Skip to main content

LUP Student Papers

LUND UNIVERSITY LIBRARIES

Weak Implementation of Boundary Conditions for the Finite-Volume Method

Fryklund, Fredrik LU (2014) In Master's Theses in Mathematical Sciences FMN820 20142
Mathematics (Faculty of Engineering)
Abstract
The Euler equations consist of conservation laws and describe a fluid in motion without viscous forces and heat conduction. They are non-linear and the solutions are often discontinuous. Therefore proofs of convergence are hard to give and the existing results are lacking. A new concept are weakly imposed characteristic boundary conditions, where a priori given boundary data only enter the scheme via ingoing characteristics. Thus a numerical solution for the boundary points is obtained as well. In combination with the node-centred finite-volume method, approximations of two-dimensional steady conservation laws can be made stable. Weakly imposed characteristic boundary conditions are compared to weakly imposed prescribed fluxes for the... (More)
The Euler equations consist of conservation laws and describe a fluid in motion without viscous forces and heat conduction. They are non-linear and the solutions are often discontinuous. Therefore proofs of convergence are hard to give and the existing results are lacking. A new concept are weakly imposed characteristic boundary conditions, where a priori given boundary data only enter the scheme via ingoing characteristics. Thus a numerical solution for the boundary points is obtained as well. In combination with the node-centred finite-volume method, approximations of two-dimensional steady conservation laws can be made stable. Weakly imposed characteristic boundary conditions are compared to weakly imposed prescribed fluxes for the steady Euler equations, where the residuals converged to 10^-11 and 10^-3, respectively. The performance of these boundary conditions is investigated further for different grid sizes and the unsteady Euler equations. (Less)
Popular Abstract (Swedish)
Se bilaga (sid iv-v) under "Files & Access".
Please use this url to cite or link to this publication:
author
Fryklund, Fredrik LU
supervisor
organization
course
FMN820 20142
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master's Theses in Mathematical Sciences
report number
LUTFMA-3030-2014
ISSN
1404-6342
other publication id
2014:E57
language
English
id
4811949
date added to LUP
2014-12-15 12:53:11
date last changed
2015-12-14 13:32:15
@misc{4811949,
  abstract     = {{The Euler equations consist of conservation laws and describe a fluid in motion without viscous forces and heat conduction. They are non-linear and the solutions are often discontinuous. Therefore proofs of convergence are hard to give and the existing results are lacking. A new concept are weakly imposed characteristic boundary conditions, where a priori given boundary data only enter the scheme via ingoing characteristics. Thus a numerical solution for the boundary points is obtained as well. In combination with the node-centred finite-volume method, approximations of two-dimensional steady conservation laws can be made stable. Weakly imposed characteristic boundary conditions are compared to weakly imposed prescribed fluxes for the steady Euler equations, where the residuals converged to 10^-11 and 10^-3, respectively. The performance of these boundary conditions is investigated further for different grid sizes and the unsteady Euler equations.}},
  author       = {{Fryklund, Fredrik}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Weak Implementation of Boundary Conditions for the Finite-Volume Method}},
  year         = {{2014}},
}