3,555 research outputs found
Recommended from our members
The numerical solution of stefan problems with front-tracking and smoothing methods
Global existence, uniqueness and stability for nonlinear dissipative bulk-interface interaction systems
We show global well-posedness and exponential stability of equilibria for a
general class of nonlinear dissipative bulk-interface systems. They correspond
to thermodynamically consistent gradient structure models of bulk-interface
interaction. The setting includes nonlinear slow and fast diffusion in the bulk
and nonlinear coupled diffusion on the interface. Additional driving mechanisms
can be included and non-smooth geometries and coefficients are admissible, to
some extent. An important application are volume-surface reaction-diffusion
systems with nonlinear coupled diffusion.Comment: 21 page
Exact solution for a two-phase Stefan problem with variable latent heat and a convective boundary condition at the fixed face
Recently it was obtained in [Tarzia, Thermal Sci. 21A (2017) 1-11] for the
classical two-phase Lam\'e-Clapeyron-Stefan problem an equivalence between the
temperature and convective boundary conditions at the fixed face under a
certain restriction. Motivated by this article we study the two-phase Stefan
problem for a semi-infinite material with a latent heat defined as a power
function of the position and a convective boundary condition at the fixed face.
An exact solution is constructed using Kummer functions in case that an
inequality for the convective transfer coefficient is satisfied generalizing
recent works for the corresponding one-phase free boundary problem. We also
consider the limit to our problem when that coefficient goes to infinity
obtaining a new free boundary problem, which has been recently studied in
[Zhou-Shi-Zhou, J. Engng. Math. (2017) DOI 10.1007/s10665-017-9921-y].Comment: 16 pages, 0 figures. arXiv admin note: text overlap with
arXiv:1610.0933
An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems
In the context of analyzing a new model for nonlinear diffusion in polymers, an
unusual condition appears at the moving interface between the glassy and rubbery phases of the
polymer. This condition, which arises from the inclusion of a viscoelastic memory term in our
equations, has received very little attention in the mathematical literature. Due to the unusual form
of the moving-boundary condition, further study is needed as to the existence and uniqueness of
solutions satisfying such a condition. The moving boundary condition which results is not solvable
by similarity solutions, but can be solved by integral equation techniques. A solution process is
outlined to illustrate the unusual nature of the condition; the profiles which result are characteristic
of a dissolving polymer
A NASTRAN implementation of the doubly asymptotic approximation for underwater shock response
A detailed description is given of how the decoupling approximation known as the doubly asymptotic approximation is implemented with NASTRAN to solve shock problems for submerged structures. The general approach involves locating the nonsymmetric terms (which couple structural and fluid variables) on the right hand side of the equations. This approach results in coefficient matrices of acceptable bandwidth but degrades numerical stability, requiring a smaller time step size than would otherwise be used. It is also shown how the structure's added (virtual) mass matrix, is calculated with NASTRAN
- …