A 3D adaptive mesh refinement algorithm for multimaterial gas dynamics

TL;DR: In this paper, the authors consider the formation of droplet clouds or sprays that subsequently burn in combustion chambers, which is caused by interfacial instabilities, such as the Kelvin-Helmholtz instability.

TL;DR: The method is tested by testing its ability to track interfaces through large, controlled topology changes, whereby an initially simple interface configuration is subjected to vortical flows, and numerical results for these strenuous test problems provide evidence for the algorithm's improved solution quality and accuracy.

TL;DR: This work provides a comprehensive review of the strategy of the CIP method, which has a compact support and subcell resolution, including a front-capturing algorithm with functional transformation, a pressure-based algorithm, and other miscellaneous physics such as the elastic–plastic effect and surface tension.

TL;DR: A design criteria for a volume-of-fluid interface reconstruction algorithm to be second-order accurate is proposed, which is that it reproduce lines in two space dimensions or planes in three space dimensions exactly.

TL;DR: An automatic, adaptive mesh refinement strategy for solving hyperbolic conservation laws in two dimensions and how to organize the algorithm to minimize memory and CPU overhead is developed.

TL;DR: This work presents an adaptive method based on the idea of multiple, component grids for the solution of hyperbolic partial differential equations using finite difference techniques based upon Richardson-type estimates of the truncation error, which is a mesh refinement algorithm in time and space.