Test problem for 1D isothermal Euler equations

san_cfd · February 25, 2011, 11:23

Hi All,

Could someone suggest a test problem for the 1D Isothermal Euler equations?

I know that the 1D Riemann (shock tube) problem is generally used.. but am having difficulty in understanding the "link" between pressure and density in the isothermal case.. can someone help me with this ?

also please suggest any other test problems?

thanks

Hooman · September 26, 2012, 06:58

Hi,

I know it has been a long time but I was wondering if you got a reply to your answer with regards to test cases?

Also were you coding this?

Thanks!

francesco_capuano · September 26, 2012, 12:52

A typical test is the Sod shock tube:

http://en.wikipedia.org/wiki/Sod_shock_tube

FMDenaro · September 26, 2012, 14:17

I am not sure about what you consider as "isothermal" flow... for example the "isoentropic" flow can be defined as the case in which the entropy is constant along the trajectory of a fluid particle, that is on the characteristic curve dx/dt = u. In this case spatial gradient of entropy are allowed (ds/dt + u ds/dx = 0).

In the classic Sod test you have one family of characteristic waves were the flow is omoentropic and Riemann invariant can be used, then the contact discontinuity and the shock wave are the other regions involved.

What test are you looking for?

Hooman · September 27, 2012, 05:28

I'm looking for a test case that involves the Euler equations (with or without energy).

February 25, 2011, 11:23	Test problem for 1D isothermal Euler equations	#1
san_cfd New Member santosh Join Date: Feb 2011 Posts: 2 Rep Power: 0	Hi All, Could someone suggest a test problem for the 1D Isothermal Euler equations? I know that the 1D Riemann (shock tube) problem is generally used.. but am having difficulty in understanding the "link" between pressure and density in the isothermal case.. can someone help me with this ? also please suggest any other test problems? thanks Hooman likes this.

September 26, 2012, 14:17		#4
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	I am not sure about what you consider as "isothermal" flow... for example the "isoentropic" flow can be defined as the case in which the entropy is constant along the trajectory of a fluid particle, that is on the characteristic curve dx/dt = u. In this case spatial gradient of entropy are allowed (ds/dt + u ds/dx = 0). In the classic Sod test you have one family of characteristic waves were the flow is omoentropic and Riemann invariant can be used, then the contact discontinuity and the shock wave are the other regions involved. What test are you looking for? Hooman likes this.

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September 26, 2012, 06:58		#2
Hooman Senior Member Join Date: Jun 2010 Posts: 111 Rep Power: 15	Hi, I know it has been a long time but I was wondering if you got a reply to your answer with regards to test cases? Also were you coding this? Thanks!

September 26, 2012, 12:52		#3
francesco_capuano Member Francesco Capuano Join Date: May 2010 Posts: 81 Rep Power: 15	A typical test is the Sod shock tube: http://en.wikipedia.org/wiki/Sod_shock_tube

September 27, 2012, 05:28		#5
Hooman Senior Member Join Date: Jun 2010 Posts: 111 Rep Power: 15	I'm looking for a test case that involves the Euler equations (with or without energy).