On the accurate and stable reconstruction of tangential velocities in C-grid ocean models (original) (raw)

Advection schemes for unstructured grid ocean models

Egs Agu Eug Joint Assembly, 2003

We study advection schemes for unstructured grid ocean models. Four linear advection schemes are investigated by solving a scalar transport equation. Schemes under consideration include continuous, nonconforming and discontinuous finite elements and finite volumes. A comprehensive derivation of the numerical schemes is presented and conservation and dispersion properties are discussed. An assessment is made by performing the test problem introduced by Hecht et al. [J. Geophys. Res. 100 (1995) 20763] in which a passive scalar field is advected through an analytical Stommel gyre. It is found that continuous finite elements and finite volumes have some difficulties to represent accurately solutions with steep gradients. As a result they are prone to generate unphysical oscillations. On the other hand, discontinuous and non-conforming finite element schemes perform better. This is due to their higher flexibility that makes them better suited to highly sheared flows.

Advection schemes for unstructured grid ocean modelling

2004

We study advection schemes for unstructured grid ocean models. Four linear advection schemes are investigated by solving a scalar transport equation. Schemes under consideration include continuous, non-conforming and discontinuous finite elements and finite volumes. A comprehensive derivation of the numerical schemes is presented and conservation and dispersion properties are discussed. An assessment is made by performing the test problem introduced by Hecht et al.[J. Geophys. Res.

Use of Orthogonal Curvilinear Grids for the Representation of the Littoral Ocean Environment

2006

The effective representation of the littoral ocean environment has been a long-standing challenge for the Modeling and Simulation (M&S) community. The need for such a representation continues to grow, as the U.S. Navy refocuses from deep ocean to littoral missions. One of the greatest challenges of the littoral region is the wide range of spatial and temporal scales that must be represented. For example, the cross-shore gradients of important oceanographic parameters are typically an order of magnitude larger than the along-shore gradients. Unfortunately, the representation techniques typically employed by the real-time M&S community are not well suited to this extreme range of scales. These representations have included regular Cartesian and geodetic grids, as supported by the IEEE 1278.1a-1998 Gridded Data protocol. This paper describes the application of grids based on an orthogonal curvilinear system to the littoral environment. Orthogonal curvilinear grids were originally developed by the computational fluid dynamics community to improve the simulation of fluid flow. Such grids are now routinely used in numerical models of the littoral ocean environment. They allow a wide range of spatial scales while preserving key boundaries and maintaining some of the traditional advantages of gridded representations. One of the distinctive advantages of the use of an orthogonal curvilinear grid systems is the economy of computational and storage resources that can be attained. Methods for generating operational grids and practical aspects of employing them in the STOW Synthetic Natural Environment are discussed. Figure 4.2. Integration of orthogonal curvilinear grids in JSAF.

A comparison of 4 advection schemes for use in unstructured grid ocean modelling

2003

Abstract: We study advection schemes for unstructured grid ocean models. Four linear advection schemes are investigated by solving a scalar transport equation. Schemes under consideration include continuous, non-conforming and discontinuous finite elements and finite volumes. A comprehensive derivation of the numerical schemes is presented and dispersion and conservation properties are discussed. An assessment is made by performing the test problem introduced by Hecht et al.[J. Geophys. Res.

Numerical representation of geostrophic modes on arbitrarily structured C-grids

Journal of Computational Physics, 2009

A C-grid staggering, in which the mass variable is stored at cell centers and the normal velocity component is stored at cell faces (or edges in two dimensions) is attractive for atmospheric modeling since it enables a relatively accurate representation of fast wave modes. However, the discretization of the Coriolis terms is non-trivial. For constant Coriolis parameter, the linearized shallow water equations support geostrophic modes: stationary solutions in geostrophic balance. A naive discretization of the Coriolis terms can cause geostrophic modes to become nonstationary, causing unphysical behaviour of numerical solutions. Recent work has shown how to discretize the Coriolis terms on a planar regular hexagonal grid to ensure that geostrophic modes are stationary while the Coriolis terms remain energy conserving. In this paper this result is extended to arbitrarily structured C-grids. An explicit formula is given for constructing an appropriate discretization of the Coriolis terms. The general formula is illustrated by showing that it recovers previously known results for the planar regular hexagonal C-grid and the spherical longitudelatitude C-grid. Numerical calculation confirms that the scheme does indeed give stationary geostrophic modes for the hexagonal-pentagonal and triangular geodesic C-grids on the sphere.

