共查询到20条相似文献，搜索用时 15 毫秒
1.
《Ocean Modelling》2007,16(1-2):61-75
There is an increasing interest to move ocean codes from classical Cartesian staggered mesh schemes to unstructured staggered grids. By using unstructured grid models one may construct meshes that follow the coastlines more accurately, and it is easy to apply a finer resolution in areas of special interest.In this paper we focus on how to approximate the Coriolis terms in such unstructured staggered grid models using equivalents of the Arakawa C-grid for the linear equations governing the propagation of the inertia-gravity waves. We base the analysis on a Delaunay triangulation of the region in question and use the Voronoi points and the midpoints on the triangle edges to define a staggered grid for the sea elevation and the velocity orthogonal to the edges of the triangles. It is shown that a standard method for the Coriolis weighting may create unphysical growth of the numerical solutions. A modified Coriolis weighting that conserves the total energy is suggested.In real applications diffusion is often introduced both for physical reasons, but often also in order to stabilise the numerical experiments. The growing modes associated with the unstructured staggered grids and equal weighting may force us to enhance the diffusion more than we would like from physical considerations. The modified weighting offers a simple solution to this problem. 相似文献
2.
《Ocean Modelling》2007,16(1-2):47-60
The symmetry and stability properties of two unstructured C-grid discretisations of the shallow water equations are discussed. We establish that a scheme in which the circumcentres of the mesh triangles are used as the surface elevation points has advantageous symmetry properties and derive a Coriolis discretisation which preserves these properties. It is shown that the resulting scheme is conservative in a discretised energy norm. We then establish that schemes in which the water surface elevations are stored at the mesh triangle centroids do not share these advantageous symmetry properties. Finally we show examples which demonstrate that the centroid based scheme is subject to unstable growing modes, particularly in long timescale, Coriolis dominated problems; while the energy conservative circumcentre based scheme suffers from no such limitation. We conclude that unstructured C-grid methods using the triangle circumcentres and the conservative Coriolis scheme derived here therefore have advantages for this sort of problem over those schemes based on centroids. 相似文献
3.
A tree-based solver for adaptive ocean modelling 总被引：1，自引：0，他引：1
The development of an adaptive (in space and time) ocean model from an existing adaptive finite-volume Navier–Stokes model is described. A flexible and efficient quadtree spatial discretisation is used which requires collocation of all variables (i.e. an A-grid discretisation). We demonstrate that the use of an approximate projection method allows for implicit damping of instabilities generally associated with the A-grid, at the expense of a relatively small amount of numerical energy dissipation, while accurately preserving dispersive properties and geostrophic balance. The finite-volume formulation also maintains second-order spatial accuracy at all solid boundaries. Test cases demonstrate the efficacy of the adaptive ocean model, and the advantages it has in terms of efficient representation of multi-scale behaviour within a single model. The model is freely available as open-source code. 相似文献
4.
An unstructured-grid procedure for SWAN is presented. It is a vertex-based, fully implicit, finite difference method which can accommodate unstructured meshes with a high variability in geographic resolution suitable for representing complicated bottom topography in shallow areas and irregular shoreline. The numerical solution is found by means of a point-to-point multi-directional Gauss–Seidel iteration method requiring a number of sweeps through the grid. The approach is stable for any time step while permitting local mesh refinements in areas of interest. A number of applications are shown to verify the correctness and numerical accuracy of the unstructured version of SWAN. 相似文献
5.
《Ocean Modelling》2008,20(2):170-182
Most ocean models in current use are built upon structured meshes. It follows that most existing tools for extracting diagnostic quantities (volume and surface integrals, for example) from ocean model output are constructed using techniques and software tools which assume structured meshes. The greater complexity inherent in unstructured meshes (especially fully unstructured grids which are unstructured in the vertical as well as the horizontal direction) has left some oceanographers, accustomed to traditional methods, unclear on how to calculate diagnostics on these meshes. In this paper we show that tools for extracting diagnostic data from the new generation of unstructured ocean models can be constructed with relative ease using open source software. Higher level languages such as Python, in conjunction with packages such as NumPy, SciPy, VTK and MayaVi, provide many of the high-level primitives needed to perform 3D visualisation and evaluate diagnostic quantities, e.g. density fluxes. We demonstrate this in the particular case of calculating flux of vector fields through isosurfaces, using flow data obtained from the unstructured mesh finite element ocean code ICOM, however this tool can be applied to model output from any unstructured grid ocean code. 相似文献
6.
