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Computing the new mesh in Lagrangian co-ordinates |
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November 21, 2023, 13:23 |
Computing the new mesh in Lagrangian co-ordinates
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#1 |
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Matthew
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Location: United Kingdom
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November 21, 2023, 15:15 |
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#2 | |
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Filippo Maria Denaro
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Quote:
what do you mean? in 1D you have only one equation but you should be aware about the global character of your problem. For example, the Burgers equation in lagrangian form is Du/Dt=0 but you can create the evolution of the regular lagrangian grid only if the characteristic lines dx/dt=u do not intersect. In other words until the u is regular. |
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November 22, 2023, 06:26 |
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#3 |
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Matthew
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I use the amount of mass as my "length" co-ordinate, and as such I have this magical property that the mass in the cell is constant for all time. I compute the density at each time-step, and mass=density*length, to find the new length, you just need to compute length=mass of cell/new density.
I don't have a hyperbolic system, so I don't have characteristics to compute with. |
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November 22, 2023, 08:34 |
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#4 | |
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Filippo Maria Denaro
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Quote:
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November 22, 2023, 08:53 |
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#5 |
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Matthew
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I have a 2D elastic system with diffusive terms that cause the shape to be deformed because I have an external heat source that is causing it to shrink. I believe I have the correct equations describing the process but I don't know how to compute the shape as it deforms as this changes the grid.
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November 22, 2023, 09:03 |
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#6 | |
Senior Member
Filippo Maria Denaro
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Quote:
Deformation will be high to have a stable computation. I don’use lagariangian grid for several issues. |
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November 22, 2023, 09:23 |
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#7 | |
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Matthew
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Quote:
Are you referring to ALE at all? |
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November 22, 2023, 10:32 |
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#8 |
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Filippo Maria Denaro
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November 22, 2023, 10:39 |
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#9 |
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Matthew
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November 22, 2023, 10:49 |
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#10 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
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Charles Peskin is a famous scientist, you can find his home page and all his papers.
However, have a look to my references here https://www.researchgate.net/publica...ructured_grids |
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Tags |
finite volume method, grid analysis |
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