I'm reading through these notes on numerical hydrodynamics. On pg17, they introduce the monotonized central difference flux limiter, which looks something like
[tex]\frac{\partial~a}{\partial~x}|_i = min\left({\frac{|a_{i+1}-a_{i-1}|}{2\Delta~x},2\frac{|a_{i+1}-a_{i}|}{\Delta~x},2\frac{|a_i-a_{i-1}|}{\Delta~x}}\right)sign\left(a_{i+1}-a_{i-1}\right)[/tex]
Now I am a bit confused about what's happening here. The first term in the min looks like a derivative, but the next two terms look like twice the derivative. Can anyone explain what exactly is going on here?
Thanks
[tex]\frac{\partial~a}{\partial~x}|_i = min\left({\frac{|a_{i+1}-a_{i-1}|}{2\Delta~x},2\frac{|a_{i+1}-a_{i}|}{\Delta~x},2\frac{|a_i-a_{i-1}|}{\Delta~x}}\right)sign\left(a_{i+1}-a_{i-1}\right)[/tex]
Now I am a bit confused about what's happening here. The first term in the min looks like a derivative, but the next two terms look like twice the derivative. Can anyone explain what exactly is going on here?
Thanks