SFB 1313 Publication by Melanie Lipp and Rainer Helmig

Our SFB 1313 researchers Melanie Lipp and Rainer Helmig published the article "A Locally-Refined Locally-Conservative Quadtree Finite-Volume Staggered-Grid Scheme" (pp 149-159) in the Springer book Droplet Interactions and Spray Processes. The book is a part of the Fluid Mechanics and Its Applications book series (FMIA, volume 121).

Abstract

Simulating flow between porous media and adjacent free-flow regions in sufficient detail becomes computationally expensive when complex flow profiles develop. This is e.g. the case if a variety of strongly coupled physical processes is involved or if the surface between the two flow domains is rough. However, it is often sufficient to only use a fine grid resolution in regions of interest. Here, we present a locally-refined quadtree finite-volume staggered-grid scheme for the two-dimensional Navier-Stokes equations. Local mass and momentum conservation at lines, at which the sides of two finer control volumes touch the side of one coarser control volume, is ensured by defining the fluxes at the sides of coarser control volumes to be equal to the negative sum of fluxes at the two sides of finer control volumes. The method has been successfully applied to locally resolve the flow details in the vicinity of dividing streamlines in a fluid-flow test case. Being developed for the fully-coupled fully-implicit solution of the Navier-Stokes equations, this locally-refined grid scheme is a good basis for increasing the efficiency of simulations of free flow, which is strongly coupled to flow in adjacent domains.