2014 **Abstract:** The discontinuous Galerkin (DG) methods designed for hyperbolic problems arising from a wide range of applications are known to enjoy many computational advantages. DG methods coupled with strong-stability-preserving explicit Runge–Kutta discontinuous Galerkin (RKDG) time discretizations provide a robust numerical approach suitable for geoscience applications including atmospheric modeling. However, a major drawback of the RKDG method is its stringent Courant–Friedrichs–Lewy (CFL) stability restriction associa…

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(74 citation statements)

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“…Notice how large the ${L}_{\infty}$ errors are for the Strang splitting. This sort of error at cube corners for Strang splitting was also seen in Guo et al (). These errors can be reduced with a smaller time step, but that jump always seems to be there.…”

confidence: 77%

“…Notice how large the ${L}_{\infty}$ errors are for the Strang splitting. This sort of error at cube corners for Strang splitting was also seen in Guo et al (). These errors can be reduced with a smaller time step, but that jump always seems to be there.…”

confidence: 77%

“…Typically in 2‐D, one would only do an x and a y sweep with dimensional splitting. However, the cubed sphere requires three sweeps across the domain, and the details of this are specified in Guo et al (). $$\begin{array}{ccc}right{\stackrel{true\xaf}{\varphi}}^{\ast}\left({t}_{n}\right)& left={\text{RHS}}_{\xi}\left(\stackrel{true\xaf}{\varphi}\left({t}_{n}\right)\right);\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}{\stackrel{true\xaf}{\varphi}}^{\ast \ast}\left({t}_{n}\right)={\text{RHS}}_{\eta}\left({\stackrel{true\xaf}{\varphi}}^{\ast}\left({t}_{n}\right)\right);\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\stackrel{true\xaf}{\varphi}\left({t}_{n+1}\right)={\text{RHS}}_{\zeta}\left({\stackrel{true\xaf}{\varphi}}^{\ast \ast}\left({t}_{n}\right)\right)& right\\ right{\stackrel{true\xaf}{\varphi}}^{\ast}\left({t}_{n+1}\right)& left={\text{RHS}}_{\zeta}\left(\stackrel{true\xaf}{\varphi}\left({t}_{n+1}\right)\right);\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}{\stackrel{true\xaf}{\varphi}}^{\ast \ast}\left({t}_{n+1}\right)={\text{RHS}}_{\eta}\left({\stackrel{true\xaf}{\varphi}}^{\ast}\left({t}_{n+1}\right)\right);\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\stackrel{true\xaf}{\varphi}\left({t}_{n+2}\right)={\text{RHS}}_{\xi}\left({\stackrel{true\xaf}{\varphi}}^{\ast \ast}\left({t}_{n+1}\right)\right)\end{array}$$ The directions ξ , η , and ζ are indicative of three global closed directed paths over the surface of the sphere.…”

confidence: 99%

“…Substituting the discretized scalar field (5) and test functions into (2), and replacing integrals by the Gaussian-Lobatto quadratures, converts the partial differential equation into a set of ordinary differential equations in time, which may be written abstractly as…”

confidence: 99%

“…They create ghost cells outside each cube panel boundary and achieve accuracy between second and fourth order. Guo et al (2014) report error growth around cube edges using Strang splitting.…”

confidence: 99%