Applications of Space-Filling-Curves to Cartesian Methods for CFD

Abstract

The proposed paper presents a variety novel uses of Space-Filling-Curves (SFCs) for Cartesian mesh methods in 0. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, most are applicable on general body-fitted meshes -both structured and unstructured. We demonstrate the use of single O(N log N) SFC-based reordering to produce single-pass (O(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including "warm starts'' on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations. Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 512 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 10% of ideal even with only around 50,000 cells in each subdomain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for finite-difference-based gradient design methods.

Numerical Modeling of Micron-Scale Flows Using the Gaussian Moment Closure

“…26,27,28 They also have narrow stencils, making them suitable for implementation on high-speed massively parallel computer architectures. 29,30,31 In the present work, the application of the Gaussian moment closure to micron-scale flows is considered. In particular, its solutions are explored using a parallel AMR Godunov-type finite-volume scheme.…”

A decade of progress on anisotropic mesh adaptation for computational fluid dynamics

“…This is why during the late 80's and the 90's a considerable amount of e↵ort was devoted to automatic mesh generation. The state-of-the-art of all the meshing technologies is wide [1], but at present, the main approaches for generality and ease of use in CFD are: multiblock grids [2], adaptive Cartesian grids [3] and unstructured mono-element meshes [4,5,6,7,8,9]. This first issue is clear, but a second one is more malicious: a "bad" mesh implies a wrong or inaccurate solution.…”

A parallel solution – adaptive method for three-dimensional turbulent non-premixed combusting flows

“…Placing nearest-neighbour blocks on the same processor can also help to reduce the overall communication costs. This is usually realized by utilizing space-filling curves which can provide rather high quality partitions at very low computational costs [99,100] due to their ''proximity preserving" mappings of a multidimensional space to one-dimensional space. In this work, a Morton ordering space-filling curve is adopted to provide nearest-neighbour ordering of the solution blocks in the multi-block hexahedral AMR meshes, and improve the parallel performance of the proposed solution method [100].…”