A study of the Hasegawa-Wakatani equations using an implicit explicit backward differentiation formula

The Hasegawa-Wakatani system of equations may be used to predict and study the behaviour of plasma flow. A recent analytical study of the use of linear multistep methods to solve the Hasegawa-Wakatani equations showed the backward differentiation formulas to be the most stable. The backward differentiation formulas require a solution of a large dense system of equations, so we implemented an implicit explicit version of the formula. We study the performance of the implicit explicit backward differentiation formula on some example problems where the behaviour of the Hasegawa-Wakatani equation is predictable. These results suggest that the implicit explicit method is appropriate to use with the Hasegawa-Wakatani equations.