Weak Implementation of Boundary Conditions for the FiniteVolume Method
(2014) In Master's Theses in Mathematical Sciences FMN820 20142Mathematics (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 nonlinear 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 nodecentred finitevolume method, approximations of twodimensional 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 nonlinear 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 nodecentred finitevolume method, approximations of twodimensional 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)
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http://lup.lub.lu.se/studentpapers/record/4811949
 author
 Fryklund, Fredrik ^{LU}
 supervisor

 Philipp Birken ^{LU}
 organization
 course
 FMN820 20142
 year
 2014
 type
 H2  Master's Degree (Two Years)
 subject
 publication/series
 Master's Theses in Mathematical Sciences
 report number
 LUTFMA30302014
 ISSN
 14046342
 other publication id
 2014:E57
 language
 English
 id
 4811949
 date added to LUP
 20141215 12:53:11
 date last changed
 20151214 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 nonlinear 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 nodecentred finitevolume method, approximations of twodimensional 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 = {{14046342}}, language = {{eng}}, note = {{Student Paper}}, series = {{Master's Theses in Mathematical Sciences}}, title = {{Weak Implementation of Boundary Conditions for the FiniteVolume Method}}, year = {{2014}}, }