PMatrix in Numerics Structure

atelcikti1 · November 6, 2020, 05:13

Hi people,

I am trying to understand SU2 jacobian matrix structure and components in depth. In numerics structure cpp file there is a Pmatrix and its inverse function. Why it is implemented? I checked where those functions called and see used in implicit application of jacobian matrix. I am aware that those are related to eigen-values and vectors of jacobian as in stated and derived in Hirsh book however what is the main reason to calculate? Any reference beside Hirsh will be appreciated.

Have a nice day.

-Ali

aerosjc · May 29, 2022, 03:01

You have to use the diagonalized form instead of the Roe matrix. It may looks like that the Roe matrix A = P lambda P^{-1}. However, it is not in fact. Because you have the entropy correction which modifies the engenvalues lambda.

November 6, 2020, 05:13	PMatrix in Numerics Structure	#1
atelcikti1 Member Join Date: Mar 2017 Posts: 61 Rep Power: 9	Hi people, I am trying to understand SU2 jacobian matrix structure and components in depth. In numerics structure cpp file there is a Pmatrix and its inverse function. Why it is implemented? I checked where those functions called and see used in implicit application of jacobian matrix. I am aware that those are related to eigen-values and vectors of jacobian as in stated and derived in Hirsh book however what is the main reason to calculate? Any reference beside Hirsh will be appreciated. Have a nice day. -Ali

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May 29, 2022, 03:01		#2
aerosjc Member Jingchang.Shi Join Date: Aug 2012 Location: Hang Zhou, China Posts: 78 Rep Power: 13	You have to use the diagonalized form instead of the Roe matrix. It may looks like that the Roe matrix A = P lambda P^{-1}. However, it is not in fact. Because you have the entropy correction which modifies the engenvalues lambda.