Lax-Friedrichs flux in H-J equations

May 9, 2003, 22:57

I want to use the Lax-Friedrichs flux to solve the Hamilton-Jacobi equations. I can't understand the meaning of the flux. For example, there is one expresssion,alpha(u+,u-)=max(abs(H1(u,v))), u(-[A,B],v(-[C,D]. [A,B] is the value range for u+ and u-,and [C,D] is the value range for v+ and v-. The problem is, I can't understand the meaning of [A,B] and [C,D]. u+ and u- denote the two upwind discretization. Thanks! Reference 1. S.Osher and C.W. Shu, High-order essentially nonoscillatory schemes fro Hamilton-Jacobi equations. J. Numer. Anal., v28,1991,ppp.907-922

May 10, 2003, 09:17

Hi there,

Yo should have a look at the following paper:

techreports.larc.nasa.gov/icase/1997/icase-1997-65.pdf

It is a good introduction to the ENO scheme and will (I think the information you require is there) help you unerstand the concepts in your question.

John.

May 9, 2003, 22:57	Lax-Friedrichs flux in H-J equations	#1
Tian Baolin Guest Posts: n/a	I want to use the Lax-Friedrichs flux to solve the Hamilton-Jacobi equations. I can't understand the meaning of the flux. For example, there is one expresssion,alpha(u+,u-)=max(abs(H1(u,v))), u(-[A,B],v(-[C,D]. [A,B] is the value range for u+ and u-,and [C,D] is the value range for v+ and v-. The problem is, I can't understand the meaning of [A,B] and [C,D]. u+ and u- denote the two upwind discretization. Thanks! Reference 1. S.Osher and C.W. Shu, High-order essentially nonoscillatory schemes fro Hamilton-Jacobi equations. J. Numer. Anal., v28,1991,ppp.907-922

May 10, 2003, 09:17	Re: Lax-Friedrichs flux in H-J equations	#2
John. Guest Posts: n/a	Hi there, Yo should have a look at the following paper: techreports.larc.nasa.gov/icase/1997/icase-1997-65.pdf It is a good introduction to the ENO scheme and will (I think the information you require is there) help you unerstand the concepts in your question. John.

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