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Sharp Fronts (sharp + front)

Distribution by Scientific Domains

Engineering	40%

Selected Abstracts

A mass-conserving Level-Set method for modelling of multi-phase flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2005
S. P. van der Pijl
Abstract A mass-conserving Level-Set method to model bubbly flows is presented. The method can handle high density-ratio flows with complex interface topologies, such as flows 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 flow is computed with a pressure correction method with the Marker-and-Cell scheme. Interface conditions are satisfied by means of the continuous surface force methodology and the jump in the density field is maintained similar to the ghost fluid method for incompressible flows. Copyright © 2005 John Wiley & Sons, Ltd. [source]

On the evolution of sharp fronts for the quasi-geostrophic equation

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 6 2005
José Luis Rodrigo
We consider the problem of the evolution of sharp fronts for the surface quasi-geostrophic (QG) equation. This problem is the analogue to the vortex patch problem for the two-dimensional Euler equation. The special interest of the quasi-geostrophic equation lies in its strong similarities with the three-dimensional Euler equation, while being a two-dimen-sional model. In particular, an analogue of the problem considered here, the evolution of sharp fronts for QG, is the evolution of a vortex line for the three-dimensional Euler equation. The rigorous derivation of an equation for the evolution of a vortex line is still an open problem. The influence of the singularity appearing in the velocity when using the Biot-Savart law still needs to be understood. We present two derivations for the evolution of a periodic sharp front. The first one, heuristic, shows the presence of a logarithmic singularity in the velocity, while the second, making use of weak solutions, obtains a rigorous equation for the evolution explaining the influence of that term in the evolution of the curve. Finally, using a Nash-Moser argument as the main tool, we obtain local existence and uniqueness of a solution for the derived equation in the C, case. © 2004 Wiley Periodicals, Inc. [source]

Adaptive moving mesh methods for simulating one-dimensional groundwater problems with sharp moving fronts

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002
Weizhang Huang
Abstract Accurate modelling of groundwater flow and transport with sharp moving fronts often involves high computational cost, when a fixed/uniform mesh is used. In this paper, we investigate the modelling of groundwater problems using a particular adaptive mesh method called the moving mesh partial differential equation approach. With this approach, the mesh is dynamically relocated through a partial differential equation to capture the evolving sharp fronts with a relatively small number of grid points. The mesh movement and physical system modelling are realized by solving the mesh movement and physical partial differential equations alternately. The method is applied to the modelling of a range of groundwater problems, including advection dominated chemical transport and reaction, non-linear infiltration in soil, and the coupling of density dependent flow and transport. Numerical results demonstrate that sharp moving fronts can be accurately and efficiently captured by the moving mesh approach. Also addressed are important implementation strategies, e.g. the construction of the monitor function based on the interpolation error, control of mesh concentration, and two-layer mesh movement. Copyright © 2002 John Wiley & Sons, Ltd. [source]