-order Combustor Flow Modeling. May 2002. Ricardo Powell, M.I.T., Master's Thesis. Impact of Aerothermal Performance Variability on Jet Engine Cost. September 2002. Toluloupe Okusanya, M.I.T., Doctoral Thesis. Algebraic Multigrid for Stabilized Finite Element Discretizations of the Navier-Stokes Equations. June 2002. (co-supervised with Peraire). David Venditti, M.I.T., Doctoral Thesis. Grid Adaptation for Functional Outputs of Compressible Flow Simulations. June 2002. Jerome Lavainne, M.I.T., Master's Thesis. Sensitivity of Compressor Repeating-Stage to Geometry Variation. September 2003. Victor Garzon, M.I.T., Doctoral Thesis. Probabilistic Aerothermal Design of Compressor Airfoils. February 2003. Apostolos Kountras, M.I.T., Master's Thesis. Probabilistic Analysis of Turbine Durability. August 2004. (co-supervised with E. Greitzer) Jean Collin, M.I.T., Master's Thesis. Impact of Aerothermal Modeling on the Estimation of Turbine Blade Life. August 2004. (co-supervised with E. Greitzer) Krzysztof Fidkowski, M.I.T., Master's Thesis. A High-order Discontinuous Galerkin Multigrid Solver for Aerodynamic Applications. June 2004. Vince Sidwell, M.I.T., Doctoral Thesis. On the Impact of Variability and Assembly on Turbine Blade Cooling Flow and Oxidation Life. May 2004. Todd Oliver, M.I.T., Master's Thesis. Multigrid Solution for High-Order Discontinuous Galerkin Discretizations of the Compressible Navier-Stokes Equations. August 2004. Caroline Lamb, M.I.T., Master's Thesis. Probabilistic Performance-Based Geometric Tolerancing of Compressor Blades. March 2005. James Lu, M.I.T., Doctoral Thesis. An a posteriori Error Control Framework for Adaptive Precision Optimization using Discontinuous Galerkin Finite Element Method. June 2005. Curtis Moeckel, M.I.T., Master's Thesis. Probabilistic turbine Blade Thermal Analysis of Manufacturing Variability and Toleranced Designs. January 2006. Douglas Quattrochi, M.I.T., Master's Thesis. Hypersonic Heat Transfer and Anisotropic Visualization with a Higher Order Discontinuous Galerkin Finite Element Method. January 2006. Laslo T. Diosady , M.I.T., Master's Thesis. A Linear Multigrid Preconditioner for the solution of the Navier-Stokes Equations using a Discontinuous Galerkin Discretization. May 2007. Krzysztof Fidkowski, M.I.T., Doctoral Thesis. A Simplex Cut-Cell Adaptive Method for High-Order Discretizations of the Compressible Navier-Stokes Equations. June 2007. James Modisette, M.I.T., Master's Thesis. An Output-Based Adaptive and Higher-Order Method for a Rotor in Hover, January 2008. Garrett Barter, M.I.T., PhD Thesis. Shock capturing with PDE-based artificial viscosity for an adaptive, higher-order discontinuous Galerkin finite element method, June 2008. Todd Oliver, M.I.T., PhD Thesis. A high-order, adaptive, discontinuous Galerkin finite element method for the Reynolds-averaged Navier-Stokes equations, September 2008. Masa Yano, M.I.T., Master's Thesis. Massively parallel solver for the high-order Galerkin least-squares method, June, 2009. Huafei Sun, M.I.T., Master's Thesis. Impact of triangle shapes using high-order discretizations and direct mesh adaptation for output error, September, 2009. Eric Liu, M.I.T., Master's Thesis. Optimization and Validation of Discontinuous Galerkin Code for the 3D Navier-Stokes Equations, January 2011. Laslo Diosady, M.I.T., Doctoral Thesis. Domain Decomposition Preconditioners for Higher-Order Discontinuous Galerkin Discretizations, September 2011. James Modisette, M.I.T., Doctoral Thesis. An Automated Reliable Method for Two-Dimensional Reynolds-Averaged Navier-Stokes Simulations. September 2011.
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