Super Simple Problem...

Bdew8556 · September 18, 2023, 01:04

hi all,

At the risk of sounding very silly, could anyone help me out with what the 'a' is equal to in these equations:

https://www.youtube.com/watch?app=desktop&v=MNqf8H7hyyc

Many thanks.

LuckyTran · September 18, 2023, 01:11

Starting from some grid, you apply FVM and discretization schemes to each cell. For implicit schemes you end up with a linear system of equations that need to be solved. The a's are the coefficients in this linear system, i.e. the elements in the matrix. Your choice of schemes will change the exact value of a's but the general method remains the same. You always get a linear system.

Bdew8556 · September 18, 2023, 01:14

Nice! thanks for that. Do you have any easy to understand (as much as is possible) examples?

LuckyTran · September 18, 2023, 01:21

An easy way to get a feel for it is to look at the classical problems and these are advection or diffusion problems. See for example a 1d and 2d example in Crank-Nicolson. Navier-Stokes is just a teeny bit more complicated with the pressure gradient, which calls for a scheme such as simple, and also having both an advection and diffusion term, which you can imagine is just like summing two matrices.

Bdew8556 · September 18, 2023, 01:52

Thanks for that, if you do come across any good illustrated examples let me know.

September 18, 2023, 01:04	Super Simple Problem...	#1
Bdew8556 Senior Member Brett Join Date: May 2013 Posts: 212 Rep Power: 14	hi all, At the risk of sounding very silly, could anyone help me out with what the 'a' is equal to in these equations: https://www.youtube.com/watch?app=desktop&v=MNqf8H7hyyc Many thanks.

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September 18, 2023, 01:11		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,754 Rep Power: 66	Starting from some grid, you apply FVM and discretization schemes to each cell. For implicit schemes you end up with a linear system of equations that need to be solved. The a's are the coefficients in this linear system, i.e. the elements in the matrix. Your choice of schemes will change the exact value of a's but the general method remains the same. You always get a linear system.

September 18, 2023, 01:14		#3
Bdew8556 Senior Member Brett Join Date: May 2013 Posts: 212 Rep Power: 14	Nice! thanks for that. Do you have any easy to understand (as much as is possible) examples?

September 18, 2023, 01:21		#4
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,754 Rep Power: 66	An easy way to get a feel for it is to look at the classical problems and these are advection or diffusion problems. See for example a 1d and 2d example in Crank-Nicolson. Navier-Stokes is just a teeny bit more complicated with the pressure gradient, which calls for a scheme such as simple, and also having both an advection and diffusion term, which you can imagine is just like summing two matrices.

September 18, 2023, 01:52		#5
Bdew8556 Senior Member Brett Join Date: May 2013 Posts: 212 Rep Power: 14	Thanks for that, if you do come across any good illustrated examples let me know.