Steady vs unsteady state analysis
AIM: Steady VS unsteady analysis.
OBJECTIVE: Compare your fastest steady-state simulation vs your fastest transient simulation and explain your results.
SOLUTION
This is the link for the previous project
In this above project, we have concluded that for all given methods and approaches the Successive Over-Relaxation method has been most efficient. The fastest steady-state simulation was achieved by the successive love relaxation method and for the transient state, it was the SOR method.
Steady-state SOR method
Transient state SOR methods
Conclusion
From the above state, we can conclude that the steady SOR method is the fastest of both methods. But it is also important to consider that the steady-state does not include the Thermal diffusivity and the time derivative term which result in a steady and a fast solution. Similarly, the transient state SOR method involves the formation term which results in higher simulation time and iteration when compared to the steady-state SOR method.
In the case of transient simulation, the implicit approach is generally more stable than the explicit. It is so because when time steps are considered explicit approaches are very sensitive to them and if a wrong time step is to consider the solution may end up resulting in inability. On the contrary, implicit solution approaches are less sensitive to time steps. This tells us that when a solution is solved implicitly we may end up with higher simulation time and iteration which may be very expensive or wastage of valuable simulation time. In other words, we can also spatial nodes are solved separately and a system of linear equations, and the time integration here is similar to the convergence loop in the steady-state simulation.
The thermal diffusivity is also factored into an important consideration for our solver. The right TD value leads to a more accurate solution. Considering we have the right value other parameters like optimum grid size and time step also take priority for an accurate and fast solution. On the same note, we gave also concluded in a previous challenge that having a smaller time step will give more precise and accurate result but may end up having a large simulation time. These are some of the factors and conditions which should be addressed when simulations of the above nature are conducted. An exact range of these factors cannot be given as they change with the given problem and its specification.