Changes between Version 62 and Version 63 of u/erica/RoeSolver
 Timestamp:
 05/17/13 16:39:24 (11 years ago)
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u/erica/RoeSolver
v62 v63 121 121 }}} 122 122 123 This vector equation has the following components for the 3D Euler equations, 124 125 {{{#!Latex 126 \vec{F}_{i+1/2} = <\rho_{i+1/2}, u_{i+1/2}, p_{i+1/2}> 127 }}} 128 129 {{{#!Latex 130 \vec{F}_L = <\rho_L, \rho_L * u_L, 0.5\rho_L*u_L^2 + \frac{p_L}{\gamma  1}> 131 }}} 132 133 {{{#!Latex 134 \vec{K}^{(1)} = <1, ua, Hua> 135 }}} 136 137 {{{#!Latex 138 \vec{K}^{(2)} = <1, u, 0.5 u^2> 139 }}} 140 141 {{{#!Latex 142 \vec{K}^{(3)} = <1, u+a, H+ua> 143 }}} 144 123 145 The results for the method are the following equations for the wavespeeds: 124 146 … … 145 167 along with their corresponding expressions for the rho, u, v, w, H, and a (listed in Toro, eqn. 11.118) that we would plug into these wave speeds and the above expressions for the eigenvalues and eigenvectors. These in turn would be used in the numerical flux for the Godunov method. 146 168 147 Note the definition169 Note in the above formalism, the following definition is used, 148 170 149 171 {{{#!Latex