[mihirmakwana6]

what is the difference between a semi-explicit and a semi-implicit time discretization scheme.



What is it that is different in both these time discretization scheme ?

Also what will be advantages and disadvantages of them.

suggest examples if any.

Please help.

[mprinkey]

I have been doing this a long time and I have never heard of "semi-explicit" schemes. Can you provide a reference?

The transient CFD methods I know exist on a spectrum with fully explicit schemes on one side and fully Implicit schemes on the other.

Explicit schemes start with a state of the flow fields (phi) at some time (and maybe a few previous times) and compute the fields at some future time. Everything is phi(n+1) = F(phi(n),phi(n-1)...) The differential operations are all applied through F and only involve known data. In particular, any element of phi(n+1) is not dependent on any other element of phi(n+1).

Implicit schemes are much more varied and include both pressure and density-based solvers. But, they ultimately solve a system that looks like G(phi(n+1)) = 0 where G is some huge nonlinear operator and will involve terms from phi(n), phi(n-1),... There are many ways that this nonlinear operator can be inverted and solved for phi(n+1), but in principle, they all will give the same answer. And the crucial difference is that EVERY element of phi(n+1) depends on all of the others.

Semi-implicit schemes live somewhere in the middle on that specturm. They arise from the realization that some terms in the fluid equations are just fine to treat explicitly (like convection). While other terms (like the pressure in incompressible flows) *must* be treated implicitly. So, you can trade off some of the absolute solution consistency of implicit schemes and pick up some of the performance of the explicit methods and have the best of both world...a scheme that is much more stable and allows larger timesteps than fully-explicit methods but is significantly faster than full implicit methods. A common example of semi-implicit time integration methods are fractional-step or projection methods. Convection is usually treated explicitly. Diffusion is either treated implicitly or explicitly or split directionally. Pressure is always treated implicitly.

I hope this helps.

[FMDenaro]

I agree. Just to give a simple example, consider an equation like

d phi /dt + Div F = 0

and integrate between tn and tn+1:

phi(tn+1) - phi(tn) + Int [tn, tn+1] Div F dt = 0

Now look at the integral that must be discretized (and of course apporximated):

1) approximation based only on values at tn -> fully explicit of any accuracy order
2) approximation based only on values at tn+1 -> fully implicit of any accuracy order
3) approximation based on values both at tn and tn+1 -> semi-implicit of any accuracy order

[kaya]

nothing to add but in different words

say :


an explicit:

you time step with your field data that you have


an implicit:

you time step with solving the equation system since u_new doesn't exist yet


a semi-implicit:



With explicit time stepping, you transfer the information from past to march in time or in other words you satisfy the equation system in the current time(explicit Euler-first example).

With implicit time stepping you satisfy your equation on a future time. You seek for a field that will be the exact solution of your equation/s. And yes, its more expensive.

If you're solving a stiff system, usually its better to use an implicit or a semi-implicit treatment then you can catch the sudden peaks in the system with less effort.

Also implicit schemes are more stable thus you can take bigger time steps.

An example would be; for a low Re flow, you would use implicit or semi-implicit on your diffusive terms. Because if you treat them explicitly you'll need to go quite low delta t values.

[adrin]

The mathematical differences between purely explicit, purely implicit and "semi-implicit" have already been provided by others, so I'll give a slightly different point of view. Semi-implicit is the standard term that is used in the field. However, this is really a matter of terminology and nothing more. "semi" is a Latin prefix meaning half, at least in this context. So, semi-implicit means half (or partially) implicit, which by default implies half-explicit (for the other "half"). In other words, semi-implicit and semi-explicit (would) have _identical_ meaning. On a lighter note, it's like asking what the difference between a half-full and half-empty glass is!

adrin

[mihirmakwana6]

Thankyou all for the answers.

I have been reading this paper

http://onlinelibrary.wiley.com/doi/1.../fld.1032/epdf

In section 3 SEMI-IMPLICIT TEMPORAL DISCRETIZATION of the paper, they discretize terms from which speed of sound arises in an implicit manner. So how does this help in converting equation (17) to equation (18) i.e why using implicit advancement for pressure terms leads to larger time stepping.

Thanks in advance.

[mihirmakwana6]

can anyone help me with this ???

[mihirmakwana6]

Originally Posted by mihirmakwana6

Thankyou all for the answers.

I have been reading this paper

http://onlinelibrary.wiley.com/doi/1.../fld.1032/epdf

In section 3 SEMI-IMPLICIT TEMPORAL DISCRETIZATION of the paper, they discretize terms from which speed of sound arises in an implicit manner. So how does this help in converting equation (17) to equation (18) i.e why using implicit advancement for pressure terms leads to larger time stepping.

Thanks in advance.

can anyone help me with this ??