7.
《Ocean Modelling》2011,39(3-4):187-202
Ocean currents flowing close to or across the equator are strongly constrained by the change in sign of f, the locally vertical component of the Earth’s rotation vector, across the equator. We investigate these currents using a shallow water model that includes both the locally vertical and locally horizontal components of the Earth’s rotation vector, thus accounting for the complete Coriolis force. We therefore avoid making the so-called “traditional approximation” that retains only the part of the Coriolis force associated with the locally vertical component of the rotation vector. Including the complete Coriolis force contributes an additional term to the fluid’s potential vorticity, which may partially balance the change in sign of f as fluid crosses the equator over suitably shaped bathymetry.We focus on the Antarctic Bottom Water, which crosses the equator northwards in the western Atlantic ocean where the local bathymetry forms an almost-zonal channel. We show that this bathymetry facilitates the current’s equatorial crossing via the action of the “non-traditional” component of the Coriolis force. We illustrate this process using both analytical and numerical solutions for flow of an abyssal current over idealised equatorial topography. We also consider the one-dimensional geostrophic adjustment of a body of fluid across the equator, and show that the “non-traditional” contribution to the fluid’s angular momentum permits a larger cross-equatorial transport. These results underline the importance of including the complete Coriolis force in studies of the equatorial ocean, particularly in the weakly-stratified abyssal ocean where the non-traditional component is most pronounced. 相似文献
8.
Numerical modelling of coastal flows is a challenging topic due to complex topography of the coastal zone, rapid flow dynamics and large density variations. Such phenomena are best simulated with unstructured grid models due to their highly flexible spatial discretisation. This article presents a three-dimensional discontinuous Galerkin finite element marine model. Discontinuous Galerkin spatial discretisation is combined with an explicit mode splitting time integration scheme. Slope limiters are introduced to guarantee high quality of the tracer fields in the presence of strong gradients. Free surface movement is accounted for by means of an Arbitrary Lagrangian Eulerian (ALE) moving mesh method. Water volume and tracers are conserved. The conservation properties and baroclinic adjustment under gravity are tested with numerical benchmarks. Finally, the model is applied to the Rhine river plume in an idealised setting. 相似文献
9.
《Coastal Engineering》2006,53(11):947-963
A spectral/hp element method for solving enhanced Boussinesq-type equations in two horizontal dimensions is introduced. The numerical model is based on the discontinuous Galerkin method on unstructured meshes with expansions of arbitrary order. Numerical computations are used to illustrate that the computational efficiency of the model increases with increasing (i) expansion polynomial order, (ii) integration time and (iii) relative depth. Thus, the spectral/hp element technique appears to offers potentially significant savings in computational time for a fixed numerical error, compared to low-order numerical methods, for large-scale and long-time simulations of dispersive wave propagation. The practical applicability of the model is illustrated by several test cases. 相似文献
10.
It is well known that the accuracy of mesh-based numerical simulations of underwater explosion strongly relies on the mesh size adopted in the analyses. Although a numerical analysis of underwater explosion can be performed with enough accuracy by using considerably fine meshes, such fine meshes may lead to substantially increase in the CPU time and the usage of computer memory. Thus, how to determine a suitable mesh size in numerical simulations is always a problem confronted when attempting to study the shock wave propagation resulting from underwater explosion and the subsequent response of structures. Considering that there is currently no universally accepted method for resolving this problem, this paper aims to propose a simple method to determine the mesh size for numerical simulations of near field underwater explosion. To this end, the mesh size effects on the shock wave propagation of underwater explosion are carefully investigated for different charge weights, through which the correlation between mesh sizes and charge weights is identified. Based on the numerical study, a dimensionless variable (λ), defined as the ratio of the radius of charge to the side length of element, is introduced to be the criterion for determining the mesh size in simulations. It is interesting to note that the presented method is suitable for various charge weights. By using the proposed meshing rule, adequate balance between solution accuracy and computational efficiency can be achieved for different blast scenarios in numerical simulations of underwater explosion. 相似文献
11.
