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

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dc.contributor.authorWang, Lai
dc.contributor.authorYu, Meilin
dc.date.accessioned2018-01-23T15:23:52Z
dc.date.available2018-01-23T15:23:52Z
dc.date.issued2018
dc.description.abstractThe 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.en_US
dc.format.extent18 pagesen_US
dc.genreconference papers and proceedingsen_US
dc.identifierdoi:10.13016/M2M61BR53
dc.identifier.citationLai 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/10.2514/6.2018-1095en_US
dc.identifier.urihttp://hdl.handle.net/11603/7703
dc.language.isoen_USen_US
dc.publisherAIAA SciTech Forumen_US
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mechanical Engineering Department Collection
dc.relation.ispartofUMBC Faculty Collection
dc.relation.ispartofUMBC Student Collection
dc.relation.ispartofseries2018 AIAA Aerospace Sciences Meeting;AIAA 2018-1095
dc.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.
dc.subjectNavier-Stokes equationsen_US
dc.subjectRosenbrock-type implicit Runge-Kutta methodsen_US
dc.subjectRosenbrock-type implicit Runge-Kuttaen_US
dc.subjectflux reconstruction/correction procedure re-constructionen_US
dc.subjectROIRKen_US
dc.subjectFR/CPRen_US
dc.subjectUMBC High Performance Computing Facility (HPCF)
dc.titleOn the parallel implementation and performance study of high-order Rosenbrock-type implicit Runge-Kutta methods for the FR/CPR solutions of the Navier-Stokes equationsen_US
dc.typeTexten_US

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