A high-order discontinuous Galerkin level set reinitialization with finite volume subcell stabilization

Date

2023-6-21

Author

Yüksel, Sıla

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This thesis focuses on creating high-order discontinuous Galerkin approaches to solve Level Set reinitialization problems utilizing Finite Volume-Subcell stabilization. Instead of using the conventional hyperbolic Level Set reinitialization, the flow of time Eikonal equation is discretized to provide an approximate signed distance function, allowing for more predictable behavior and quicker convergence rates near the interface. Equations for Level Set reinitialization on unstructured triangular meshes are formulated in a nodal discontinuous Galerkin framework. To dampen out high frequency solution components close to kinks, a Finite Volume-Subcell stabilization is applied. The accuracy and stability of the method and its ability to conserve mass are verified through numerical tests involving both smooth and nonsmooth cases.

Subject Keywords

Discontinuous Galerkın Method, Level Set reinitialization, Finite Volume- Subcell stabilization, high-order, GPU, Hamilton-Jacobi, Eikonal

URI

https://hdl.handle.net/11511/104736

Collections

Graduate School of Natural and Applied Sciences, Thesis