Per-Olof Persson

  
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Contact Info

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
 
  

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.


Animation (DivX, 24.0MB)

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.

Animation (DivX, 870kB)

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.






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.

Low amplitude

Animation (DivX, 6.1MB)



High amplitude

Animation (DivX, 12.3MB)




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:



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.

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.

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: