Changes between Version 70 and Version 71 of u/erica/RoeSolver
- Timestamp:
- 05/17/13 16:55:09 (12 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 non-linear 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 wave-speeds are as follows,156 Finally, the derived expressions for the wave-speeds are as follows, 154 157 155 158 {{{#!Latex
