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MusclHancock

v9	v10
9	9	[[Image(compare2.png, 35%)]]
10	10
11		The higher order schemes ~~as you can see here~~ are 'dispersive'. That is, they suffer from slight sign errors in the position of the wave, with the numerical solution either lagging behind or ahead of the true solution.
	11	The higher order schemes, as you can see here, are 'dispersive'. That is, they suffer from slight sign errors in the position of the wave, with the numerical solution either lagging behind or ahead of the true solution.
12	12
13	13	The above plots show that 2nd order schemes largely perform better than 1st order schemes in regions of 'smooth flow'. However, it is well known that these same higher order accurate schemes can produce spurious oscillations near large gradients. This is due to the higher order schemes no longer being monotone (i.e. having strictly non-negative coefficients in their conservation update formula). Here is a plot showing the same 4 schemes listed above, but for a step function initial condition: