Finite Element Grid Resolution Based OnSecond And Fourth-order Truncation ErrorAnalysis

Presently, many numerical modelers use the inadequate wavelength to grid size (Ax) ratio criterion as an aid in designing grids to solve the shallow water equations. Recent research has shown that grids designed using a local truncation error analysis (LTEA) are a very attractive alternative to the wavelength to Ax criterion. By computing grid spacing such that the local second-order truncation error is limited, we have shown the need for high resolution in areas on the continental shelf very near the coast and in the vicinity of the shelf break and slope. This paper will examine the effects of combining the first through the fourthorder truncation error terms. Here the finite element grid generation is accomplished by computing grid spacing such that the local truncation error is limited. Our analysis shows that the inclusion of the first through the fourth-order truncation errors has a dramatic effect on the allowable grid size throughout our idealized one-dimensional (1-D) domain. We show the variable grid generated using truncation error analysis to be highly accurate in capturing the physics of our idealized 1-D domain. We reaffirm that the wavelength to AJC criterion is insufficient. Introduction Coastal hydrodynamic models are including larger domains and increasing levels of localized detail. The Western North Atlantic Tidal (WNAT) model domain, Figure 1, provides an explicit example of just how large domain sizes have grown [Westerink et al*; Blain et al ]. This domain size is justified when one considers the simplicity of open ocean boundary conditions on deep ocean boundaries for both tide and storm surge computations. The total area, 8.347 xlO& kirr , coupled with the need for near shore detail indicates the use of a finite element based model. Generating a finite element grid for such large domains is typically accomplished using an inadequate criterion, namely the one-dimensional (1-D), linear, frictionless, constant topography wavelength to grid size ratio. This ratio is computed as: (i) Transactions on the Built Environment vol 9, © 1995 WIT Press, www.witpress.com, ISSN 1743-3509