Dissipation rate by energy spectra, on central differencing and WENO

MichaelBham · February 15, 2022, 00:36

Dear all,

I calculated the energy spectra of channel flow with Lagrangian particles, with WENO and central differencing(CD) as convection schemes. As expected, CD generates more oscillations than WENO.

However,
(a)CD scheme produces no numerical dissipation while WENO produces some. It was expected that the CD result has lower dissipation rate than WENO.

(b) Since CD generates more oscillation, it has larger velocity fluctuation u', indeed larger E(k). Meanwhile, the total dissipation rate is calculated as the integral of (k**2 * E(k) dk) along all wavenumbers, so that CD has higher dissipation rate than WENO.

(a) and (b) contradict. Which part is wrong?

FMDenaro · February 15, 2022, 06:00

Before any comments, could you detail the setup of your simulation ?
Could you also show the plot of the energy spectra ? Are they averaged for a sufficient number of samples? What is the distance from the wall?

February 15, 2022, 00:36	Dissipation rate by energy spectra, on central differencing and WENO	#1
MichaelBham New Member Michael Join Date: Jan 2022 Location: Birmingham, UK Posts: 8 Rep Power: 4	Dear all, I calculated the energy spectra of channel flow with Lagrangian particles, with WENO and central differencing(CD) as convection schemes. As expected, CD generates more oscillations than WENO. However, (a)CD scheme produces no numerical dissipation while WENO produces some. It was expected that the CD result has lower dissipation rate than WENO. (b) Since CD generates more oscillation, it has larger velocity fluctuation u', indeed larger E(k). Meanwhile, the total dissipation rate is calculated as the integral of (k*2 E(k) dk) along all wavenumbers, so that CD has higher dissipation rate than WENO. (a) and (b) contradict. Which part is wrong?

February 15, 2022, 06:00		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,897 Rep Power: 73	Before any comments, could you detail the setup of your simulation ? Could you also show the plot of the energy spectra ? Are they averaged for a sufficient number of samples? What is the distance from the wall?