Module 1: Introduction to Finite Difference Method and Fundamentals of CFD
Lecture 6:
Major advantages and disadvantages of explicit and implicit methods
| Advantages |
| Disadvantages |
Explicit Method
The solution algorithm is simple to set up
for a given must be less than a specific limit imposed by stability constraints.
This requires many time steps to carry out the calculations over a given interval of t.
Implicit Method
Stability can be maintained over much larger values of .
Fewer time steps are needed to carry out the calculations over a given interval.
More involved procedure is needed for setting up the solution algorithm than that for explicit method.
Since matrix manipulations are usually required at each time step, the computer time per time step is larger than that of the explicit approach.
Since larger can be taken, the truncation error is often large, and the exact transients (time variations of the dependent variable for unsteady flow simulation) may not be captured accurately by the implicit scheme as compared to an explicit scheme.
Apparently finite-difference solutions seem to be straightforward. The overall procedure is to replace the partial derivatives in the governing equations with finite difference approximations and then finding out the numerical value of the dependent variables at each grid point. However, this impression is indeed incorrect! For any given application, there is no assurance that such calculations will be accurate or even stable! We shall soon discuss about accuracy and stability.
must be less than a specific limit imposed by stability constraints. 
. 
can be taken, the truncation error is often large, and the exact transients (time variations of the dependent variable for unsteady flow simulation) may not be captured accurately by the implicit scheme as compared to an explicit scheme. 
