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In the turbulent accretion problem, whether automated mesh refinement yields any benefits is not clear.
We observe that Jain's scheme with a local mesh refinement yields numerical solutions which exhibit the expected fourth-order convergence rate.
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For instance, bisection-based mesh-refinements yield | T ′ | ≤ | T | / 2, if T ′ ∈ T ℓ + 1 ∖ T ℓ is a son of T ∈ T ℓ ∖ T ℓ + 1. Extensions of the analysis of [15].
This new boundary condition eliminates the stress singularity at the contact line; the resulting problem is thus well-posed and yields solutions that converge with mesh refinement.
It is demonstrated that using filament capturing at a given resolution yields gains in accuracy comparable to introducing an additional level of mesh refinement at significantly lower cost.
The overall mesh refinement causes the CPU time cost to greatly increase as the mesh is refined.
Lecture 19 (October 28): Mesh refinement and coarsening.
Teyssier, R. Cosmology hydrodynamics with adaptive mesh refinement.
For coarser model, like bunny, mesh refinement is necessary.
Mesh refinement studies are also performed.
Bryan, G. L. et al. Enzo: an adaptive mesh refinement code for astrophysics.
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