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We propose theadaptive hybrid particle-grid flow mapmethod, a novel flow-map approach that leverages Lagrangian particles to simultaneously transport impulse and guide grid adaptation, introducing a fully adaptive flow map-based fluid simulation framework. The core idea of our method is to maintain flow-map trajectories separately on grid nodes and particles: the grid-based representation tracks long-range flow maps at a coarse spatial resolution, while the particle-based representation tracks both long and short-range flow maps, enhanced by their gradients, at a fine resolution. This hybrid Eulerian-Lagrangian flow-map representation naturally enables adaptivity for both advection and projection steps. We implement this method inCirrus, a GPU-based fluid simulation framework designed for octree-like adaptive grids enhanced with particle trackers. The efficacy of our system is demonstrated through numerical tests and various simulation examples, achieving up to 512 × 512 × 2048 effective resolution on an RTX 4090 GPU. We achieve a 1.5 to 2× speedup with our GPU optimization over the Particle Flow Map method on the same hardware, while the adaptive grid implementation offers efficiency gains of one to two orders of magnitude by reducing computational resource requirements. The source code has been made publicly available at: https://wang-mengdi.github.io/proj/25-cirrus/.
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Optimized wavelet‐based adaptive mesh refinement algorithm for numerical modeling of three‐dimensional global‐scale atmospheric chemical transport
Abstract Substantial numerical difficulties associated with the computational modeling of multiscale global atmospheric chemical transport impose severe limitations on the spatial resolution of nonadaptive fixed grids. The crude spatial discretization introduces a large amount of numerical diffusion into the system, which, in combination with strong flow stretching, causes large numerical errors. To resolve this issue, we have developed an optimized wavelet‐based adaptive mesh refinement (OWAMR) method. The OWAMR is a three‐dimensional adaptive method that introduces a fine grid dynamically only in the regions where small spatial structures occur. The algorithm uses a new two‐parameter adaptation criterion that significantly (by factors between 1.5 and 2.7) reduces the number of grid points compared with the more conventional one‐parameter grid adaptation used by wavelet‐based adaptive techniques and high‐order upwind schemes, which enable one to increase the accuracy of approximation of the advection operator substantially. It has been shown that the method simulates the dynamics of a pollution plume that travels on a global scale, producing less than 3% error. To achieve such accuracy, conventional three‐dimensional nonadaptive techniques would require five orders of magnitude more computational resources. Therefore, the method provides a realistic opportunity to model accurately a variety of the most demanding multiscale problems in the area of atmospheric chemical transport, which are difficult or impossible to simulate on existing computational facilities with conventional fixed‐grid techniques.
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- Award ID(s):
- 1832089
- PAR ID:
- 10456547
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Quarterly Journal of the Royal Meteorological Society
- Volume:
- 146
- Issue:
- 729
- ISSN:
- 0035-9009
- Page Range / eLocation ID:
- p. 1564-1574
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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