A high-order finite difference method for moving immersed domain boundaries and material interfaces
Name
final_AIAA_SciTech2023_James[15].pdf
Description
Accepted version
Size
1.72 MB
Format
Adobe PDF
Checksum (MD5)
c1432c9530a9e9c596fffe081e6c6907
Author(s)
Gabbard, James
van Rees, Wim M.
Date Issued
June 2024
Journal
Journal of Computational Physics
Publisher
Elsevier BV
Citation
Gabbard, James and van Rees, Wim M. 2024. "A high-order finite difference method for moving immersed domain boundaries and material interfaces." Journal of Computational Physics, 507.
Version
Author's final manuscript
Abstract
We present a high-order sharp treatment of immersed moving domain boundaries and material interfaces, and apply it to the advection-diffusion equation in two and three dimensions. The spatial discretization combines dimension-split finite difference schemes with an immersed boundary treatment based on a weighted least-squares reconstruction of the solution, providing stable discretizations with up to sixth order accuracy for diffusion terms and third order accuracy for advection terms. The temporal discretization relies on a novel strategy for maintaining high-order temporal accuracy in problems with moving boundaries that minimizes implementation complexity and allows arbitrary explicit or diagonally-implicit Runge-Kutta schemes. The approach is broadly compatible with popular PDE-specialized Runge-Kutta time integrators, including low-storage, strong stability preserving, and diagonally implicit schemes. Through numerical experiments we demonstrate that the full discretization maintains high-order spatial and temporal accuracy in the presence of complex 3D geometries and for a range of boundary conditions, including Dirichlet, Neumann, and flux conditions with large jumps in coefficients.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution-Noncommercial-ShareAlike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.jcp.2024.112979
