Question on runge-Kutta 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 time-marching technique to advance the solution in time.

I'm wondering whether it is possible to implement a fourth-order Runge-Kutta scheme together with SIMPLER.

THanks.

The backward Euler scheme is actually a particularization of a Runge-Kutta scheme (order 1). In principle you can use a Runge-Kutta 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