Moving boundaries: an Eulerian approach

摘要

For many problems, it is advantageous to maintain a grid which is fixed in space while allowing internal boundaries of the fluid and/or solid regions to move within it. This is appropriate wherever drastic changes in the conformation of these boundaries occur, as the necessity of remeshing is avoided. Mesh generation is also greatly simplified. Various approaches are shown to model the boundary movement of the fluid interface, sediment, solidified fluid, and elastic materials within the fixed grid. The movement of fluid boundaries is accomplished with a variant of the Volume-of-Fluid (VOF) method whereby a quantity representing the amount of fluid in each of the computational cells is advected through the fixed- mesh. Erosion and deposition of sediment is computed by means of a sediment scour model; the local rate of erosion is based on the local shear stress present at the packed sediment/fluid interface, and deposition is predicted with a Stokes flow approximation. The packed bed interface conforms according to the sediment concentration and the packing fraction of the sediment. Molten metal can solidify as the temperature drops below its freezing point. The solidified "fluid" is then treated just like a solid whose surface grows or shrinks as determined from the amount of heat flux causing freezing and/or melting. Elastic stresses are computed in solidified regions by the addition of an elastic stress computation into the momentum balance within the same fixed grid with the VOF method predicting the solidified material/air interface.