Comparison of 2D triangular C-grid shallow water models

Computers & Fluids, 2018

An ideal two-dimensional (2D) shallow water model should be able to simulate correctly various types of waves including pure gravity and inertia-gravity waves. In this paper, two different triangular C-grid methods are considered, and their dispersion of pure gravity waves, frequencies of inertia-gravity waves and geostrophic balance solutions are investigated. The proposed C-grid methods employ different spatial discretization schemes for coupling shallow water equations together with the various reconstruction techniques for tangential velocity estimation. The proposed reconstruction technique for the second method, which is analogous to a hexagonal C-grid scheme, is shown to be energy conservative and satisfies the geostrophic balance exactly while it supports the unphysical geostrophic modes for hexagonal C-grid. Because of the importance of the application of 2D shallow water models on fully unstructured grids, particular attention is also given to various types of isosceles triangles that may appear in such grids. For the gravity waves, the results of the phase speed ratio of the computed phase speeds over the analytical one are shown and compared. The non-dimensional frequencies of various modes for inertiagravity waves are also investigated and compared in terms of being monotonic and isotropic respect to the continuous solution. The analyses demonstrate some advantages of the first method in phase speed behaviour for gravity waves and monotonicity of inertia-gravity dispersion. The results of the dispersion analysis are verified through a number of numerical tests. The first method, which is shown to have a better performance, examined through more numerical tests in presence of various source terms and results confirm its capability.

An overset grid method for integration of fully 3D fluid dynamics and geophysics fluid dynamics models to simulate multiphysics coastal ocean flows

2014

It is now becoming important to develop our capabilities to simulate coastal ocean flows involved with distinct physical phenomena occurring at a vast range of spatial and temporal scales. This paper presents a hybrid modeling system for such simulation. The system consists of a fully three dimensional (3D) fluid dynamics model and a geophysical fluid dynamics model, which couple with each other in two-way and march in time simultaneously. Particularly, in the hybrid system, the solver for incompressible flow on overset meshes (SIFOM) resolves fully 3D small-scale local flow phenomena, while the unstructured grid finite volume coastal ocean model (FVCOM) captures largescale background flows. The integration of the two models are realized via domain decomposition implemented with an overset grid method. Numerical experiments on performance of the system in resolving flow patterns and solution convergence rate show that the SIFOM-FVCOM system works as intended, and its solutions compare reasonably with data obtained with measurements and other computational approaches. Its unparalleled capabilities to predict multiphysics and multiscale phenomena with highfidelity are demonstrated by three typical applications that are beyond the reach of other currently existing models. It is anticipated that the SIFOM-FVCOM system will serve as a new platform to study many emerging coastal ocean problems. 549 in these examples play pivotal roles in our daily life, environments, resources for energy, etc. For example, the oil spill in the Gulf of Mexico has become the largest environmental disaster in US history, and it will have a profound impact on ecological as well as economic systems . Here and hereafter, the scales refer to observation scales such as characteristic length and time, or, process scales such as those in data analysis.

Unstructured Orthogonal Meshes for Modeling Coastal and Ocean Flows

2013

In this thesis a z?layer unstructured C-grid finite volume hydrostatic model is presented. An efficient and highly scalable implicit technique for the solution of the free surface equation is combined with an Eulerian approach for the advection of momentum. A consistent velocity reconstruc- tion procedure which not only satisfies the continuity law but also guarantees the discrete kinetic energy conservation is presented. It is shown that an ac- curate velocity reconstruction procedure is of crucial importance not only for discretization of the Coriolis term, but also for the correct advection of mo- mentum, especially in the multilayer case. Unlike other z?layer models the method presented here ensures that the staircase representation of bathymetry and free surface has no influence on the vertical structure of the flow. The method is therefore guaranteed to be strictly momentum conservative, also in the layers containing the free surface and bed. A number of test cases are present...

Delaunay mesh generation for an unstructured-grid ocean general circulation model

2000

An incremental method is presented to generate automatically boundary-fitted Delaunay triangulations of the global ocean. The method takes into account Earth curvature and allows local mesh refinement in order to resolve topological or dynamical features like midocean ridges or western boundary currents. Crucial issues like the nodes insertion process, the boundary integrity problem or the creation of inner nodes are explained. Finally, the quality of generated triangulations is discussed.