Thomas-Fermi equation with non-spherical boundary conditions

1987 ◽  
Vol 70 (2) ◽  
pp. 284-294 ◽  
Author(s):  
M Friedman ◽  
A Rabinovitch ◽  
Y Rosenfeld ◽  
R Thieberger
Keyword(s):  
Boundary Conditions ◽  
Thomas Fermi ◽  
Spherical Boundary ◽  
Spherical Boundary Conditions

Group-theoretical methods in geophysics

1976 ◽  
Vol 348 (1652) ◽  
pp. 81-93 ◽  
Keyword(s):  
Finite Dimension ◽  
Convergent Series ◽  
Matrix Elements ◽  
Field Equations ◽  
Infinite Dimensional ◽  
Spherical Boundary ◽  
The Matrix ◽  
Boundary Perturbations ◽  
Spherical Boundary Conditions ◽  
Radial Operators

A group-theoretical technique is described whereby a linear system of tensor field equations of arbitrary rank and form, but with spherical or almost spherical boundary conditions, can be represented by an infinite-dimensional matrix equation. The matrix elements are in general radial operators, and formulae are given which enable them to be calculated explicitly. Particular reference is made to geophysical systems, where boundary perturbations, parameter fields and forcing fields may be expressed in terms of convergent series of spherical harmonics, and a truncated matrix of an appropriate finite dimension will represent the system to the desired accuracy.

scholarly journals Moving and reactive boundary conditions in moving-mesh hydrodynamics

2020 ◽  
Vol 494 (4) ◽  
pp. 4616-4626 ◽  
Author(s):  
Logan J Prust
Keyword(s):  
Boundary Conditions ◽  
Moving Boundary ◽  
Initial Conditions ◽  
Moving Boundaries ◽  
Moving Mesh ◽  
Test Cases ◽  
Conserved Quantities ◽  
Common Envelope ◽  
Gravitational Forces ◽  
Spherical Boundary

ABSTRACT We outline the methodology of implementing moving boundary conditions into the moving-mesh code manga. The motion of our boundaries is reactive to hydrodynamic and gravitational forces. We discuss the hydrodynamics of a moving boundary as well as the modifications to our hydrodynamic and gravity solvers. Appropriate initial conditions to accurately produce a boundary of arbitrary shape are also discussed. Our code is applied to several test cases, including a Sod shock tube, a Sedov–Taylor blast wave, and a supersonic wind on a sphere. We show the convergence of conserved quantities in our simulations. We demonstrate the use of moving boundaries in astrophysical settings by simulating a common envelope phase in a binary system, in which the companion object is modelled by a spherical boundary. We conclude that our methodology is suitable to simulate astrophysical systems using moving and reactive boundary conditions.

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