On two small-scale circulation mechanisms of fine-aerosol transport in the atmospheric surface layer
I. G. Granberg M. S. Artamonova E. M. Dobryshman 《Izvestiya Atmospheric and Oceanic Physics》2010,46(7):865-871
Small-scale processes are taken to mean the disturbances of the atmospheric basic background which are caused by the thermal
inhomogeneity of the underlying surface and under which one can neglect the effects of both centripetal and Coriolis accelerations.
Slight disturbances suggest the use of linearized hydrothermodynamic equations of a weakly compressible atmosphere. Two models
are considered. In one of the models, circulation over a weakly sloping barchan is analyzed using a refined model of mountain—valley
circulation (the well-known Prandtl model). The other model, which is a model of a thermal spot in a geostrophic flow, can
conditionally be called “anticonvective.” This problem is solved using the method of universal functions for parabolic equations
with variable coefficients. 相似文献
12.
A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing time. The advection and horizontal diffusion terms in the momentum equation are discretized by an integral interpolation method on the orthogonal unstructured staggered mesh and, while it has the attractive property of being conservative. The pressure-correction algorithm is employed for the non-hydrostatic pressure in order to achieve second-order temporal accuracy. A conservative scalar transport algorithm is also applied to discretize k-ε equations in this model. The eddy viscosity is calculated from the k-ε turbulent model. The resulting model is mass and momentum conservative. The model is verified by two examples to simulate unsteady small amplitude free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field,and then applied to simulate the tidal flow in the Bohai Sea. 相似文献
13.
Two diagnostic dynamic models for flow in hyperbolic and elliptic regions of a geophysical fluid are developed and compared. As the main interest here is in local dynamical processes, these models are used to study trajectories near stagnation points in the flow field. The simplest model presumes a balance between the Coriolis and geopotential accelerations. This model is equivalent to the classic approach that characterizes these regimes by the quadratic equation for the eigenvalues of the velocity gradient. However, since that model imposes geostrophic dynamics, the eigenvalues of the velocity gradient can be replaced by the local curvature or Hessian of the geopotential scaled by Coriolis. The general model adds both local and inertial accelerations to the dynamical balance. In contrast to the classic result the consequent frequency equation is a quartic that involves both the Hessian of the geopotential field, the components of the velocity gradient, and Coriolis. Roots of this equation give two distinct time scales, which are interpreted as Lagrangian time scales. Motion of the geopotential field produces a third Eulerian time scale. Critical trajectories are those whose initial positions and velocities are such that they are independent of the Lagrangian time scales. These simple models establish that within hyperbolic and elliptic regions of the geopotential field there may be trajectories whose time scales differ radically from even their nearest neighbors.A characteristic of critical trajectories in the ocean is that they often are found near stagnation points. These may be hard to identify even in model simulations, but a similar quantity, the null in the geopotential gradient, might be easier to obtain. To analyze the relation between the critical trajectories, stagnation points, and gradient null, evolution models for the later two objects are proposed. For a steady geopotential all three coincide. However with a time varying geopotential, they are distinct even though all have the same time scale. The analysis provides a metric for the separation of all three objects. 相似文献
14.
We introduce a mixed discontinuous/continuous finite element pair for ocean modelling, with continuous quadratic layer thickness and discontinuous velocity. We investigate the finite element pair applied to the linear shallow-water equations on an f-plane. The element pair has the property that all geostrophically balanced states which strongly satisfy the boundary conditions have discrete divergence equal to exactly zero and hence are exactly steady states of the discretised equations. This means that the finite element pair has excellent geostrophic balance properties. We also show that the element pair applied to the non-rotating linear shallow-water equations does not have any spurious small eigenvalues. We illustrate these properties using numerical tests and provide convergence calculations which show that the numerical solutions have errors which decay quadratically with element edge length for both velocity and layer thickness. 相似文献
15.
