I read a paper Accelerated implicit-explicit Runge-Kutta schemes for locally stiff systems - ScienceDirect about IMES， is pyfr using IMEX scheme ?
No, IMEX is a implicit explicit scheem where the phyiscial system is split somehow and an implicit scheme is used on one part and explicit is used on another part. This is particularly useful on stiff systems with some different distinct time scales. Like a reacting flow for example.
PyFR doesn’t currently support this although in the past we have dabbled with line implicit schemes for boundary layers. Currently, only fully explicit or implicit time stepping is supported with the implicit scheme using DIRK solved via dual time stepping with RK smoothers.
Is the DIRK scheme only be used in ac-navier-stokes system ?
What nonlinear and linear solver is used in implicit scheme , Newton-GMRES ?
Implicit time stepping is currently supported for all physical systems. Given the way PyFR seperates time integration from the spatial scheme, all physical time integration schemes are supported on all systems currently.
No PyFR doesn’t use GMRES or similar methods, we use a dual time stepping approach which can be couple to several convergence accleration approaches. See this paper for more details: Redirecting