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Hey everyone,

I’m trying to simulate a 1D Shallow Water wave in FORTRAN using the Lax Wendroff Method. The case is fairly simple. I have a wave generator on one end of a water pool and a wall boundary on another. The waves start travelling towards the wall and are ‘reflected off’ the wall. The problem which I’m facing is the Boundary Condition on the wall.

My generated wave starts travelling towards the wall and once it reaches the wall, my solution crashes. I need an appropriate ‘reflective boundary condition’ at the wall. As you guys already know, the Lax Wendroff Method employs a half time step. The governing PDE’s are attached in the image. The discretised equations are also attached.

Since h and A are the unknowns we are dealing with, I need the following BC at the wall:

HNP102(1)=? !1/2 Time Step, denotes n

ANP102(1)=? !plus half

and

HNP1(1)=? !full time step, denotes n

ANP1(1)=? !plus 1.

I read a similar code where

HNP1(1)=HNP1(2)

ANP1(1)=ANP1(2) was used but in my case it did not work.

I’m trying to simulate a 1D Shallow Water wave in FORTRAN using the Lax Wendroff Method. The case is fairly simple. I have a wave generator on one end of a water pool and a wall boundary on another. The waves start travelling towards the wall and are ‘reflected off’ the wall. The problem which I’m facing is the Boundary Condition on the wall.

My generated wave starts travelling towards the wall and once it reaches the wall, my solution crashes. I need an appropriate ‘reflective boundary condition’ at the wall. As you guys already know, the Lax Wendroff Method employs a half time step. The governing PDE’s are attached in the image. The discretised equations are also attached.

Since h and A are the unknowns we are dealing with, I need the following BC at the wall:

HNP102(1)=? !1/2 Time Step, denotes n

ANP102(1)=? !plus half

and

HNP1(1)=? !full time step, denotes n

ANP1(1)=? !plus 1.

I read a similar code where

HNP1(1)=HNP1(2)

ANP1(1)=ANP1(2) was used but in my case it did not work.