Assistant Professor, Aerospace Engineering Department

KRZYSZTOF J. FIDKOWSKI Assistant Professor, Aerospace Engineering Department University of Michigan

Education

2007 MIT – Aeronautics & Astronautics, Ph.D. 2004 MIT – Aeronautics & Astronautics, S.M. 2003 MIT – Aerospace Engineering, S.B. 2003 MIT – Physics, S.B.

Employment and Research Experience

2008-present: Assistant Professor, Aeronautics and Astronautics, University of Michigan

2007-2008: Postdoctoral Associate, Aerospace Computational Design Laboratory, MIT Advisor: Karen E. Willcox Implemented large-scale parallel model reduction simulations for use in initial condition inverse problems and Bayesian statistical inference applications. Performed model reduction simulations with over 8.5 million degrees of freedom on a massively parallel architecture. Additionally investigated methods for design under uncertainty, with the particular application of a gust-load alleviation system for the next generation of high wing aspect-ratio, low fuel-burn aircraft.

2004-2007: Research Assistant, Doctoral Level, Aeronautics and Astronautics, MIT Advisor: David L. Darmofal Investigated a triangular and tetrahedral cut-cell adaptive method for high-order discontinuous Galerkin (DG) discretizations of the compressible Navier-Stokes equations. The idea of cut-cell mesh generation addresses the well-known difficulty of quality mesh generation around complex geometries. The use of triangular and tetrahedral elements allows for the possibility of anisotropic adaptation in arbitrary directions. In an output-based adaptive framework, an automatic geometry-to-solution procedure is possible.

2004: Fellowship Practicum, DOE Argonne National Laboratory Explored and implemented a DG discretization of the unsteady incompressible Navier- Stokes equations. Studied the effect of discretization choices on the stability and accuracy of steady and unsteady solvers.

2003-2004: Research Assistant, Master’s Level, Aeronautics and Astronautics, MIT Implemented a p-multigrid solver for the DG discretization of the two- and three- dimensional Euler equations. Developed a line creation algorithm for connecting strongly-coupled elements together to relieve stiffness of the implicit solver.

2002-2003: Undergraduate Researcher, Aerospace Computational Design. Laboratory, MIT Analyzed a p-multigrid solver with element block and element line smoothing for the DG discretization of the linear advection equation in one and two dimensions. Implemented a DG discretization and studied the eigenvalue footprint of the smoothing and multigrid operators. 2001-2002: Undergraduate Researcher, Gas Turbine Laboratory, MIT Studied heat-transfer properties of film-cooled gas turbine engine components using computational methods. Designed time-effective, accurate, computational meshes for performing parameter studies of the film cooling problem.

2001: Research Experience for Undergraduates, University of Washington Investigated a discrete inverse scattering problem on networks, the target application being the ability to recover properties of a black-box system based solely on observations at limited exterior nodes. Characterized the required structure of recoverable networks.

2000-2001: Undergraduate Researcher, Laboratory for Nuclear Science, MIT Explored the effect of gas composition on electron drift properties under varying electric and magnetic fields, the application being drift tube particle detectors, in which a precise relationship between electric field and drift velocity is sought for particle path reconstruction. Conducted controlled experiments of different gases at the MIT cyclotron facility.

2000: Research Experience for Undergraduates, University of California, San Diego Performed adaptive optics research at the Center for Astrophysics and Space Sciences. Wrote image processing code and performed data reduction on infrared images of a high- redshift merging radio galaxy. Resulting data was used in a journal publication.

Professional Activities

 Associate Member, AIAA Fluid Dynamics Technical Committee  University of Michigan Center for Research on Learning and Teaching Advisory Board  Reviewer for: o SIAM Journal of Scientific Computing o AIAA Journal o Journal of Computational Physics o International Journal of Numerical Methods in Fluids o Mathematical Modelling of Natural Phenomena

Honors and Awards

 Air Force Office of Scientific Research Young Investigator Award, 2011  Department of Energy Computational Science Graduate Fellowship, 2003-2007.  Tau Beta Pi, Phi Kappa Sigma, Sigma Pi Sigma.  Salisbury Award for Superior Achievement in Aeronautics and Astronautics, 2003.  Boston Area Physics Contest Winner, 2001.  National Merit Finalist, 1999.

