Simple 1D viscous flow in Lagrangian co-ordinates

hunt_mat · July 19, 2023, 15:48

Quote:

Originally Posted by FMDenaro

You realize now that you have to write the system with the full momentum equation by adding -(1/rho) dp/dx. Then you can use the iso-entropic relation (if you problem allows such hypothesis) and close the system of two equations.

In LeVeque's book, he does this to obtain a very very simple system of equations that may be solved via the method of characteristics. However, my thoughts are how to solve a mathematically idealised system of equations.

LuckyTran · July 19, 2023, 15:49

The length of your elastic rod is governed by your BC's, which you have completed omitted. And that is just the start because you have to come up with compatibility conditions.

Even in cartesian, you have no measure for the length of a rod if the BCs aren't at fixed locations.

Aside: I can't say I have ever met anyone that has confused a Dorodnitzjn transformation for a Lagrangian, and certainly never a mathematician.

hunt_mat · July 19, 2023, 15:59

I didn't specify any boundary conditions, correct. The condition for the length is given by differentiating the total mass in Eulerian co-ordinates. The boundary conditions are essentially only there to fill in the boundary points.

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July 19, 2023, 15:49		#22
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,675 Rep Power: 66	The length of your elastic rod is governed by your BC's, which you have completed omitted. And that is just the start because you have to come up with compatibility conditions. Even in cartesian, you have no measure for the length of a rod if the BCs aren't at fixed locations. Aside: I can't say I have ever met anyone that has confused a Dorodnitzjn transformation for a Lagrangian, and certainly never a mathematician.

July 19, 2023, 15:59		#23
hunt_mat Senior Member Matthew Join Date: Mar 2022 Location: United Kingdom Posts: 175 Rep Power: 4	I didn't specify any boundary conditions, correct. The condition for the length is given by differentiating the total mass in Eulerian co-ordinates. The boundary conditions are essentially only there to fill in the boundary points.