Engineering topics

Tsiveriotis, K.

Publications and source records attributed to Tsiveriotis, K..

4 records

NASA NTRS1993

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

Tsiveriotis, K.↗

NASA NTRS1992

Spatiotemporal chaos near the onset of cellular growth during thin-film solidification of a binary alloy

Thin-film solidification experiments with a succinonitrile-acetone alloy are used to observe the long time-scale dynamics of cellular crystal growth at growth rates only slightly above the critical value VC = Vc(lambda sub c) for the onset of morphological instability. Under these conditions only very small amplitude cells are observed with wavelengths near the value predicted by linear stability theory lambda = lambda sub c. At long times, microstructures with wavelengths significantly finer than lambda suc c form by nucleation at defects across the interface. These interfaces do not have a unique microstructure, but seem to exhibit spatiotemporal chaos on a long time scale caused by the continual birth and death of cells by tip splitting and cell annihilation in grooves.

Lee, J. T. C.↗

NASA NTRS1992

Boundary-conforming mapping applied to computations of highly deformed solidification interfaces

A new boundary-conforming mapping is developed for the calculation of highly deformed cellular solidification interfaces in a model of directional solidification of a binary alloy. The mapping is derived through a variational formulation that is designed so that the grid penetrates the grooves between cells along the interface without causing a loss of ellipticity of the mapping equations. A finite element/Newton method is presented for simultaneous solution of the free boundary problem described by the solutal model of directional solidification and the mapping equations. Results are compared to previous calculations and demonstrate the importance of accurate representation of the interface shape for understanding the solution structure.

Tsiveriotis, K.↗

NASA NTRS1989

Bifurcation structure and the Eckhaus instability

The bifurcation diagram corresponding to the Eckhaus stability curve has been constructed for the one-dimensional Swift-Hohenberg equation in a finite domain. Finite-amplitude solutions with particular spatial wavelength recover linear stability, as predicted by the Eckhaus curve, after a sequence of secondary bifurcations from the branch of solutions with this wavelength. No connectivity between the primary-solution branches is admissible if the stability predicted by this bifurcation diagram is to correspond to the prediction of the Eckhaus analysis. The Eckhaus curve does not exist if nonlinear couplings destroy this pattern. This is demonstrated by analysis of a coupled pair of Swift-Hohenberg equations.

Tsiveriotis, K.↗