Many industrial and natural processes involve the transport of conserved quantities. Typically, the modeling of these processes involves the solution of partial differential equations in domains with well-defined boundaries. However, there is a wide class of problems that involve free or moving boundaries. In these problems, the location of one or more of the domain boundaries is an unknown in the problem (a free boundary), or a boundary on which balance conditions have to be met, and moves through the domain. The classical example is the tracking of the solid/liquid interface during the melting of ice-the Stefan Problem.
Mauricio Fabbri, Space Research Institute, Laboratory for Materials and Sensors, Campos, Brazil
James A. Luoma, Graduate Student Researcher
Daniela Mansutti, I.A.C., Rome, Italy
99/85 |
"Free and Moving Boundary Problems in Geophysical Systems," V.R. Voller and J.B. Swenson, University of Minnesota Supercomputing Institute Research Report UMSI 99/85, April 1999. |
99/86 |
"An Adaptive-Mesh Control-Volume Approach for Groundwater Flow Through an Earthen Dam," J.B. Swenson, M. Bakker, and V.R. Voller, University of Minnesota Supercomputing Institute Research Report UMSI 99/86, April 1999. |
This work is focusing on the development of computational tools for the analysis of free surface and moving boundary problems. Early work was in the area encountered in materials processing; in particular, solidification and polymer processes. More recently, problems in earth sciences have been undertaken. Recent efforts involved a study of microsegregation processes in a casting. These efforts also continued work of moving boundaries in geo-morphology problems.
The aim of the current proposal is to continue the solidification work. An investigation of the effect of micro-scale process in the two phase mushy region of a binary alloy on macrosegregation predictions is being studied. Further work is developing some initial ideas for investigating problems that involve hydraulic fracturing-a moving boundary problem that has an interesting fluid-structural interaction. Finally, the work is initiating research on sediment transport in the environment. Sediment transport from the mountain peaks to the bottom of the ocean trenches occurs across multiple physical regimes, each governed by a distinct set of transport mechanisms. At the interface between regimes, the sediment mass must balance. Any imbalance needs to be accounted for by moving the regime interface (a moving boundary) or creating a cliff (mass storage).
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