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MusclHancock

-              v30
+              v31
 [[latex($ \frac{\partial \vec{u}}{\partial t} + \frac{\partial f(\vec{u})}{\partial x} = 0 $)]]
 where u is the vector of conserved variables and f is the flux function. Adhering to the IVBP known as the Riemann Problem, we solve this system of equations using the fully discrete, explicit, conservative formula:
+where u is the vector of conserved variables (u=u(x,t)), and f is the flux function. Adhering to the IVBP known as the Riemann Problem (i.e. constant left and right data states separated by an initial discontinuity), we solve this system of equations using the fully discrete, explicit, conservative formula:
 [[latex($ u_i^ {n+1} = u_i ^n + \frac{\triangle t}{\triangle x}[f_{i-1/2} - f_{i+1/2}]$)]]
 …
   [[Image(MusclReconstruction.png, 35%)]]
+ Using these end values, one has the new Riemann problem:
+  [[latex($ \frac{\partial \vec{u}}{\partial t} + \frac{\partial f(\vec{u})}{\partial x} = 0 $)]]
+  [[latex($ u(x,0) = { \frac{u_i^r, x\<0}{u_{i+1}^l, x\>0} $)]]
+ where 0 is the local origin, i.e. any given intercell boundary.
 At this point, we are left with a higher order accurate code, but not one that is free of spurious oscillations near large gradients. To circumvent this, we need to add a TVD measure.