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2D_Godunov

v4	v5
17	17	[[latex($\vec{u}^n = \{ \vec{u}^n_{i,j} \} ~\forall ~i,~\forall~j$)]]
18	18
19		To solve the Euler equations for this given initial condition, we split the 2D Euler equations into 2, 1D initial value problems (IVPs). In the x-split direction, we have
	19	where u is the vector of primitive variables. To solve the Euler equations for this given initial condition, we split the 2D Euler equations into 2, 1D initial value problems (IVPs). In the x-split direction, we have
20	20
21	21	[[latex($\frac{\partial }{\partial t} \begin{pmatrix} \rho \\ \rho u \\ E \\ \rho v \end{pmatrix} + \frac{\partial }{\partial x} \begin{pmatrix} \rho u \\ \rho u^2 + p \\ u(E+p) \\ \rho u v \end{pmatrix} = 0$)]]