Artificial Diffusion

Mudit2208 · May 5, 2020, 11:11

Hello, I want to know how to show the effect of artificial diffusion by using first order Upwind scheme for convective terms?

FMDenaro · May 5, 2020, 12:05

Use the linear wave equation, discretize using a first order explicit time integration and write the modified equation

Mudit2208 · May 5, 2020, 12:15

Thanks for your reply. But i am solving steady state Navier stokes equation for Lid driven cavity problem. I am required to demonstrate the effect of artificial diffusion using first order upwind scheme for convective terms. Could you please help me with this?

FMDenaro · May 5, 2020, 12:29

Quote:

Originally Posted by Mudit2208

Thanks for your reply. But i am solving steady state Navier stokes equation for Lid driven cavity problem. I am required to demonstrate the effect of artificial diffusion using first order upwind scheme for convective terms. Could you please help me with this?

Show the expression of the local truncation error of the discretization of the convective term. What term is present? What is the meaning in terms of the physics you are solving?

sbaffini · May 5, 2020, 20:53

Two possible ways are:

1) Use second order as well and compare the two

2) Solve for a flow with analytical solution and detect the actual viscosity given by the numerical solution

In both cases it is required to work at fixed mesh size, otherwise the numerical viscosity would change

May 5, 2020, 11:11	Artificial Diffusion	#1
Mudit2208 New Member Mudit Mehta Join Date: Mar 2020 Posts: 15 Rep Power: 6	Hello, I want to know how to show the effect of artificial diffusion by using first order Upwind scheme for convective terms?

May 5, 2020, 12:05		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,896 Rep Power: 73	Use the linear wave equation, discretize using a first order explicit time integration and write the modified equation vesp and Mudit2208 like this.

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May 5, 2020, 12:15		#3
Mudit2208 New Member Mudit Mehta Join Date: Mar 2020 Posts: 15 Rep Power: 6	Thanks for your reply. But i am solving steady state Navier stokes equation for Lid driven cavity problem. I am required to demonstrate the effect of artificial diffusion using first order upwind scheme for convective terms. Could you please help me with this?

May 5, 2020, 20:53		#5
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,195 Blog Entries: 29 Rep Power: 39	Two possible ways are: 1) Use second order as well and compare the two 2) Solve for a flow with analytical solution and detect the actual viscosity given by the numerical solution In both cases it is required to work at fixed mesh size, otherwise the numerical viscosity would change