Koji Hidaka 《Journal of Oceanography》1972,28(2):48-62
It is widely recognized that the geostrophic flows computed by the dynamic method of Bjerknes and collaborators represent the actual currents pretty faithfully. However, what would be the reason that a geostrophic current derived by only retaining the terms of Coriolis and the pressure gradient forces in the hydrodynamical equations agrees so closely with the actual ocean current of the same area? In this attempt was assumed an imaginative ocean of homogeneous water and uniform depth on a rotating earth but with neither continent nor islands. The average wind distribution observed along several meridians over the Pacific Ocean was assumed to prevail in this sea throughout with no variation in east-west direction. Taking the curvature of the earth surface, rotation of the earth, Coriolis forces, pressure gradients and the horizontal and vertical eddy viscosity into account, the equations of motion were solved and velocity components were derived for all latitudes. A comparison of the east-west components thus obtained with the corresponding components of the geostrophic flows, reveals that they agree well in higher latitudes but there appears a remarkable disagreement in lower latitudes. This means that a special care must be taken in replacing the existing currents with the geostrophic flows at lower latitudes. 相似文献
16.
A numerical simulation algorithm based on the finite volume discretisation is presented for analyzing ship motions. The algorithm employs a fractional step method to deal with the coupling between the pressure and velocity fields. The free surface capturing is fulfilled by using a volume of fluid method in which the interface between the liquid (water) and gas (air) phases are computed by solving a scalar transport equation for the volume fraction of the liquid phase. The computed velocity field is employed to evaluate the acting forces and moments on the vessel. Using the strategy of boundary-fitted body-attached mesh and calculating all six degrees-of-freedom of motion in each time step, time history of ship motions including displacements, velocities and accelerations are evaluated.To verify the proposed algorithm, a series of verification tests are conducted. First, a two-dimensional asymmetrical wedge slamming is simulated as a simple type of a common case for high-speed vessels. Then, the steady-state forward motion of a high-speed planing catamaran is investigated. Results of both test cases show good agreement with experimental data. It is concluded that the proposed algorithm can be a promising strategy for both performance prediction and design of high-speed vessels. 相似文献
17.
文章基于Delaunay三角化的思想实现了非结构化数值网格生成技术,并LOP(Local Optimization Procedure)算法对网格进行了优化。用有限体积法在非结构三角形网格上对平面二维潮流方程进行了数值求解。实例应用分析表明,文中的数值网格生成技术和有限体积方法相结合用于求解具有复杂几何边界区域内的潮流问题能取得很好的结果。 相似文献
18.
《Ocean Modelling》2002,4(3-4):347-361
An energy-conserving discretisation of the shear and buoyancy production terms for turbulent kinetic energy is derived. In contrast to `ad hoc' numerical schemes, this guarantees that all mean kinetic and potential energy which is lost or gained due to vertical mixing is exactly subtracted or added to the turbulent kinetic energy budget. It is further shown in a numerical wind-entrainment experiment that this new methods results in significantly more stable numerical solutions. 相似文献
19.
G.J. Gorman M.D. Piggott C.C. Pain C.R.E. de Oliveira A.P. Umpleby A.J.H. Goddard 《Ocean Modelling》2006,12(3-4):436-452
A method for generating high quality unstructured computational meshes for applications in geophysical, and specifically ocean, modelling is presented. The method generates a three-dimensional mesh which is optimised to approximate the bathymetry to a user-specified accuracy, which itself may be defined as a function of space and bathymetry. To do this a mesh optimisation method is employed which allows the formation of highly anisotropic elements aligned with bathymetric variations of high curvature. In addition a coastal recovery algorithm, based upon feature decimation and edge recovery, is described. 相似文献
20.
A two-dimensional scour model based on coupled system of shallow water equations (SWEs) and sediment transport on unstructured mesh is developed. The coupled system of hydrodynamic and morphodynamic equations is solved by finite volume method using Godunov scheme. Roe's approximate Riemann solver is used to calculate the inviscid fluxes. The use of unstructured mesh makes the model applicable to complex domains. However, it is difficult to evaluate the eigenvalues and eigenvectors of the Jacobian matrix in the global coordinate. The method proposed herein to deal with this difficulty is to transform the system into the local coordinate with one of the axes in the same direction as the interface outward normal vector. In the local coordinate system, the Jacobian matrix is simplified and the eigenvalues are analyzed using asymptotic method. Regular expansion breaks down when the flow is near critical. Uniformity of the expansion is achieved by changing the scales. Rotational invariance theorem is used to relate the interfacial fluxes in the global and local coordinate systems. Special treatment of the source term on unstructured grid makes the scheme stable and physically balanced (both mass and momentum). The method proposed in this paper for the eigen-system is very efficient comparing to iterative numerical methods. Results from the test cases show good agreement with the experiments. 相似文献