Lax-Friedrichs flux

panou · July 30, 2011, 10:02

Have anyone a paper which explain how lax-friedrich(approximate riemann solver) is derived?

Also if we suppose that (u+) is the values of a volume , (u-) the values of neighbour volumes and F the flux then the lax-friedrichs flux gives:

F=0.5*( (F+) + (F-) ) - a*( (u-) - (u+) )

This is applied by all faces of a initial volume regardless of its outward unit vector?

cfdnewbie · July 30, 2011, 12:45

There's nothing too fancy about the LF-flux....its the average, penalized by the jump to add a strong dissipative constant.... not sure about the original paper, anybody has a hint???

you compute your F by the formula given above, and then do int (F*n) dx to take the normal into account...

hope this helps a bit!

panou · July 30, 2011, 17:09

Yes , sure. The third term is the dissipative term. Simply , i did not know if it has a complex theory under of it (due to appearance of eigenvectors as dissipative multiplier). With other words, i want to learn what assumptions do for to solve approximate the Riemann problem and finally result at this simply relation.

For other cases as HLLC or HLL there is a assumption on a number of waves. Here?

cfdnewbie · July 31, 2011, 03:52

Quote:

Originally Posted by panou

For other cases as HLLC or HLL there is a assumption on a number of waves. Here?

Hm, I'm only familiar with the LOCAL LF (also called Rusanov), where the a in your equation above is the local largest EV.... so that's your fastest wave...

July 30, 2011, 10:02	Lax-Friedrichs flux	#1
panou New Member aaaaaaaaaaaaaa Join Date: Apr 2011 Posts: 23 Rep Power: 15	Have anyone a paper which explain how lax-friedrich(approximate riemann solver) is derived? Also if we suppose that (u+) is the values of a volume , (u-) the values of neighbour volumes and F the flux then the lax-friedrichs flux gives: F=0.5( (F+) + (F-) ) - a( (u-) - (u+) ) This is applied by all faces of a initial volume regardless of its outward unit vector?

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July 30, 2011, 12:45		#2
cfdnewbie Senior Member cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 20	There's nothing too fancy about the LF-flux....its the average, penalized by the jump to add a strong dissipative constant.... not sure about the original paper, anybody has a hint??? you compute your F by the formula given above, and then do int (F*n) dx to take the normal into account... hope this helps a bit!

July 30, 2011, 17:09		#3
panou New Member aaaaaaaaaaaaaa Join Date: Apr 2011 Posts: 23 Rep Power: 15	Yes , sure. The third term is the dissipative term. Simply , i did not know if it has a complex theory under of it (due to appearance of eigenvectors as dissipative multiplier). With other words, i want to learn what assumptions do for to solve approximate the Riemann problem and finally result at this simply relation. For other cases as HLLC or HLL there is a assumption on a number of waves. Here?