A partitioned second‐order method for magnetohydrodynamic flows at small magnetic reynolds numbers

This article aims to study the partitioned method for magnetohydrodynamic flows at small magnetic Reynolds numbers. We design a partitioned second‐order method and show that this method is stable under a time step ( ) restrict condition. Our method can decouple the magnetohydrodynamic equations so that we can solve two relatively simple subproblems separately at each time step, which is computationally economic. A complete theoretical analysis of error estimates is also given. Finally, we present numerical experiments to support our theory.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1966–1986, 2017