ADAPTIVE MESH REFINEMENT METHOD APPLIED TO SHALLOW WATER MODEL: A MASS CONSERVATIVE PROJECTION

The utility of static and adaptive mesh refinement (SMR and AMR, respectively) are examined for idealized tropical cyclone (TC) simulations in a two-dimensional spectral element f-plane shallow-water model. The SMR simulations have varying sizes of the statically refined meshes (geometry based) while the AMR simulations use a potential vorticity (PV) threshold to adaptively refine the mesh to the evolving TC. Numerical simulations are conducted for four cases: (i) TC-like vortex advecting in a uniform flow, (ii) binary vortex interaction, (iii) barotropic instability of a PV ring, and (iv) barotropic instability of a thin strip of PV. For each case, a uniform grid high-resolution “truth” simulation is compared to two different SMR simulations and three different AMR simulations for accuracy and efficiency. The multiple SMR and AMR simulations have variations in the number of fully refined elements in the vicinity of the TC. For these idealized cases, it is found that the SMR and AMR simulations are able to resolve the vortex dynamical processes (e.g., barotropic instability, Rossby wave breaking, and filamentation) as well as the truth simulations, with no significant loss in accuracy in the refined region in the vortex vicinity and with significant speedups (factors of 4–15, depending on the total number of refined elements). The overall accuracy is enhanced by a greater area of fully refined mesh in both the SMR and AMR simulations.

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Analyzing the Adaptive Mesh Refinement (AMR) Characteristics of a High-Order 2D Cubed-Sphere Shallow-Water Model

Monthly Weather Review ◽

10.1175/mwr-d-16-0197.1 ◽

2016 ◽

Vol 144 (12) ◽

pp. 4641-4666 ◽

Cited By ~ 6

Author(s):

Jared O. Ferguson ◽

Christiane Jablonowski ◽

Hans Johansen ◽

Peter McCorquodale ◽

Phillip Colella ◽

...

Keyword(s):

Shallow Water ◽

Adaptive Mesh Refinement ◽

Large Scale ◽

Mesh Refinement ◽

Adaptive Mesh ◽

High Order ◽

Water Model ◽

Test Cases ◽

Shallow Water Model ◽

Cubed Sphere

Abstract Adaptive mesh refinement (AMR) is a technique that has been featured only sporadically in atmospheric science literature. This paper aims to demonstrate the utility of AMR for simulating atmospheric flows. Several test cases are implemented in a 2D shallow-water model on the sphere using the Chombo-AMR dynamical core. This high-order finite-volume model implements adaptive refinement in both space and time on a cubed-sphere grid using a mapped-multiblock mesh technique. The tests consist of the passive advection of a tracer around moving vortices, a steady-state geostrophic flow, an unsteady solid-body rotation, a gravity wave impinging on a mountain, and the interaction of binary vortices. Both static and dynamic refinements are analyzed to determine the strengths and weaknesses of AMR in both complex flows with small-scale features and large-scale smooth flows. The different test cases required different AMR criteria, such as vorticity or height-gradient based thresholds, in order to achieve the best accuracy for cost. The simulations show that the model can accurately resolve key local features without requiring global high-resolution grids. The adaptive grids are able to track features of interest reliably without inducing noise or visible distortions at the coarse–fine interfaces. Furthermore, the AMR grids keep any degradations of the large-scale smooth flows to a minimum.

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