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AMR vs high order schemes. (English) Zbl 1112.76050
Summary: Adaptive Mesh Refinement (AMR) schemes are generally considered promising because of the ability of the scheme to place grid points or computational degrees of freedom at the location in the flow where truncation errors are unacceptably large. For a given order, AMR schemes can reduce work. However, for the computation of turbulent or non-turbulent mixing when compared to high order non-adaptive methods, traditional 2nd order AMR schemes are computationally more expensive.
We give precise estimates of work and restrictions on the size of the small scale grid and show that the requirements on the AMR scheme to be cheaper than a high order scheme are unrealistic for most computational scenarios.

76M20 Finite difference methods applied to problems in fluid mechanics
76F25 Turbulent transport, mixing
76V05 Reaction effects in flows
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
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