Mid term project -Steady state vs unsteady analysis

Steady-state Analysis

Unsteady state Analysis :-

Conclusion:-

• The steady state solver is obviously faster. beacause of the mathematical simplication problem will prove here. Theere is no thermal diffusivity and no time inntegration.
• If no numerical diffusion and solution will always be stable. we choose dx and dy in correct number iteration.
• In transient solvers the explicit schemes easy to solve because in this case we have system of liear equation (nodes) that can be solve idependentley without the iteration.
• This scheme actually work in steady case because time integation will judge the converge loop in steady case.
• Implicit solver rrequire iteration untill convergence in spatial node plus then the time integration than the explicit solvers. theefore more expensive.
• In transient solver we need to asssume the new factor as K=alpha*dt/(dx^2)
• It determine wheather our transient schemes are converge or diverge. the thermal diffusivity is given so we must carfull with spatial node size and time step. Usually the num of nodes will be selected based on the geometry and then the time step must be chosen accordingly for convergence
• Implicit solver are more stable this s maximum the maximum value of k in which the method is stable k value have maximum time step size that can be is higher.
• The higher time step for convergence but the solution will always be smaller time step.