Assessment of high-order IMEX methods for incompressible flow

Research output: Contribution to journalResearch articleContributedpeer-review


This paper investigates the competitiveness of semi-implicit Runge-Kutta (RK) and spectral deferred correction (SDC) time-integration methods up to order six for incompressible Navier-Stokes problems in conjunction with a high-order discontinuous Galerkin method for space discretization. It is proposed to harness the implicit and explicit RK parts as a partitioned scheme, which provides a natural basis for the underlying projection scheme and yields a straight-forward approach for accommodating nonlinear viscosity. Numerical experiments on laminar flow, variable viscosity and transition to turbulence are carried out to assess accuracy, convergence and computational efficiency. Although the methods of order 3 or higher are susceptible to order reduction due to time-dependent boundary conditions, two third-order RK methods are identified that perform well in all test cases and clearly surpass all second-order schemes including the popular extrapolated backward difference method. The considered SDC methods are more accurate than the RK methods, but become competitive only for relative errors smaller than ca (Formula presented.).


Original languageEnglish
Pages (from-to)954-978
Number of pages25
JournalInternational journal for numerical methods in fluids
Issue number6
Publication statusPublished - 7 Feb 2023

External IDs

Mendeley b2b6d268-6bb5-352f-a15f-c4b28bf50d4d
Scopus 85147529254
WOS 000928830800001
ORCID /0000-0001-6727-8769/work/142246632



  • IMEX Runge-Kutta methods, discontinuous Galerkin, spectral deferred correction, spectral element method, Spectral deferred correction, Spectral element method