Prof. Georg May
Contact
Schinkelstr. 2
52056 Aachen
Germany
Phone: +492418099133
Fax: +4924180628498
email: see here...
Education
 B.E. Thayer School of Engineering, Dartmouth College, Hanover, NH, 2000
 Dipl. Ing., Institut für Luft und Raumfahrt, RWTH Aachen, Germany, 2001
 PhD, Departmenf of Aeronautics and Astronautics, Stanford University, Stanford, CA, 2006
Professional Career
 20062007  Research Associate, Departmenf of Aeronautics and Astronautics, Stanford University, Stanford, CA
Research Interests
HighOrder Numerical Methods for Conservation Laws
Here the focus is on highorder accurate numerical methods for partial differential equations (PDE), in particular those of the hyperbolic type. I am interested in suitable highorder accurate algorithms for general unstructured meshes.There is considerable demand for the numerical solution of differential equations in rather complex computational domains. For example, the Euler or NavierStokes equations are routinely solved for full aircraft configuration by lower order methods. This has motivated the use of unstructured mesh technologies, which makes meshing of the computational domain simple, but the formulation of highorder accurate numerical algorithms much more challenging.
Hyperbolic PDE are known to admit discontinuous solutions in finite time, even for smooth initial data. A well known example are the compressible Euler equations, which allow compression shocks for sufficiently high Mach numbers. This necessitates the development of shock capturing schemes, which have matured over the years for ower order accuracy, and are widely used in industrial applications. Extensions to high order schemes, however, still leave a lot to be desired.
I have been involved in the development of the Spectral Difference (SD) Method. The SD method uses a local pseudospectral representation of the solution on unstructured meshes to achieve arbitrary order of accuracy. Liu, Vinokur and Wang proposed the baseline scheme for hyperbolic PDE in 2004. My own research, which has been carried out at the Aerospace Computing Laboratory at Stanford University in collaboration with Professor ZJ Wang at Iowa State University, has concentrated on the following contributions:
 Investigation of linear and nonlinear stability properties
 Extension of the scheme to the compressible NavierStokes equations
 Ensure stability and monotonicity in transonic and supersonic fluid flow through appropriate limiting procedures
 Development of an h/pMultigrid procedure
Kinetic Schemes for the NavierStokes Equations
Conventional techniques for the NavierStokes equations necessitate the use of different discretization stecils for the inviscid and viscous flux components. While these techniques often have a physically sound motivation, algorithmically it can be quite challenging to discretize the NavierStokes equations on general meshes, i.e. arbitrary polyhedra.GasKinetic finite volume schemes offer an attractive alternative in that they allow the discretization of the NavierStokes equations on a simple and universal nextneighbor stencil. This is accomplished by applying the discretization to the gaskinetic distribution function, rather than the macroscopic variables. The connection between the mesoscopic and macroscopic level is established by the governing gaskinetic equations, i.e. the Boltzmann or BGK equations and related framework from kinetic gas theory, such as the ChapmanEnskog expansion.
The discretization of the Navier Stokes equations can be accomplished by first computing gradients of the macroscopic variables, and subsequent discretization of a reconstructed gaskinetic distribution function, which is a function of the macroscopic variables and their gradients, and must be consistent to the NavierStokes order of accuracy in ChapmanEnskog expansion. Written in terms of the macroscopic variables this amounts to a nonlinear reconstruction and averaging of flow variables and their gradients to approximate convective and viscous fluxes.
Numerical Algorithms for General Unstructured Meshes
I am interested in the software engineering aspects related to creating flexible computational tools for modeling physics on general unstructured meshes. There are numerous challenges related to computational geometry, algorithmic details (such as multigrid techniques) for solvers that operate on arbitrary polyhedral meshes. This is true even for loworder approximations, and for any type of physics problem. In this context I have been involved in the design and developed of computational architectures for modeling compressible fluid flow on arbitrary polyhedral meshes.Publications

Woopen, M, May, G., and Schütz, J.: "Adjointbased error estimation and mesh adaptation for hybridized discontinuous Galerkin methods", Int. J. Numer. Meth. Fluids 76(11), pp. 811–834, 2014. 

Woopen, M, Balan, A., May, G., and Schütz, J.: "A Comparison of Hybridized and Standard DG Methods for TargetBased hpAdaptive Simulation of Compressible Flow", Computers & Fluids 98, pp. 3–16, 2014. 

Gerhard, N., Iacono, F., May, G., Müller, S., Schäfer, R.: "A HighOrder Discontinuous Galerkin Discretization with MultiwaveletBased Grid Adaptation for Compressible Flows", J. Sci. Comput. in press, 2014. 

Balan, A. Woopen, M., May, G.: "A Hybridized Discontinuous Galerkin Method for ThreeDimensional Compressible Flow Problems", AIAA Paper 140938, American Institute of Aeronautics and Astronautics, 2014. 

Schütz, J., May, G.: "An Adjoint Consistency Analysis for a Class of Hybrid Mixed Methods", IMA J. Numer. Anal. 34 (3), pp. 12221239, 2013. 

Balan, A. Woopen, M., May, G.: "AdjointBased HpAdaptation for a Class of HighOrder Hybridized Finite Element Schemes for Compressible Flows", AIAA Paper 132938, American Institute of Aeronautics and Astronautics, 2013. 

