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MusclHancock

v41	v42
32	32	for each element of u, where f is the numerical flux. For the 1st order Godunov scheme studied previously, f was taken to simply be the physical flux of 2 adjacent cells (this is the so called 'Godunov numerical flux'), evaluated using the solution of the Local Riemann Problem (LRP) at the intercell boundary. We have seen various approximation methods to this Godonov scheme, some which estimate the solution of the Riemann problem itself along these intercell boundaries, and others that instead approximate the numerical flux at these boundaries. Next, we will see how the MH scheme produces a 2nd-order accurate solution to the problem. The MH scheme proceeds as follows, being broken down into 3 distinct steps.
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34		1. 'Data reconstruction' - this is the first step of the MH scheme, and is responsible for providing higher order accuracy by fitting a piece-wise linear function to the initial piece-wise constant data. Note that this steps maintains conservation. Such a piece-wise linear function is of the form:
	34	1. 'Data reconstruction' - this is the first step of the MH scheme, and is responsible for providing higher order accuracy by fitting a piece-wise linear function to the initial piece-wise constant data. Note that this step maintains conservation. Such a piece-wise linear function is of the form:
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36	36	[[latex($u_i(x) = u_i^n + (x - x_i) \frac{\triangle _i }{\triangle x}, x \in [0, \triangle x]$)]]