In all of these studies, the construction of a mesh in order to simulate the physical domain requires time and effort and subsequently dictates the storage requirements of the model. Many of these early models are discussed in Pepper and Wang (2009). Numerically creating mass-consistent 3D wind fields has been employed for many years and has been especially effective in modeling atmospheric dispersion. Selection of node placement in mesh-free applications is addressed in Atluri and Zhu (1998), Choi and Kim (1999), and Gewali and Pepper (2010). In many situations where explicit mesh generation is difficult, the meshless method is emerging as an alternative to mesh-based methods. In a meshless method, there is no need to compute mesh elements induced by the selected nodes in the domain the meshless method uses a group of nodes to derive a solution without the need for a connectivity relationship. There has been increasing research interest for applying meshless (or mesh free) methods to obtain approximate solutions of differential equations (see Atluri and Zhu 1998 Balachandran et al. Meshless methods are becoming popular, principally due to their abilities to deal with complex geometrical problems with inhomogeneous or variable properties, the use of general-purpose algorithms, and the lack of a mesh requirement. Localized mesh adaptation has been shown to help alleviate global meshing requirements and improve accuracy ( Pepper and Wang 2009). Extracting realistic estimates of 3D wind from sparse meteorological data requires the use of numerical modeling-typically employing procedures based on extensive numerical meshing involving finite-difference, finite-volume, and finite-element methods (FDM, FVM, and FEM, respectively). Unfortunately, the lack of adequate meteorological data makes this particularly difficult. An accurate depiction of 3D wind fields, especially in complex terrain, is crucial when conducting atmospheric studies.
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