On the parallel implementation and performance study of high-order Rosenbrock-type implicit Runge-Kutta methods for the FR/CPR solutions of the Navier-Stokes equations
MetadataShow full item record
Type of Work18 pages
conference papers and proceedings
Citation of Original PublicationLai Wang and Meilin Yu. "On the parallel implementation and performance study of high-order Rosenbrock-type implicit Runge-Kutta methods for the FR/CPR solutions of the Navier-Stokes equations", 2018 AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, (AIAA 2018-1095) https://doi.org/10.2514/6.2018-1095
RightsThis item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please contact the author.
Rosenbrock-type implicit Runge-Kutta methods
Rosenbrock-type implicit Runge-Kutta
ﬂux reconstruction/correction procedure re-construction
The Rosenbrock-type implicit Runge-Kutta (ROIRK) methods only require one Jaco-bian matrix evaluation per time step rather than per stage as other types of implicit Runge-Kutta (IRK) methods need. This feature makes ROIRK attractive for numerical simulations using implicit methods. We present the parallel implementation of several matrix-based ROIRK methods with ﬂux reconstruction/correction procedure re-construction (FR/CPR) formulations for solving the 3D Navier-Stokes equations. In this study, METIS has been utilized to partition the mesh in the preprocessing. The complex-step derivative approximation is employed to evaluate the Jacobi matrix, ac-curate to machine zero. The GMRES solver in the PETSc library is used to iteratively solve the linear system. The ROIRK methods have demonstrated high order of ac-curacy in numerical simulations. The scalability study reveals that the matrix-based ROIRK methods have good parallel eﬃciency. With the block Jacobi preconditioner, it is observed that the linear systems resulting from ROIRK3-3 are stiﬀer than those from ROIRK2-2 and ROIRK4-6. This makes the scalability of ROIRK3-3 worse than ROIRK2-2 and ROIRK4-6 taking the number of stages into account.