Teaching Experience

 Winter 2009, Fall 2009, Winter 2010, Fall 2010, Winter 2011: Undergraduate Aerodynamics, AE 325, University of Michigan  Fall 2008: Graduate Computational Fluid Dynamics, AE 523, University of Michigan  Spring 2008: Undergraduate Computational Methods for Aerospace Engineering , 16.90, MIT (co-instructor)  Spring 2007: Undergraduate Aerodynamics, 16.100, MIT (co-instructor)  2004-2007: Graduate Resident Tutor at MIT. Among other responsibilities, assisted students individually with homework in freshman-level mathematics and physics.

Research Interests

Interested in the development of robust, scalable, and adaptive solution techniques for computational fluid dynamics. Sub-topics include numerical error estimation, large-scale model reduction, development of parallel algorithms, and uncertainty quantification.

Current and recent research projects include:

 Unsteady output-based error estimation and mesh adaptation  Adaptive RANS calculations with the discontinuous Galerkin method  Gradient-enhanced response surface construction, applied to radiation hydrodynamics simulations  Uncertainty quantification in nuclear reactor thermal-hydraulics codes  Stochastic-space adaptive methods for uncertainty quantification  Entropy-adjoint approach to mesh refinement  Probabilistic approach to contaminant source inversion  Cut-cell mesh generation  Nonlinear model reduction for inverse problems

Publications

Journal Publications

10. K.J. Fidkowski and Y. Luo. Output-based Space-Time Mesh Adaptation for the Compressible Navier-Stokes Equations. Journal of Computational Physics. In Review. 9. K.J. Fidkowski. Output Error Estimation Strategies for the Space-Time Discontinuous Galerkin Method. International Journal for Numerical Methods in Engineering. In Review. 8. K.J. Fidkowski, and D.L. Darmofal. Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics: Overview and Recent Results. AIAA Journal 2011, Accepted. 7. K.J. Fidkowski, and P.L. Roe. An Entropy Adjoint Approach to Mesh Refinement. SIAM Journal on Scientific Computing, 32(3), 2010, pp 1261-1287. 6. D. Galbally, K. Fidkowski, K. Willcox, and O. Ghattas, Nonlinear Model Reduction for Uncertainty Quantification in Large-Scale Inverse Problems. International Journal for Numerical Methods in Engineering. 81(12), 2009, pp 1581-1603. 5. K.J. Fidkowski and D.L. Darmofal. A triangular cut–cell adaptive method for high–order discretizations of the compressible Navier–Stokes equations. Journal of Computational Physics. 225, 2007, pp 1653-1672. 4. D.W. Milanes, D.R. Kirk, K.J. Fidkowski, I.A. Waitz. Gas turbine engine durability impacts of high- fuel-air ratio combustors: near wall reaction effects on film-cooled backward-facing step heat transfer. Journal of Engineering for Gas Turbines and Power, 128-2, 2006, pp 318-325. 3. K.J. Fidkowski, T.A. Oliver, J. Lu, and D.L. Darmofal. p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations. Journal of Computational Physics. 207:1, July 2005, pp 92-113. 2. A. Quirrenbach, J.E. Roberts, K.J. Fidkowski, W. de Vries, and W. van Breugel. Keck Adaptive Optics Observations of the Radio Galaxy 3C294: A Merging System at z = 1.786? The Astrophysical Journal, 556:108-112, 2001 July 20. 1. J.J.Kirchner, U.J.Becker, R.B.Dinner, K.J.Fidkowski, and J.H.Wyatt. Optimization of drift gases for accuracy in pressurized drift tubes. Nuclear Instruments and Methods in Physics Research, A474, 2001 February 16.

