Multiwavelet discontinuous Galerkin-accelerated Exact Linear Part (ELP) method for the shallow-water equations on the cubed sphere

The attributes of this approach are demonstrated on standard tests for the shallow-water equations on the sphere. The addition of multiwavelets to the discontinuous Galerkin method, which has the benefit of being scalable, flexible, and conservative, provides a hierarchical scale structure that can be exploited to improve computational efficiency in both the spatial and temporal dimensions.

This paper explains how combining a multiwavelet discontinuous Galerkin method with exact-linear-part time evolution schemes, which can remain stable for implicit-sized time steps, can help increase the time-step size for shallow-water equations on the sphere.