Development of a Terrestrial Dynamical Core for E3SM at SIAM CSE

slides

Developing a predictive understanding of the terrestrial water cycle at local to global scale is essential for accurate assessment of water resources. Higher spatial resolution in the land component of the Energy Exascale Earth System Model (E3SM) alone is insufficient to meet the U.S. Department of Energy’s (DOE’s) 10-year vision. Next-generation terrestrial models need to move beyond one-dimensional systems by including scale appropriate three-dimensional physics formulations. To this end, we are developing a dynamical core which is tailored to solving thermal mass balance. The method of choice should converge linearly in the velocity in the presence of discontinuous coefficients and non-orthgonal grids. We choose to implement a mixed finite element based on the Brezzi-Douglas-Marini (BDM1) mixed finite element spaces analyzed by Wheeler and Yotov [M. F. Wheeler and I. Yotov, A multipoint flux mixed finite element method, SIAM J. Numer. Anal. 44:5 (2006) 2082-2106.]. In their method, the drawback of the resulting saddle point problem is overcome by using a vertex-centered quadrature rule, decoupling the velocity systems around the vertices of the mesh. This allows for the velocity system to be eliminated locally, resulting in a cell-centered stencil for pressure only. In this talk we describe the challenges in efficiently implementing such a method as well as present strategies for scaling the solution from the watershed to continental scales.