Question on rungeKutta scheme
Hi,
I'm trying to solve a low Mach number, variable density flow using SIMPLER algorithm of Patankar. It's an unsteady problem where I've used first order Euler backward scheme for the time discretisation. I use a timemarching technique to advance the solution in time. I'm wondering whether it is possible to implement a fourthorder RungeKutta scheme together with SIMPLER. THanks. 
The backward Euler scheme is actually a particularization of a RungeKutta scheme (order 1). In principle you can use a RungeKutta scheme for the time discretization.

the potential problem of RK method
as it is unsteady problem ,
your starting point should be higher accuracy in time. but if you use high order RK method of, or AB method is the same, assuming you using explicit version then there is a limitation of time step for stability consideration... so , if you need higher accuracy, three time level method should be a good choice in fact, the whole accuracy should both consider spatial and temporal terms if it is second order in spatial, there is no need for 4th order temporal scheme 
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