Cell-vertex discretization of shallow water equations on mixed unstructured meshes

Abstract

Finite-volume discretizations can be formulated on unstructured meshes composed of different polygons. A staggered cell-vertex finite-volume discretization of shallow water equations is analyzed on mixed meshes composed of triangles and quads. Although triangular meshes are most flexible geometrically, quads are more efficient numerically and do not support spurious inertial modes of triangular cell-vertex discretization. Mixed meshes composed of triangles and quads combine benefits of both. In particular, triangular transitional zones can be used to join quadrilateral meshes of differing resolution. Based on a set of examples involving shallow water equations it is shown that mixed meshes offer a viable approach provided some background biharmonic viscosity (or the biharmonic filter) is added to stabilize the triangular part of the mesh.

Assessment of the Finite-volumE Sea ice-Ocean Model (FESOM2.0) – Part 1: Description of selected key model elements and comparison to its predecessor version

“…The Finite-Element Sea ice-Ocean Model version 1.4 (FE-SOM1.4; Wang et al, 2014), the first mature global multiresolution unstructured-mesh model intended for simulating the global ocean general circulation for climate research, set a milestone in the development of this new generation of ocean models. The success of FESOM1.4 was based on the experience gained with its predecessor versions (Danilov et al, 2004;Wang et al, 2008;Timmermann et al, 2009). The studies performed with FESOM1.4 proved the value of global multi-resolution unstructured meshes for simulating local ocean dynamics (Wang et al, 2016aWekerle et al, 2017) and exploring their global effects (Rackow et al, 2016;Scholz et al, 2014;Sein et al, 2018;Sidorenko et al, 2011Sidorenko et al, , 2018 with acceptable computational costs.…”

Designing variable ocean model resolution based on the observed ocean variability

“…The coefficient of biharmonic viscosity includes contributions from the Smagorinsky and modified Leith parameterizations [see e.g., Fox‐Kemper and Menemenlis , ], which are bounded from above by with v v =0.02 m/s. The biharmonic filter described in Danilov and Androsov [] is used to more efficiently couple the neighboring velocity points. Its magnitude is tuned to have the similar effect as the biharmonic operator with the coefficient for v f =0.007 m/s, where h is the triangle side.…”

“…with v v 50.02 m/s. The biharmonic filter described in Danilov and Androsov [2015] is used to more efficiently couple the neighboring velocity points. Its magnitude is tuned to have the similar effect as the biharmonic operator with the coefficient v f h 3 for v f 50.007 m/s, where h is the triangle side.…”

Океанологические Модели Негидростатической Динамики. Обзор, "Фундаментальная И Прикладная Гидрофизика"

“…Об этом свидетельствуют и отдельные рабо-ты, и возникающие системные модели с возможностями НГ приложений: [73]; CARDINAL (Coastal ARea Dynamics INvestigation ALgorithm), [70,71]; ROMS (Regional Oceanic Modeling System), [25]; NBfOM (Nonhydrostatic Body-fitted Oceanic Model), [26]; ICOM (Integrated Coastal Ocean Modeling) [68]; SUSTANS (Stanford Unstructured Nonhydrostatic), [69]; ADCIRC (Advanced CIRCulation Model), [74]; SELFE (Semi-implicit Euler -Lagrangian Finite -Element model), [75]; UnTRIM (Unstructured 3-D hydrodynamic model), [76]; FESOM -coastal (Finite -Element Sea -ice Ocean Model [77] -вот далеко не полный перечень системных моделей.…”