User talk:Differentialpi/Riemann problem/Comments

Hi,

I think Riemann problem should be defined under advection equations not conservative equations as

${\frac {\partial {\vec {q}}}{\partial t}}+A{\frac {\partial {\vec {q}}}{\partial x}}=0$

where ${\vec {q}}$ is a variable vector in $R^{m\times 1}$, and $A$ is a matrix in $R^{m\times m}$, because the core of Riemann problem is similarity solution so that we can have characteristic line and so on. So if we have equations in conservative form

${\frac {\partial {\vec {q}}}{\partial t}}+{\frac {\partial {\vec {f}}({\vec {q}})}{\partial x}}=0$

we need to get Jacobian matrix ${\frac {\partial {\vec {f}}({\vec {q}})}{\partial x}}$ corresponding to $A$.

DongLi1985 (talk) 13:15, 29 December 2008 (UTC)