Grid, staggered

D.E. Burton, Exact Conservation of Energy and Momentum in Staggered-Grid Hydrodynamics with Arbitrary Connectivity, UCRL-JC-104258, Lawrence Livermore National Laboratory, Livermore, CA, 1990. 

Fig. 24. Positions at which the key variables are evaluated for a typical computational cell in the staggered-grid configuration.

The discretization stencil (Fig. 17.14) uses a staggered grid in which the axial velocities are represented on the control-volume faces and all other variables are represented at the control-volume centers (nodes) [307], The nodes are separated by Az, which is variable on a nonuniform mesh. The inlet at the top and the solid surface at the bottom correspond to nodes and the faces are halfway between nodes. The first axial velocity (face 1) is evaluated just above the surface at z — Az/2. The inlet velocity, however, is taken at the top node,... 

Fig. 17.14 Finite-volume, staggered-grid, spatial-difference stencil for the transient compressible stagnation-flow equations. Grid points, which are at control-volume centers, are used to represent all dependent variables except axial velocity, which is represented at the control-volume faces. The grid indexes are shown on the left and the face indexes on the right. The right-facing protuberance on the stencils indicates where the time derivative is evaluated. For the pressure-eigenvalue equation there is no time derivative.

Figure 12-3 The concept of electric and magnetic loops in a staggered grid in discretizing Maxwell s equations (according to Wang and Hohman, 1993). The electric loop is formed by four E components parallel to the edges of one face of a prism, and the magnetic loop is composed of four adjacent B components.

As a result of scaling we obtain a system of linear equations for discretized values of the electromagnetic field on a staggered grid,... 

Figure 12-5 The staggered grid for electromagnetic field discretization in the electromagnetic potential method. The normal components of electric field E are defined at the centers of the cell faces, while the tangential components of magnetic field H are defined on the cell edges.

For a staggered grid arrangement, velocity correction can be related to pressure corrections at the two nodes around it ... 

Not only dynamic models have been adopted investigating these phenomena. Lopez de Bertodano [94] for example used a 3D steady finite volume method (FVM) (PHOENICS) with a staggered grid arrangement to simulate turbulent... 

In order to study properties of the schemes, we principally consider the steady state convection and diffusion of a property with a source term in a one dimensional domain as sketched Fig 12.3 using a staggered grid for the velocity components so that the rr-velocity components are located at the w and e GCV faces. Preliminary, we assume that the velocity is constant and constant fluid properties. The convective and diffusive processes are then governed by a balance equation of the form ... 

To generalize the mass loss (or gain) rate term formulation, a staggered grid arrangement is used shifting the velocity index notation ... 

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