J. Schütz, M. Woopen and G. May: "A combined hybridized discontinuous Galerkin / hybrid mixed method for viscous conservation laws", in: Hyperbolic Problems: Theory, Numerics, Applications, Proceedings of the Fourteenth International Conference on Hyperbolic Problems, Padova, Italy, pp. 915922, AIMS, 2013. 

Wang, Z. J., May, G. et al.: "Highorder CFD methods: current status and perspective", Int. J. Numer. Meth. Fluids 72(8), pp. 811–845, 2013. 

Schütz J., May, G.: "A Hybrid Mixed Method for the Compressible NavierStokes Equations", J. Comp. Phys 240, pp. 5875, 2013. 

J. Schütz, S. Noelle, C. Steiner, May, G.: "A Note on Adjoint Error Estimation for OneDimensional Stationary Conservation Laws with Shocks", SIAM J. Numerical Analysis 51(1), pp. 126136, 2013 

Schütz, J., Woopen, M., May, G.: "A Hybridized DG/Mixed Scheme for Nonlinear AdvectionDiffusion Systems, Including the Compressible NavierStokes Equations ", AIAA Paper 120729, American Institute of Aeronautics and Astronautics, 2012. 

Balan, A., Schöberl, J.,May, G.: "A Stable HighOrder Spectral Difference Method for Hyperbolic Conservation Laws on Triangular Elements", J. Comput. Phys. 231(5), pp. 2359–2375, 2012. 

May, G., Iacono, F., Balan, A.: "TimeRelaxation Methods for HighOrder Discretization of Compressible Flow Problems", Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2011 (ICNAAM‐2011), AIP Conf. Proc. 1389, 903906 (2011). 

Iacono, F., May, G., Müller, S. and Schäfer, R.: "A Discontinuous Galerkin Discretization with MultiwaveletBased Grid Adaptation for Compressible Flows", AIAA Paper 110200, American Institute of Aeronautics and Astronautics, 2011. 

Schütz J., May, G.: "A Numerical Study of AdjointBased Mesh Adaptation for Compressible Flow Simulation", AIAA Paper 110213, American Institute of Aeronautics and Astronautics, 2011. 

May, G.: "On the connection between the spectral difference method and the discontinuous Galerkin method", Commun. Comput. Phys., 9, pp.10711080, 2011. 

May, G., Jameson, A.: "Efficient Relaxation Methods for HighOrder Discretization of Steady Problems", in: Adaptive highorder methods in Computational Fluid Dynamics (Wang, Z. J., ed.), World Scientific Publishing, 2011. 

Balan, A., May, G., Schöberl: "A Stable Spectral Difference Method for Triangles", AIAA Paper 110047, American Institute of Aeronautics and Astronautics, 2011. 

Iacono, F., May, G., Wang, Z. J.: "Relaxation Techniques for HighOrder Discretizations of Steady Compressible Inviscid Flows", 40^{th} AIAA Computational Fluid Dynamics Conference, Chicago, IL, AIAA Paper 104991, 2010. 

G. May, F. Iacono, A. Jameson: " A hybrid multilevel method for highorder discretization of the Euler equations on unstructured meshes", J. Comp. Phys. 229(10), 2010. 

Iacono, F., May, G.: "Convergence Acceleration for Simulation of SteadyState Compressible Flows Using HighOrder Schemes", 19^{th} AIAA Computational Fluid Dynamics Conference, San Antonio, TX, AIAA Paper 094132, 2009. 

Iacono, F., May, G., Jameson, A.: "Efficient Algorithms for HighOrder Discretization of the Euler and NavierStokes Equations", 47^{th} AIAA Aerospace Sciences Meeting and Exhibit, Orlando, FL, AIAA Paper 090182, 2009. 

May, G., Jameson, A.: "An improved gaskinetic BGK finitevolume method for threedimensional transonic flow" ,J. Comp. Phys. 220(2), pp. 856878, 2007 

Wang, Z.J., Liu, Y., May, G., Jameson, A.: "Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations" , J. Sci. Comput. 32 (1) pp. 5471, July, 2007 

May, G., Jameson, A.: "A Spectral Difference Method for the Euler and NavierStokes Equations on Unstructured Meshes", AIAA20060304, 44^{th} AIAA Aerospace Sciences Meeting and Exhibit, January 912, 2006, Reno, NV. 

May, G., Jameson, A.: "HighOrder Accurate Methods for HighSpeed Flow", AIAA20055251, 17^{th} AIAA Computational Fluid Dynamics Conference, Toronto, Ontario, June 69, 2005. 

May, G., Jameson, A.: "Improved Gaskinetic Multigrid Method for ThreeDimensional Computation of Viscous Flow", AIAA20055106, 17^{th} AIAA Computational Fluid Dynamics Conference, Toronto, Ontario, June 69, 2005. 

May, G., Jameson, A.: "Unstructured Algorithms for Inviscid and Viscous Flows Embedded in a Unified Solver Architecture: Flo3xx", AIAA20050318, 43^{rd} AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV, January 1013, 2005. 

May, G., Jameson, A.: "Calculating ThreeDimensional Transonic Flow Using a GasKinetic BGK FiniteVolume Method", AIAA20051397, 43^{rd} AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV, January 1013, 2005. 

May, G., Van der Weide, E., Jameson, A., and Shankaran, S.: "Drag Prediction of the DLRF6 configuration", AIAA20040396, 42^{nd} AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV, January 58, 2004. 