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Full threaded tree algorithms for adaptive refinement fluid dynamics simulations. (English) Zbl 0934.76057
Summary: We describe a fully threaded tree (FTT) algorithm for adaptive mesh refinement of regular meshes. By using a tree threaded at all levels, we avoid traversals for finding nearest neighbors. All operations on a tree including tree modifications are $${\mathcal O}(N)$$, where $$N$$ is a number of cells, and can be performed in parallel. An implementation of the tree requires $$2N$$ words of memory. In this paper, FTT algorithm 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. We present an adaptive-mesh time-stepping algorithm 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. Finally, we describe a filtering algorithm for removing high-frequency noise during mesh refinement, and discuss some test examples. $$\copyright$$ Academic Press.

##### MSC:
 76M20 Finite difference methods applied to problems in fluid mechanics 76N15 Gas dynamics (general theory) 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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