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Ph.D. Theses

Solving fluid-rigid object interaction problems by discontinuous Galerkin methods

By Peng Hu
Advisor: Joseph E. Flaherty
July 11, 2005

Multi-material interaction is wide spread in fluid mechanics, biomechanics, meteorology and many other fields. Therefore, the ability to numerically simulate the effects of two or more different, yet inter-related physical materials is important. Solving multi-materials interaction problems is still difficult and several open problems remain. Key problems are tracing the interfaces properly and applying correct interface conditions. Here, we are particularly interested in applications involving the motion of a high-speed rigid object in a compressible inviscid fluid. The basic characteristics of these problems include both the continuous change of the computational domain with respect to time and the strong discontinuities in the fluid because of the movement of the object.

Two different approaches - a moving mesh approach and a fixed mesh approach, are considered. In our moving mesh approach, a mesh is defined over a domain excluding the rigid body, and then modified by using a spring analogy model during calculation to follow the object. In our fixed mesh approach, a novel idea is provided by using a level set function to implicitly track the fluid-solid interface; therefore, no mesh motion or modification is required. The interface boundary conditions are also captured implicitly by combining a Ghost Fluid technique with the level set approach.

The discontinuous Galerkin method (DGM) is used to numerically solve the Euler equations associated with a compressible inviscid fluid. The numerical tests give satisfactory results for both approaches, and serve to verify the correctness of our theoretic approximation and numerical implementation. The fixed mesh approach is a much more efficient approach because of not having to move the mesh. It also has a wide-spread applicability to handle problems with complex movement and/or complex geometry. This approach is also dimension free and easy to implement. The moving mesh approach provides a more natural way to consider the fluid-rigid object interaction problem and it provides an accurate way to simulate the interface interaction.

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