Juliacon 2024

As a physical field can exhibit significant inhomogeneity in space and time, a static mesh may lead to computational inefficiencies or inaccurate numerical results. Adaptive Mesh Refinement (AMR) addresses this challenge by redistributing computational resources based on the evolving features of the solution, resulting in a balance between efficiency and accuracy. Besides, the tree-based Cartesian enables a versatile description of boundaries of the computational domain and discontinuous solutions therein[1].
The ongoing project focuses on the numerical solution of kinetic equations. The high concentration of solution and the associated steep slopes highlight the necessity of adaptive discretization[2]. Based on P4est.jl[3] and MPI.jl[4], we develop the distributed quadtree/octree-based solver for multi-scale complex flows across a wide range of regimes. The lightning talk will first introduce the theoretical underpinnings and then showcase the applicability of the solver through comprehensive benchmarks. The pros and cons of the implementation using Julia will be discussed.
References
[1] Wang, Zhi Jian. “A Quadtree-based adaptive Cartesian/Quad grid flow solver for Navier-Stokes equations.” Computers & Fluids 27 (1998): 529-549.
[2] Chen, Songze et al. “A unified gas kinetic scheme with moving mesh and velocity space adaptation.” J. Comput. Phys. 231 (2012): 6643-6664.
[3] J. Lampert, M. Schlottke-Lakemper, H. Ranocha. https://github.com/trixi-framework/P4est.jl
[4] Byrne, Simon, Lucas C. Wilcox, and Valentin Churavy. "MPI. jl: Julia bindings for the Message Passing Interface." Proceedings of the JuliaCon Conferences. Vol. 1. No. 1. 2021.