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Implement boundary conditions in finite-volume code for conservation laws

0

$begingroup$

For the numerical solution of scalar hyperbolic conservation laws using finite volume schemes.
In order to implement the boundary conditions and the numerical
fluxes, make use of Ghost cells.
Consider the following flux functions.

• 
  $f ( u ) = a u$ with parameter $a in mathbb R $
  


• 
  $f ( u ) = frac 1 2 u ^ 2 $
  and the following numerical fluxes


• central scheme


• upwind scheme


• Lax-Wendroff scheme

How can the two flux functions be written in terms of the following schemes? And the boundary conditions have to be implemented using the ghost cell method.

numerical-methods hyperbolic-equations finite-volume-method

share|cite|improve this question

edited Mar 26 at 8:36

Harry49

8,78831346

asked Mar 21 at 11:43

Junia ShelomiJunia Shelomi

133

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What is your question ??
  $endgroup$
  – Fred
  Mar 21 at 11:45
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  How can the two flux functions be written in terms of the following schemes and the boundary conditions have to be implemented using the ghost cell method.
  $endgroup$
  – Junia Shelomi
  Mar 22 at 19:08
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What type of boundary condition are you interested in? (periodic, outflow, Dirichlet, etc.) What programming language do you use?
  $endgroup$
  – Harry49
  Mar 26 at 8:37
  
  

  
  
  
  

add a comment | 

0

$begingroup$

For the numerical solution of scalar hyperbolic conservation laws using finite volume schemes.
In order to implement the boundary conditions and the numerical
fluxes, make use of Ghost cells.
Consider the following flux functions.

• 
  $f ( u ) = a u$ with parameter $a in mathbb R $
  


• 
  $f ( u ) = frac 1 2 u ^ 2 $
  and the following numerical fluxes


• central scheme


• upwind scheme


• Lax-Wendroff scheme

How can the two flux functions be written in terms of the following schemes? And the boundary conditions have to be implemented using the ghost cell method.

numerical-methods hyperbolic-equations finite-volume-method

share|cite|improve this question

edited Mar 26 at 8:36

Harry49

8,78831346

asked Mar 21 at 11:43

Junia ShelomiJunia Shelomi

133

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What is your question ??
  $endgroup$
  – Fred
  Mar 21 at 11:45
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  How can the two flux functions be written in terms of the following schemes and the boundary conditions have to be implemented using the ghost cell method.
  $endgroup$
  – Junia Shelomi
  Mar 22 at 19:08
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What type of boundary condition are you interested in? (periodic, outflow, Dirichlet, etc.) What programming language do you use?
  $endgroup$
  – Harry49
  Mar 26 at 8:37
  
  

  
  
  
  

add a comment | 

$begingroup$

For the numerical solution of scalar hyperbolic conservation laws using finite volume schemes.
In order to implement the boundary conditions and the numerical
fluxes, make use of Ghost cells.
Consider the following flux functions.

• 
  $f ( u ) = a u$ with parameter $a in mathbb R $
  


• 
  $f ( u ) = frac 1 2 u ^ 2 $
  and the following numerical fluxes


• central scheme


• upwind scheme


• Lax-Wendroff scheme

How can the two flux functions be written in terms of the following schemes? And the boundary conditions have to be implemented using the ghost cell method.

numerical-methods hyperbolic-equations finite-volume-method

share|cite|improve this question

edited Mar 26 at 8:36

Harry49

8,78831346

asked Mar 21 at 11:43

Junia ShelomiJunia Shelomi

133

$endgroup$

share|cite|improve this question

edited Mar 26 at 8:36

Harry49

8,78831346

asked Mar 21 at 11:43

Junia ShelomiJunia Shelomi

133

share|cite|improve this question

edited Mar 26 at 8:36

Harry49

8,78831346

asked Mar 21 at 11:43

Junia ShelomiJunia Shelomi

133

edited Mar 26 at 8:36

Harry49

8,78831346

edited Mar 26 at 8:36

Harry49

8,78831346

asked Mar 21 at 11:43

Junia ShelomiJunia Shelomi

133

asked Mar 21 at 11:43

Junia ShelomiJunia Shelomi

133