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The modeling of lightning strike behavior and estimation of the subsequent electric discharge is of great practical importance. In this study, a complete two-dimensional physics-based analytic formulation is presented for elevated grounded systems that can be envisioned to be contained within two non-concentric circular domains. The inner circle encompasses the body or system of interest, and the periphery of the outer circle addresses the cloud coverage. The potential field between the circular domains is modeled as the sum of two separate contributions. The first is formulated in terms of an eigen-function expansion involving simple radial functions and Legendre polynomials, while the second contribution is developed using two different approaches. The first approach utilizes an eigen-function expansion incorporating spherical Bessel functions and Legendre polynomials, while the second approach uses a Green's function expansion also involving orthogonal polynomial functions. Each of the contributions to the total potential field leads to linear systems of equations that are solved for the unknown series expansion coefficients. The accuracy of the potential field solution is investigated with regard to convergence, stability, and error compared with an exact solution. The potential field solution is then used as the basis to evaluate leader formation, as a function of elevation, extent of cloud coverage, and propagation angle of the downward leader. Regions of high risk to lightning strikes on the grounded structure are developed in terms of joint probability functions. The electric discharge is estimated using electric current and is shown to be in the range of presently available information.

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