Equations that involve two or more variables e.g Riemann's equations for fluid flow, or Navier Stokes equation(NSE) in general that have four variables including energy terms are highly coupled and nonlinear. Is it possible to solve them efficiently using the ADI procedure? If yes can anyone help me with the procedure or methodology?
Yes, surely. Please see my page and papers on using ADI for solving compressible N-S equations for 2D flows.
Dear sir,
I went to your page, but i found most of your papers on wind turbine. Was not able to get to the N-S equation solution. Could you kindly suggest me any of your paper that will help me out.
Please see my PhD thesis in the following link:
http://sedaghat.iut.ac.ir/sites/sedaghat.iut.ac.ir/files//file_pubwdet/sedaghat-phd-thesis.pdf
Thank your sir. I was able to get the thesis. I hope i can contact you. If i need to understand anything from your thesis.
ADI means that in handling the unknows on the left hand side of equation system, you alternate the direction in space. Coupling is a different issue. They are two different issues.
Sir, my question was like if i have three equation with three dependent variables linked, do i need to solved these equation one after the another ( means first equation discretised and solved to get the variables then next and so on) using ADI approach or am i suppose to discretise them together and then use the solver.
It depends! For some problem, the coupling is not strong, solve them all at once might be an efficient approach. For some problem that the coupling is so strong that may change the physical regimes locally or temporarily during the iteration, you might want to split one or more variable. The thermohydrodynamic lubrication is one typical example. In that problem, the viscosity is strongly couple with the temperature. We need to solve the continuity and momentum equation till almost converged and then goes to the energy and viscosity iteration loop.