SUMMARYA mass-conserving Level-Set method to model bubbly ows is presented. The method can handle high density-ratio ows with complex interface topologies, such as ows with simultaneous occurrence of bubbles and droplets. Aspects taken into account are: a sharp front (density changes abruptly), arbitrarily shaped interfaces, surface tension, buoyancy and coalescence of droplets=bubbles. Attention is paid to mass-conservation and integrity of the interface.The proposed computational method is a Level-Set method, where a Volume-of-Fluid function is used to conserve mass when the interface is advected. The aim of the method is to combine the advantages of the Level-Set and Volume-of-Fluid methods without the disadvantages. The ow is computed with a pressure correction method with the Marker-and-Cell scheme. Interface conditions are satisÿed by means of the continuous surface force methodology and the jump in the density ÿeld is maintained similar to the ghost uid method for incompressible ows.
A method is described to compute threedimensional two-phase flow, allowing large density ratios and coalescence and break-up of bubbles. The level set method is used to describe interfaces, and the volume-offluid method is used to ensure mass conservation. Efficiency in computing the interface dynamics is achieved by using a functional relation between the level set and volume-of-fluid functions. Difficulties and remedies in re-initialization of the level set function and inaccurate compution of surface tension are discussed. Test cases for validation are described, and demanding two-bubble computations to show the generality and the versatility of the method are presented. Dedicated to Wolfgang Hackbusch on the occasion of his 60th birthday. Communicated by G. Wittum.
This work aims to model the optimal control of dike heights. The control problem leads to so-called Hamilton-Jacobi-Bellman (HJB) variational inequalities, where the dike-increase and reinforcement times act as input quantities to the control problem. The HJB equations are solved numerically with an Essentially Non-Oscillatory (ENO) method. The ENO methodology is originally intended for hyperbolic conservation laws and is extended to deal with diffusion-type problems in this work. The method is applied to the dike optimisation of an island, for both deterministic and stochastic models for the economic growth.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.