Changes between Version 103 and Version 104 of u/erica/RoeSolver
 Timestamp:
 05/31/13 14:57:11 (11 years ago)
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u/erica/RoeSolver
v103 v104 142 142 As stated above, the Rho flux is given by: 143 143 144 [[latex($\vec{F}_{i+1/2} = \vec{F}_L + \lambda* alpha*\vec{K}$)]]144 [[latex($\vec{F}_{i+1/2} = \vec{F}_L + \lambda*\alpha*\vec{K}$)]] 145 145 146 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 alphais the wave speed, all with corresponding expressions given in detail above.146 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. 147 147 148 148 For the case of sonic rarefactions, the lambda in the above equation for Roe's flux must be adjusted, and following the HartenHyman approach, is taken to be: 149 149 150 [[latex($\lambda ' = (u_La_L)*\frac{u starastarL\lambda}{ustarastarLu_L+a_L}$)]]150 [[latex($\lambda ' = (u_La_L)*\frac{u_*a_{*L}\lambda}{u_*a_{*L}u_L+a_L}$)]] 151 151 152 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 11.4.3.152 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. 153 153 154 154 Here is a screen shot of my code: