September 2007
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New Conservative Remap Method in FLAG
Los Alamos mathematical modeling and analysis researchers Sam Schofield and Rao Garimella have implemented a new, prototype conservative remap method in the FLAG Arbitrary-Lagrangian-Eulerian (ALE) code that is based on exact intersections of the old mesh with the relaxed mesh. In ALE calculations, the mesh moves and distorts with time. When the mesh becomes tangled or of poor quality (Fig. 1a), it is smoothed, the solution values are mapped, in a conservative manner, from the old to the smoothed mesh (Fig. 1b), and the simulation continues. In the FLAG code (LANL ASC Code Project B), the existing remap method is based on approximating the changes in the values in the mesh cells between the new and old meshes. Because of accuracy constraints, it is limited to small displacements.
With our new remap method, the smoothed mesh cells are intersected with a linear reconstruction of the field values on the old mesh to determine how much of each conserved quantity is located in the new mesh cell. Materials are remapped by intersecting the new mesh cell with any reconstructed interfaces on the old mesh. There is no loss of accuracy for large displacements between the meshes and monotonicity is guaranteed if the linear reconstruction is monotonic.
Figures 1a and 1b contrast the old vs the new remap. The new intersection-based remap allows the mesh smoother to take larger steps, maintaining a quality mesh.
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Fig. 1a. Old Remap Method |
Fig. 1b. Intersection-based Remap |
Figures 2a and 2b contrast the old vs the new remap. The corner coupling in the new method better maintains the material shape when moving diagonally across the mesh.
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Fig. 2a. Old Remap Method |
Fig. 2b. Intersection-based Remap |
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Last Modified September 27, 2007
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