2000 character limit reached
Analysis of the particle relaxation method for generating uniform particle distributions in smoothed particle hydrodynamics (2403.00623v1)
Published 1 Mar 2024 in math.NA, cs.NA, and physics.comp-ph
Abstract: We establish a theoretical framework of the particle relaxation method for uniform particle generation of Smoothed Particle Hydrodynamics. We achieve this by reformulating the particle relaxation as an optimization problem. The objective function is an integral difference between discrete particle-based and smoothed-analytical volume fractions. The analysis demonstrates that the particle relaxation method in the domain interior is essentially equivalent to employing a gradient descent approach to solve this optimization problem, and we can extend such an equivalence to the bounded domain by introducing a proper boundary term. Additionally, each periodic particle distribution has a spatially uniform particle volume, denoted as characteristic volume. The relaxed particle distribution has the largest characteristic volume, and the kernel cut-off radius determines this volume. This insight enables us to control the relaxed particle distribution by selecting the target kernel cut-off radius for a given kernel function.
- Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 181(3):375–389, 1977.
- Leon B Lucy. A numerical approach to the testing of the fission hypothesis. Astronomical Journal, vol. 82, Dec. 1977, p. 1013-1024., 82:1013–1024, 1977.
- A sph approach for large deformation analysis with hypoplastic constitutive model. Acta Geotechnica, 10:703–717, 2015.
- Crksph–a conservative reproducing kernel smoothed particle hydrodynamics scheme. Journal of Computational Physics, 332:160–209, 2017.
- Grand challenges for smoothed particle hydrodynamics numerical schemes. Computational Particle Mechanics, 8:575–588, 2021.
- Towards consistence and convergence of conservative sph approximations. Journal of Computational Physics, 301:394–401, 2015.
- Robustness and accuracy of sph formulations for viscous flow. International Journal for Numerical Methods in Fluids, 60(10):1127–1148, 2009.
- Truncation error in mesh-free particle methods. International Journal for Numerical Methods in Engineering, 66(13):2064–2085, 2006.
- High-order velocity and pressure wall boundary conditions in eulerian incompressible sph. Journal of Computational Physics, 434:109793, 2021.
- Development of a new pre-processing tool for sph models with complex geometries. In 6th International SPHERIC workshop, pages 117–124, 2011.
- Algorithms for uniform particle initialization in domains with complex boundaries. Computer Physics Communications, 265:108008, 2021.
- Generating optimal initial conditions for smoothed particle hydrodynamics simulations. Publications of the Astronomical Society of Australia, 32:e048, 2015.
- An isotropic unstructured mesh generation method based on a fluid relaxation analogy. Computer Methods in Applied Mechanics and Engineering, 350:396–431, 2019.
- A cad-compatible body-fitted particle generator for arbitrarily complex geometry and its application to wave-structure interaction. Journal of Hydrodynamics, 33(2):195–206, 2021.
- Level-set based pre-processing algorithm for particle-based methods. arXiv preprint arXiv:2209.04424, 2022.
- Initial particle arrangement for the arbitrarily complex geometry of mesh-free methods. Computational Particle Mechanics, 10(3):663–675, 2023.
- Sphinxsys: An open-source meshless, multi-resolution and multi-physics library. Software Impacts, 6:100033, 2020.
- Dualsphysics: from fluid dynamics to multiphysics problems. Computational Particle Mechanics, 9(5):867–895, 2022.
- Mutual interactions, potentials, and individual distance in a social aggregation. Journal of mathematical biology, 47:353–389, 2003.
- Marek Bodnar and Juna Jose Lopez Velazquez. Derivation of macroscopic equations for individual cell-based models: a formal approach. Mathematical methods in the applied sciences, 28(15):1757–1779, 2005.
- Weerapat Pittayakanchit. The global stability of the solution to the morse potential in a catastrophic regime. 2016.
- Density functional theory of electronic structure. The Journal of Physical Chemistry, 100(31):12974–12980, 1996.
- Classical dynamical density functional theory: from fundamentals to applications. Advances in Physics, 69(2):121–247, 2020.
- A physics-motivated centroidal voronoi particle domain decomposition method. Journal of Computational Physics, 335:718–735, 2017.
- A consistent parallel isotropic unstructured mesh generation method based on multi-phase sph. Computer Methods in Applied Mechanics and Engineering, 363:112881, 2020.
- A feature-aware sph for isotropic unstructured mesh generation. Computer Methods in Applied Mechanics and Engineering, 375:113634, 2021.
- Nonlocal aggregation models: A primer of swarm equilibria. SIAM REVIEW, 55(4):709–747, 2013.
- Level set methods and dynamic implicit surfaces, volume 1. Springer New York, 2005.
- Charles Kittel. Introduction to solid state physics. John Wiley & sons, inc, 2005.
- A novel partitioning method for block-structured adaptive meshes. Journal of Computational Physics, 341:447–473, 2017.