Talk:MUSCL scheme

message: Maybe, it would be better to illustrate MUSCL more in original context of upwind Godunov schemes, as it is in famous van Leer's serial of papers, and not only in semi-discrete central Godunov schemes, which is quite new concept. But I also use it now in Kurganov-Tadmor variation. --Vladimír Fuka 17:07, 7 September 2006 (UTC)
replies: text: Possibly. I will think about it. Griffgruff 11:24, 17 May 2007 (UTC)
thread_title: Historical perspective

message: Proper style of citation in Harvard system (author, date) is not to repeat author's name in parenthesis when it is used in the sentence , for example: ... as shown by Godunov (1959) ... contrary to ... as shown in (Godunov, 1959) ...  See http://en.wikipedia.org/wiki/Harvard_system . If you don't mind, I will repair it.
--Vladimír Fuka 16:54, 21 October 2006 (UTC)
thread_title: Proper citation

message: The Kurganov and Tadmor scheme starts with F* reconstruction using the local maximum of the flux jacobian \partial F/\partial u. Isn't this exactly the same as the local Lax-Friedrichs method, originally described by Rusanov in J. Comp. Math. Phys. USSR, 1 (1961)? (Source: Randall J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, 2002, see pp. 232,233) --ArthurVanDam 15:25, 14 May 2007 (UTC)
replies: text: Yes, you are correct. In fact Kurganov and Tadmor acknowledge this in their paper. I will shortly add someting to this effect. Thank you for your feedback and kind comments on my talk page. Griffgruff 11:22, 17 May 2007 (UTC)
replies: text: Reference to Rusanov and local Lax-Friedrichs fluxes now included. Griffgruff 13:37, 18 May 2007 (UTC)
thread_title: Rusanov contribution

message: Currently the local propagation speed in the KT scheme is given as
:  a_{i \pm \frac{1}{2} } \left( t \right) = \max \left[ 
\rho \left( \frac{\partial F \left( u_{i}   \left( t \right) \right)}{\partial u} \right) ,
\rho \left( \frac{\partial F \left( u_{i \pm 1} \left( t \right) \right)}{\partial u} \right), 
\right] 
However, in Eq. (3.2) of the original paper it is defined as 
:  a_{i + \frac{1}{2} } \left( t \right) = \max \left[ 
\rho \left( \frac{\partial F \left( u^L_{i+1/2}   \left( t \right) \right)}{\partial u} \right) ,
\rho \left( \frac{\partial F \left( u^R_{i+1/2} \left( t \right) \right)}{\partial u} \right), 
\right] 
So instead of using the cell values they use the extrapolated ones. Am I missing something here? Or is this a mistake on the page? Arno Mayrhofer (talk) 04:01, 6 February 2015 (UTC)
replies: text: Thank you for spotting this error, which I have now corrected. Graham W. Griffiths (talk) 09:58, 6 February 2015 (UTC)
thread_title:  Local propagation speed in the KT scheme 

message: In chapter Linear reconstruction
Formula
: u^L_{i + 1/2} = u_i + 0.5 \phi \left( r_i \right) \left( u_{i} - u_{i-1} \right),
  u^R_{i + 1/2} = u_{i+1} - 0.5 \phi \left( r_{i} \right)  \left( u_{i+1} - u_{i} \right),
should be corrected to
: u^L_{i + 1/2} = u_i + 0.5 \phi \left( r_i \right) \left( u_{i+1} - u_{i} \right),
  u^R_{i + 1/2} = u_{i+1} - 0.5 \phi \left( r_{i+1} \right)  \left( u_{i+1} - u_{i} \right),
In chapter Example: 1D Euler equations
Formula
: \rho^L_{i + \frac{1}{2}} = \rho_{i}   + 0.5 \phi \left( r_{i} \right) \left( \rho_{i+1} - \rho_{i} \right),
  \rho^R_{i + \frac{1}{2}} = \rho_{i+1} - 0.5 \phi \left( r_{i+1} \right)  \left( \rho_{i+2} - \rho_{i+1} \right),
should be corrected to
: \rho^L_{i + \frac{1}{2}} = \rho_{i}   + 0.5 \phi \left( r_{i} \right) \left( \rho_{i+1} - \rho_{i} \right),
  \rho^R_{i + \frac{1}{2}} = \rho_{i+1} - 0.5 \phi \left( r_{i+1} \right)  \left( \rho_{i+1} - \rho_{i} \right),
82.206.66.51 (talk) 16:09, 1 February 2016 (UTC)
thread_title:  Indices in formulas 

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thread_title:  External links modified