Runge-Kutta IMEX schemes for the Horizontally Explicit/Vertically Implicit (HEVI) solution of wave equations

The stability limits of a number of variations of trapezoidal implicit and some Runge-Kutta IMEX schemes are found and the schemes are tested on two vertical slice cases using the compressible Boussinesq equations split into various combinations of implicit and explicit terms. Some of the Runge-Kutta schemes are found to be beneficial over trapezoidal, especially since they damp high frequencies without dropping to first-order accuracy. We test schemes that are not formally accurate for stiff systems but in stiff limits (nearly incompressible) and find that they can perform well. The scheme ARK2(2,3,2) performs the best in the tests.