Conference Papers

11. K.J. Fidkowski, M.A. Ceze, and P.L. Roe. Drag Output Error Estimation Using the Entropy Adjoint Approach. Submitted to the 2011 AIAA CFD Conference. 10. M.A. Ceze, and K.J. Fidkowski. An Optimization Approach for Solving the Steady-State Flow Equations. Submitted to the 2011 AIAA CFD Conference. 9. S.M. Kast, K.J. Fidkowski, and P.L. Roe. An Unsteady Entropy Adjoint Approach for Adaptive Solution of the Shallow-Water Equations. Submitted to the 2011 AIAA CFD Conference. 8. Y. Luo and K.J. Fidkowski. Output-Based Space Time Mesh Adaptation for Unsteady Aerodynamics. AIAA Paper Number 2011-491, 2011. 7. M.A. Ceze and K.J. Fidkowski. Output-Driven Anisotropic Mesh Adaptation for Viscous Flows Using Discrete Choice Optimization. AIAA Paper Number 2010-0170, 2010. 6. K.J. Fidkowski and P.L. Roe. Entropy-based Mesh Refinement, I: The Entropy Adjoint Approach. AIAA Paper Number 2009-3790, 2009. 5. K.J. Fidkowski and D.L. Darmofal. Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics: Overview and Recent Results 47th AIAA Aerospace Sciences Meeting. AIAA Paper Number 2009-1303, 2009. 4. K.J. Fidkowski, F. Engelsen, K.E. Willcox and I. Kroo. Stochastic Gust Analysis Techniques for Aircraft Conceptual Design AIAA Paper Number 2008-5848, 2008. 3. K.J. Fidkowski and D.L. Darmofal. An adaptive simplex cut–cell method for discontinuous Galerkin discretizations of the Navier–Stokes equations. AIAA Paper Number 2007-3941, 2007. 2. T.A. Oliver, K.J. Fidkowski, and D.L. Darmofal. Multigrid solution for a high-order discontinuous Galerkin discretization of the compressible Navier-Stokes equations. Third International Conference on Computational Fluid Dynamics, Toronto, Canada, 2004. 1. K.J. Fidkowski and D.L. Darmofal. Development of a higher-order solver for aerodynamic applications. 42nd AIAA Aerospace Sciences Meeting., AIAA Paper Number 2004-0436, 2004.

Presentations

11. Output-Based Space Time Mesh Adaptation for Unsteady Aerodynamics. 2011 AIAA Aerospace Sciences Meeting, January 2011. 10. Entropy-Based Mesh Refinement, I: The Entropy Adjoint Approach. 2009 AIAA Computational Fluid Dynamics Conference, June 2009.

9. Progress in Mesh-Adaptive Discontinuous Galerkin Methods for CFD, German Aerospace Center Seminar, May 2009 (Invited). (Similar presentation at NASA Ames in June 2009)

8. Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics: Overview and Recent Results (Invited), 2009 AIAA Aerospace Sciences Meeting, January 2009.

7. Towards Automated Mesh Adaptation Using Simplex Cut Cells. K.J. Fidkowski. Computational Research in Boston Seminar (Invited), October 2007. (Similar presentation at NASA Ames in December 2007, and at a Computation for Design and Optimization seminar in May 2008).

6. A Cut-Cell Adaptive Method for High-Order Discretizations of the Compressible Navier-Stokes Equations. K.J. Fidkowski. 2007 Computational Science Graduate Fellowship Conference in Washington D.C. June 2007.

5. An Adaptive Simplex Cut-Cell Method for Discontinuous Galerkin Discretizations of the Navier- Stokes Equations, K.J. Fidkowski and D.L. Darmofal. 18th AIAA Computational Fluid Dynamics Conference in Miami Fl. June 2007.

4. An Automated, Adaptive Cut-Cell Method for Triangles and Tetrahedra. K.J. Fidkowski, University of Michigan, February 1, 2007.

3. p-Multigrid solution of high-order discontinuous Galerkin discretizations of the Euler and compressible Navier-Stokes equations. K.J. Fidkowski, D.L. Darmofal. 12th Copper Mountain Conference on Multigrid Methods in Copper Mountain, Colorado. April 3, 2005.

2. Shock capturing and robust output-based adaptation for DG. G.E. Barter, K.J. Fidkowski, D.L. Darmofal. 7th World Congress on Computational Mechanics in Los Angeles, CA. July 16, 2006.

1. Development of a higher-order solver for aerodynamic applications. K.J. Fidkowski, D.L. Darmofal. 42nd AIAA Aerospace Sciences Meeting and Exhibit in Reno, NV. January 4, 2004.

Technical Reports

1. K.J. Fidkowski and D.L. Darmofal. Output–based adaptive meshing using triangular cut cells. M.I.T. Aerospace Computational Design Laboratory Report. ACDL TR-06-2, 2006

Dissertation

2. K.J. Fidkowski. A simplex cut-cell adaptive method for high-order discretizations of the compressible Navier-Stokes equations. MIT PhD Thesis. June 2007. 1. K.J. Fidkowski. A High-order Discontinuous Galerkin Multigrid Solver for Aerodynamic Applications. MIT Master's Thesis. June 2004.