Hello,

Is there any criteria for the time steps doing transient calculation with heat transfer in solids?

I found one for the convective mass transport saying

2*dt*nu/rho < L^2

L ... mean mesh size dt ... time step rho ... density nu ... dynamic viscosity

Is that criteria correct?

Is it possible to compare the energy-equation with the one for mass transport, so that I get a similar criteria for heat transport in solids?:

2*dt*lambda/(rho*cp) < L^2

L ... mean mesh size dt ... time step rho ... desnity lambda ... heat conduct. of solid cp ... spec. heat

Thanks in advance for every answer Mike

Hi,

It depends on whether you use an explicit or implicit method for time discretization. Usually:

Explicit: 2*dt*lambda/(rho*cp) < L^2 (as you have pointed out)

Implicit: No restrictions for convergence (only for accuracy)

Semi-implicit (Crank-Nicolson): No retrictions for convergence but a restriction to avoid unphysical results:

dt*lambda/(rho*cp) < L^2

Hope this helps,

Gorka

Hello,

Thank you very much - that really helps a lot, Gorka.

I have an implicit scheme, so it should be only a question of accuracy.

Do you have any advice how I can measure or see accuracy without having experimental data? Or is there any hint how to choose the time steps in fully imclicit scheme?

Mike

Hi,

The Implicit scheme is first order accurate unless you use results from the two previous time-steps (n and n-1, being n+1 the new time step, in which you evaluate the terms). Therefore, you should use small time steps if you want to obtain accurate results. Sorry but I don´t know any specific criterium.

Gorka