Changes between Version 103 and Version 104 of u/erica/RoeSolver

Timestamp:

05/31/13 14:57:11 (11 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/RoeSolver

@@ -142 +142 @@
 As stated above, the Rho flux is given by:
 
-[[latex($\vec{F}_{i+1/2} = \vec{F}_L + \lambda*alpha*\vec{K}$)]]
+[[latex($\vec{F}_{i+1/2} = \vec{F}_L + \lambda*\alpha*\vec{K}$)]]
 
-Where [[latex($\vec{K}_{i+1/2}$)]] is the vector of ''numerical'' fluxes, [[latex($\vec{F}_L$)]] is the vector of physical fluxes for the left state, lambda and [[latex($\vec{K}$)]] are the eigenvalues and eigenvectors, and alpha is the wave speed, all with corresponding expressions given in detail above. 
+Where [[latex($\vec{K}_{i+1/2}$)]] is the vector of ''numerical'' fluxes, [[latex($\vec{F}_L$)]] is the vector of physical fluxes for the left state, [[latex($\lambda$)]] and [[latex($\vec{K}$)]] are the eigenvalues and eigenvectors, and [[latex($\alpha$)]] is the wave speed, all with corresponding expressions given in detail above. 
 
 For the case of sonic rarefactions, the lambda in the above equation for Roe's flux must be adjusted, and following the Harten-Hyman approach, is taken to be:
 
-[[latex($\lambda ' = (u_L-a_L)*\frac{ustar-astarL-\lambda}{ustar-astarL-u_L+a_L}$)]]
+[[latex($\lambda ' = (u_L-a_L)*\frac{u_*-a_{*L}-\lambda}{u_*-a_{*L}-u_L+a_L}$)]]
 
-for a left sonic rarefaction. For a right sonic rarefaction, the coefficients are slightly adjusted. Note that the entropy fix requires estimates for the velocity and sound speed of the star region, ustar and astarL. We get estimates of these using the Roe approach for linearizing the Euler equations. They are listed in Toro, section 11.4.3.
+for a left sonic rarefaction. For a right sonic rarefaction, the coefficients are slightly adjusted. Note that the entropy fix requires estimates for the velocity and sound speed of the star region, [[latex($u_*$)]] and [[latex($a_{*L})]]. We get estimates of these using the Roe approach for linearizing the Euler equations. They are listed in Toro, section 11.4.3.
 
 Here is a screen shot of my code: