Changes between Version 35 and Version 36 of u/erica/MusclHancock
 Timestamp:
 06/18/13 12:49:14 (11 years ago)
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u/erica/MusclHancock
v35 v36 85 85 [[Image(evolve.png, 35%)]] 86 86 87 3. 88 87 3. Solve the new Riemann problem 88 89 [[latex($ \frac{\partial \vec{u}}{\partial t} + \frac{\partial f(\vec{u})}{\partial x} = 0 $)]] 90 91 92 [[latex($ u(x,0) = \{ ^{\bar{u}_i^r,~~~~ x <0}_{\bar{u}_{i+1}^l, ~~x>0} $)]] 93 94 using the evolved extrapolated boundary values. The solution of this problem is then used in the Godunov flux, which is used in updating cell i. Recall the Godunov flux is simply, 95 96 [[latex($ f_{i+1/2} = f(u_{i+1/2}(x/t=0))$)]] 97 98 i.e. the numerical flux at the intercell boundary equals the physical flux evaluated at the similarity solution of the LRP (local Riemann Problem) at that boundary. 89 99 90 100 101 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. There are some different ways of doing this, i.e. limited slopes, fluxlimiters, and slope limiters. Here we focus on slope limiters. 91 102 92 93 94 95 96 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. 103 = Slope Limiters = 97 104 98 105 = Algorithm Outline =