My research focus is vortex particle methods for flow simulation. In the last decade I have created a number of Eulerian, Lagrangian, and hybrid vortex methods in both two- and three-dimensions. In addition, I am interested in GPU and parallel programming, computational geometry, cellular automata, and high-resolution image rendering and display.
The most capable vortex methods stem from discretization of vorticity as Lagrangian vortex blobs, with the vorticity-velocity inversion calculated using a multipole-accelerated treecode, Fast Multipole Method, or Vortex-in-Cell method. Applied Scientific Research is currently conducting advanced research in vortex particle methods, including Large-Eddy Simulation, efficient parallel treecodes, and GPGPU for vortex simulation. Publications that I have been involved with at ASR follow.
M. Stock, A. Gharakhani, and C. Stone, Modeling Rotor Wakes with a Hybrid OVERFLOW-Vortex Method on a GPU Cluster [PDF paper] [PDF slides] [Movie at YouTube], AIAA 28th AIAA Applied Aerodynamics Conference, 28 Jun-1 Jul 2010, Chicago, IL.
M. Stock and A. Gharakhani, A GPU-accelerated Boundary Element Method and Vortex Particle Method [PDF paper] [PDF slides], AIAA 40th Fluid Dynamics Conference and Exhibit, 28 Jun-1 Jul 2010, Chicago, IL.
M. Stock and A. Gharakhani, Toward efficient GPU-accelerated N-body simulations [PDF paper] [PDF slides], 46th AIAA Aerospace Sciences Meeting, 7-10 January 2008, Reno, NV.
A. Gharakhani and M. Stock, 3-D Vortex simulation of flow over a circular disk at an angle of attack, 17th AIAA Computational Fluid Dynamics Conference, 6-9 June 2005, Toronto, Canada.
A. Gharakhani, J. Sitaraman, M. Stock, A Lagrangian vortex method for simulating flow over 3-D objects, 2005 ASME Fluids Engineering Division Summer Meeting, June 19-23, Houston, TX.
My dissertation research concerned three-dimensional vortex sheet methods for inviscid simulation. At the time, the only three-dimensional vortex sheet methods could not track flows for very long times because they were limited either by rectangular or curvature-dependent discretization methods. My donation to the field was a front-tracking vortex sheet method that used edge splitting and node merging to accomplish long-time simulation of inviscid vortex sheet flows. The research spawned a paper appearing in the Journal of Computational Physics.
M. Stock, W.J.A. Dahm, G. Tryggvason, Impact of a vortex ring on a density interface using a regularized inviscid vortex sheet method, Journal of Computational Physics, 227/21, pp. 9021-9043, Nov. 2008, 2.5 MB PDF
M. Stock, A Regularized Inviscid Vortex Sheet Method for Three Dimensional Flows With Density Interfaces, PhD thesis, University of Michigan, Ann Arbor, 2006, 7.0 MB PDF
In the process of conducting this research, I assembled a summary of the major aspects of vortex methods research as well as 415 literature references. It is a living document, and thus contains not only references and questions, but my throughts regarding various lines of research. I am making it available in the hopes that newcomers to the field might find it useful.
M. Stock, Summary of Vortex Methods Literature, unpublished, 2007, 1 MB PDF