| dc.description.abstract | This dissertation presents a novel surface tracking, and advection algorithm for incompressible fluid flows in two and three dimensions. This method based on the volume-of-fluid (VOF) method, is named VOF-with-center-of-mass-and-Lagrangian-particles (VCLP), and it uses spatially and temporally localized Lagrangian particles (LPs) inside a finite volume framework. The fluid surface is recaptured and reconstructed piecewise using the mean slope, mean curvature, and
fluid estimated using new methods from the local spatial distribution of the volume fluid fraction values. The reconstructed surfaces are either a finite plane or part of a spherical surface, in 3D and line segments or circular arcs, in 2D. The fluid mass inside each cell is discretized spatially by LPs and distributed as blue noise. LPs are then advected cell by cell with a choice of two different advection schemes in time using interpolated velocity and approximated acceleration fields. VCLP continuously tracks the center of mass of the fluid parcels in the Lagrangian way and this helps to reduce the errors due to numerical acceleration resulting from lack of information to reconstruct the interface accurately. LPs enable VCLP to work with structured and unstructured grids in two and three dimensions and might work for Courant–Friedrichs–Lewy numbers larger than one. LPs exist only inside a single fluid cell at a given time-step, allowing it to work without constraints on domain size and storage memory, unlike standard Lagrangian methods. LPs make it easy to adjust
computational accuracy vs. speed by only changing the number of LPs. VCLP’s performance is evaluated using standard benchmark tests such as translation, rotation, single vortex, deformation, and Zalesk’s tests from the literature. VCLP is applied to TSUNAMI2D, a 2D Navier-Stokes model to simulate the dam-break problem and breaking waves. | |
