SUMMARYMesh convergence order is a key for certiÿcation of the accuracy of numerical solutions. A few available results and tools in mesh adaption are synthetized in order to specify a mesh converging method for adaptive calculation of compressible ows including shocks or viscous layers. The main design property for this method is early second-order convergence, where early means that the second-order convergence is obtained with coarse meshes.

This paper is mainly concerned with Nd:YAG laser induced plasmas in air at different pressures. A modelling of the formation of laser plasmas is presented. The preionization phase is described using time differential equations that are solved in the basis of the Crank–Nicolson second order scheme. Moreover, the following dynamic phase, described as a strong shock wave expanding out of the focal volume, is simulated by using a two-dimensional compressible flow calculation code. The evolution of pressure, temperature, densities and velocities are analysed and compared with experimental measurements. The mean electron density of the plasma measured through an interferometric method leads to ( ), which correlates with computed results.

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