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2D_Godunov

-              v5
+              v6
 [[latex($\vec{u}^n = \{ \vec{u}^n_{i,j} \} ~\forall ~i,~\forall~j$)]]
 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
+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, this becomes
 [[latex($\frac{\partial }{\partial t} \begin{pmatrix} \rho \\ \rho u \\ E \\ \rho v \end{pmatrix} + \frac{\partial }{\partial x} \begin{pmatrix} \rho u \\ \rho u^2 + p \\ u(E+p) \\ \rho u v \end{pmatrix} = 0$)]]
 and in the y-direction we have,
+and in the y-direction this is,
 [[latex($\frac{\partial }{\partial t} \begin{pmatrix} \rho \\ \rho v \\ E \\ \rho u \end{pmatrix} + \frac{\partial }{\partial y} \begin{pmatrix} \rho v \\ \rho v^2 + p \\ v(E+p) \\ \rho u v \end{pmatrix} = 0$)]]