Changes between Version 49 and Version 50 of u/erica/RoeSolver
 Timestamp:
 05/16/13 16:46:33 (11 years ago)
Legend:
 Unmodified
 Added
 Removed
 Modified

u/erica/RoeSolver
v49 v50 44 44 }}} 45 45 46 The eigen 46 The eigenvalues and vectors are derived straightforwardly from the Jacobian, using typical methods. 47 47 48 Now, we can either assume the independent variables u, rho, etc. of these functions for alpha, lambda, and K are 1) reference states which we set, or 2) some general averaged versions of the variables, which we have to solve for. Toro goes through the algebraic analysis for the general case for the Euler equations. The results are as follows.48 Now, we assume the independent variables u, rho, etc. of these functions for alpha, lambda, and K are reference states (associated with hat notation) which we use to solve for any general, averaged versions of the variables (associated with tilde notation). Toro goes through the algebraic analysis for the general case for the Euler equations. The results are as follows. 49 49 50 50 = RoePike Approach for Euler Equations = 51 51 52 For the xsplit, 3dimensional Euler equations, we have the following eigen 52 For the xsplit, 3dimensional Euler equations, we have the following eigenvalues and vectors: 53 53 54 54 {{{#!Latex … … 60 60 61 61 {{{#!Latex 62 \vec{K}^1 = <1, ua, v, w, Hua>, ~\vec{K}^2 = <1,u,v,w,V^2/2>, ~\vec{K}^3 = <0,0,1,0,v>, ~\vec{K}^4 = <0,0,0,1,w>, ~\vec{K}^5 = <1, u+a, v, w, H+ua> 62 \vec{K}^1 = <1, ua, v, w, Hua>, 63 }}} 64 {{{#!Latex 65 \vec{K}^2 = <1,u,v,w,V^2/2>, 66 }}} 67 {{{#!Latex 68 \vec{K}^3 = <0,0,1,0,v>, 69 }}} 70 {{{#!Latex 71 \vec{K}^4 = <0,0,0,1,w>, 72 }}} 73 {{{#!Latex 74 \vec{K}^5 = <1, u+a, v, w, H+ua> 63 75 }}} 64 76