scholarly journals Numerical solution of free-boundary problems in fluid mechanics. Part 1. The finite-difference technique

1984 ◽  
Vol 148 ◽  
pp. 1-17 ◽  
Author(s):  
G. Ryskin ◽  
L. G. Leal
Keyword(s):  
Finite Difference ◽  
Free Boundary ◽  
Fluid Mechanics ◽  
Free Boundary Problems ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
Boundary Problems ◽  
Boundary Shape ◽  
Curvilinear Coordinate ◽  
Ultimate Equilibrium

We present here a brief description of a numerical technique suitable for solving axisymmetric (or two-dimensional) free-boundary problems of fluid mechanics. The technique is based on a finite-difference solution of the equations of motion on an orthogonal curvilinear coordinate system, which is also constructed numerically and always adjusted so as to fit the current boundary shape. The overall solution is achieved via a global iterative process, with the condition of balance between total normal stress and the capillary pressure at the free boundary being used to drive the boundary shape to its ultimate equilibrium position.

scholarly journals On integrability and exact solvability in deterministic and stochastic Laplacian growth

2020 ◽  
Vol 15 ◽  
pp. 3
Author(s):  
Igor Loutsenko ◽  
Oksana Yermolayeva
Keyword(s):  
Free Boundary ◽  
Fluid Mechanics ◽  
Integrable Systems ◽  
Stochastic Models ◽  
Free Boundary Problems ◽  
Exact Results ◽  
Laplacian Growth ◽  
Quantum Integrable Systems ◽  
Boundary Problems ◽  
Exact Solvability

We review applications of theory of classical and quantum integrable systems to the free-boundary problems of fluid mechanics as well as to corresponding problems of statistical mechanics. We also review important exact results obtained in the theory of multi-fractal spectra of the stochastic models related to the Laplacian growth: Schramm-Loewner and Levy-Loewner evolutions.

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