Fully Threaded Tree Algorithms for Adaptive Refinement Fluid Dynamics Simulations

A fully threaded tree (FTT) for adaptive mesh refinement (AMR) of regular meshes is described. By using a tree threaded at all levels, tree traversals for finding nearest neighbors are avoided. All operations on a tree including tree modifications areO(N), whereNis a number of cells and can be performed in parallel. An implementation of the tree requires 2Nwords of memory. In this paper, FTT is applied to the integration of the Euler equations of fluid dynamics. The integration on a tree can utilize flux evaluation algorithms used for grids, but requires a different time-stepping strategy to be computationally efficient. An adaptive-mesh time-stepping algorithm is described in which different time steps are used at different levels of the tree. Time stepping and mesh refinement are interleaved to avoid extensive buffer layers of fine mesh which were otherwise required ahead of moving shocks. A filtering algorithm for removing high-frequency noise during mesh refinement is described. Test examples are presented, and the FTT performance is evaluated.

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