CFD Online Discussion Forums - What is the efficient scheme?

(1). When you are solving a transient problem, the un-steady equation is used. And you will be marching in time to solve the transient problem. (2). The time step used must be small enough to resolve the transient motion of fluid, because it is an initial value problem. (3). For steady-state problem, the equation will be independent of the time, and time steps. Therefore, there is no need to worry about the use of time step. (4). But, sometimes, it is possible to obtain steady-state solution by time marching. There is no guarantee that such approach will lead to a steady-state solution. (5). In this case, it is possible to increase the time step to reach the steady-state solution. The time steps used are no longer the real time steps. (6). Sometimes, there is additional stability limit on the time step used, in the transient formulation or scheme. (part of the problem comes from the truncation error or accuracy) In this case, the time step of the explicit method under the stability limit is linked directly to the physics (or accuracy) of the solution. As a result, the time step used must be relatively small in the marching methods.(explicit method) (7). For obtaining steady-state solution using a transient approach, implicit methods can be used to increase the time step (no longer the real time step) for stability reason.