Introduction

Any lightning model is a mathematical construct designed to reproduce certain aspects of the physical processes involved in the lightning discharge. No modeling is complete until the model predictions are compared with experimental data; that is, model testing, often called validation, is a necessary component of any modeling. In the following, we will present various models of the different lightning processes, some models being applicable to more than one lightning process.

Return stroke

General overview

We define four classes of lightning return-stroke models. Most published models can be assigned to one, or sometimes two, of these four classes. The classes are primarily distinguished by the type of governing equations.

(i) The first class of models comprises the gas dynamic or “physical” models, which are primarily concerned with the radial evolution of a short segment of the lightning channel and its associated shock wave. These models typically involve the solution of three gas dynamic equations (sometimes called hydrodynamic equations), representing the conservation of mass, of momentum, and of energy, coupled to two equations of state. Principal model outputs include temperature, pressure, and mass density as a function of the radial coordinate and time.

(ii) The second class of models comprises the electromagnetic models, which are usually based on a lossy, thin-wire antenna approximation to the lightning channel. These models involve a numerical solution of equations to find the current distribution along the channel from which the remote electric and magnetic fields can be computed.

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