This paper presents the algorithms for solving the moving boundary problem with the finite element method. A moving boundary problem is that solid surfaces move to the inside of a structural domain by regression caused by erosion, burning, sublimation and crack. In order to solve the moving boundary problem, automatic mesh generation and ALE algorithms are required. In general, hexahedral elements are preferred to tetrahedral elements in the finite element method due to accuracy of numerical results. However, automatic hexahedral mesh generation in arbitrary and complex 3D model remains a challenge. Layering and subdomain division algorithm is proposed to remove these geometric constraints and generate reasonable-quality meshes. Layering algorithm transforms 3D shape into a representative 2D shape layer. This layer is decomposed into subdomains of rectangular shape using subdomain division algorithm. After extending the decomposed 2D layers to 3D space, a hexahedral mesh is generated in the extended 3D subdomain.
ALE algorithm updates the history data to moved mesh. Finite Volume Method(FVM) is widely used in updating of integration point history data, but elements used for update are limited to the control volume. In order to consider elements other than the control volume, an interpolation method using the overlap volume between elements is applied for the history data update of integration points.
The proposed algorithms for the moving boundary problem are implemented to analyze a test model regressing solid domain by burning. When the solid boundary moves to the inside, reconstruction of the inner mesh and history data update using ALE algorithm is performed. If the quality of mesh is worse or topology change occurs as the cumulative movement of boundary increases, remeshing is performed using the automatic hexahedral mesh generation algorithm. The test model simulation results show that proposed algorithms gives continuous boundary motions and stable numerical solutions. It is verified that the proposed algorithm can be effectively used in the analysis of moving boundary problems. Finally, hexahedral mesh generation is performed using suggested parallel algorithm. In order to test the usability of the parallel algorithm, runtime to generate mesh for two dam models are evaluated. The test results show that the suggested parallel algorithm achieves reasonable speedup on a cluster system and can be effectively used to reduced time for generating hexahedral mesh.