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July 15, 2019, 08:25 
Governing equations vs Transport equations

#1 
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Mandeep Shetty
Join Date: Apr 2016
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This is a basic question. But I did not find any explanations for this. How are governing equations, like mass, momentum, energy conservations equations, different from 'Transport equation'?. Is a conservation equation, like energy equation (heat equation), a transport equation for the temperature?


July 15, 2019, 09:49 

#2  
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Filippo Maria Denaro
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Quote:
Transport equation is a general denomination for the advectiondiffusion PDE, see https://en.wikipedia.org/wiki/Convec...usion_equation The equation is not necessarily related to a flow problem, for example they are often referred as to the transport of chemical species (advecion velocity prescribed). On the other hand, when we use the conservative form of mass, momentum and total energy we could see those as a more complex expression of the simple advectiondiffusion equation. Do not worry if you read in literature some discrepancy 

July 15, 2019, 10:19 

#3 
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Lucky
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The mass, momentum, and energy equations (and many others) in CFD are indeed transport equations. The heat equation is a transport equation for the internal energy (or enthalpy depending on formulation) and an equation of state is usually invoked to write in with temperature as the primitive variable.
In general (widespread in nonfluids fields), a governing equation need not be a transport equation and a transport equation need not be a governing equation. A governing equation need not be a conservation either (economics, the stock market, etc...). In fluids, the main governing equations that you play with just happen to be transport equations based on the principles of mass, momentum, and energy conservation laws and they all are referring to the same thing. 

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governing equations, navier stokes equation, transport equation 
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