Per-Olof Persson |
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Per-Olof Persson
Department of Mathematics, 2-363A
Massachusetts Institute of Technology
Cambridge, MA 02139
Phone: (617) 253-4989
Fax: (617) 253-4358
E-mail: "lastname" at mit.edu
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Research
High-order accurate methods for computational mechanics
My current research interests are in high-order accurate methods for computational fluid and solid mechanics. Some examples are shown below, and for more details vist our 3DG Group web page.
Kelvin-Helmholtz Instability:
This example, inspired by Munz et at (2003), shows how a large
scale acoustic wave interacts with small scale flow features, leading
to vorticity generation. The problem is solved using a Discontinuous
Galerkin method with polynomials of degree 7, and it is a good example
of the importance of high-order discretizations in order to accurately
capture and propagate the acoustic waves. Also, due to the highly
nonlinear behaviour it is clear that simplifications based on linearized
Euler or the Lighthill Analogy would give incorrect results.
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Animation (DivX, 24.0MB)
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Volumetric Membrane Models:
By using a high-order discontinuous Galerkin formulation for
dynamic analysis of solids, highly anisotropic tetrahedral elements
can be used without reducing the accuracy or introducting locking.
This allows for modeling of thin structures such as membranes without
specialized models. The example shows a square membrane which is
clamped at one edge and subject to a gravitational force. The
aspect ratio of the elements is 1/200.
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Animation (DivX, 870kB)
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Flow around Wedge Box geometry:
The Wedge Box is a simple but representative model geometry
for aeroacoustics computations. The figures show pressure
distribution and streamlines for a laminar flow field.
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Pitching Airfoil:
In this model, an HT13 airfoil is attached to a translating and
heaving point by a torsoidal spring. The fluid properties are
Re = 5000 and Mach = 0.2. The leading edge is forces to a sinuoidal
vertical motion, and the moment equation is solved simultaneously
with the flow in order to capture the interaction between the
fluid and the spring.
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Low amplitude

Animation (DivX, 6.1MB)
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High amplitude

Animation (DivX, 12.3MB)
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Mesh generation for implicit geometries
In my Ph.D. thesis I developed new techniques for mesh generation using
implicit geometry representations. I applied the methods on problems in
shape optimization, fluid dynamics on deforming domains, and meshing
of biological images.
DistMesh:
Gilbert Strang and I have
developed a short and simple MATLAB code based on the results of our
research on mesh generation. We believe it will be highly useful for
teaching purposes and as a starting point for more specialized meshing
codes. It is available as free software at the webpage below:
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Mesh Size Functions:
Many mesh generators, including DistMesh, depend on a good
a priori mesh size function. It should take into account
curvature and feature size of the geometry, and external size
functions such as user specifications or adaptive error
estimators. In addition, the gradients of the size functions
have to be bounded to ensure high quality elements. We compute
curvature and feature sizes directly from the implicit geometry
definition, and solve our gradient limiting equation
to obtain an optimal size function.
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Moving Meshes:
The iterative nature of the mesh generator makes it particularly useful
for meshing moving geometries. When the geometry boundary moves we can
update our unstructured mesh by applying a few additional iterations
starting from the last good configuration.
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Applications:
Since the mesh generator uses an implicit representation of the
geometry it can be combined with the level set method.
Hamilton-Jacobi equations are used to propagate the geometry
boundary on a background grid, and the physical problems are
solved using the finite element method on an unstructured mesh
generated by our mesh generator. This combines the best of the
level set method and the finite element method for modeling
physical problems with moving boundaries and interfaces. We have
studied a few applications of this:
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