Multiwavelet Discontinuous Galerkin Accelerated ELP Method for the Shallow Water Equations on the Cubed Sphere

Abstract

In this paper we present a new approach to increase the time-step size for an explicit discontinuous Galerkin numerical method. The attributes of this approach are demonstrated on standard tests for the shallow-water equations on the sphere. The addition of multiwavelets to 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.