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)