A fictitious domain method with distributed Lagrange multipliers on adaptive quad/octrees for the direct numerical simulation of particle-laden flows

In this article, we extend our Distributed Lagrange Multiplier/Fictitious Domain method previously implemented on simple regular Cartesian grids to quadtree/octree adaptive grids. The objective is improve both the accuracy and efficiency of DLM/FD particle-resolved simulation by extending its computing capabilities through dynamic local mesh refinement. main features numerical method, such as a first-order operator splitting time algorithm second-order reconstruction velocity field close boundary immersed rigid bodies (of arbitrary shape), are unchanged. We within Basilisk, parallel platform solve partial differential equations structure grid specific design rules Basilisk impose special treatment some operations performed in DLM/FD-Uzawa algorithm. new computational then tested validated set flow configurations including challenging problem accurately lubrication interaction forces without resorting using any ad hoc correction. Finally, illustrate potential code compute complex particle-laden that were not attainable past with grid.