Changes between Version 70 and Version 71 of u/erica/RoeSolver
 Timestamp:
 05/17/13 16:55:09 (11 years ago)
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u/erica/RoeSolver
v70 v71 103 103 \vec{V}^2 = u^2 + v^2 + w^2 104 104 }}} 105 The Euler equations are a set of nonlinear PDE's, which comprise an eigenvalue problem. The eigenvalues for the equations are functions of the solution to the equations themselves. This means that the waves, which propagate with speeds = to their eigenvalues, distort the solution, and the solution distorts them over space and time. Thus the solution to the Riemann 105 106 106 107 and e being the specific internal energy, which for ideal gases is, … … 122 123 }}} 123 124 124 Note that the vector equation for the numerical flux makes up 3 equations for the 3D Euler equations, one for each component of the following vectors: the vector of numerical fluxes in conserved form, 125 Note that the vector equation for the numerical flux makes up 3 equations for the 3D Euler equations, one for each component of the following vectors: 126 127 the vector of numerical fluxes in conserved form, 125 128 {{{#!Latex 126 129 \vec{F}_{i+1/2} = <\rho_{i+1/2}, ~p_{i+1/2}, ~E_{i+1/2}> … … 151 154 }}} 152 155 153 The derived expressions for the wavespeeds are as follows,156 Finally, the derived expressions for the wavespeeds are as follows, 154 157 155 158 {{{#!Latex