SIParCS 2016 - Francois Hebert

Francois Hébert, Cornell University

Assessing the errors from dimensional splitting in a discontinuous Galerkin transport code

(Slides)  (Recorded Talk)

The discontinuous Galerkin (DG) method is becoming an increasingly popular tool for numerically solving differential equations that arise in atmospheric modeling, due to its high order of convergence, geometric flexibility, and excellent parallel efficiency. Traditionally, 3D weather and climate models use numerical schemes in which the vertical and horizontal dimensions are treated separately. These dimensionally split schemes are favored because they allow for more efficient time-stepping, but they can also introduce increased error in the spatial discretization. Recent work has analyzed the magnitude of these dimensional-splitting errors in low-order numerical methods restricted to two dimensions, but there has not yet been a study of their importance when working in three dimensions or using a more advanced high-order method. As a result, it is unclear whether the traditional dimensionally split approach has benefit over a fully 3D approach when using the DG method. To resolve this question, we undertake a new study of the errors arising from dimensional splitting in a 3D DG method.

In this work, we present the newly developed 3D MPI-parallel transport code used in our study. We verify the code's convergence properties using known test cases and its scaling properties using the Yellowstone supercomputer. We then compare numerical results for the evolution of the transport equation using a full 3D DG method vs. a dimensionally split DG method, and we assess the errors that arise from the dimensional splitting.

Mentor: Ram Nair, CISL