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Gravitational lensing surveys have now become large and precise enough that the interpretation of the lensing signal has to take into account an increasing number of theoretical limitations and observational biases. Because the lensing signal is strongest at small angular scales, only numerical simulations can reproduce faithfully the non‐linear dynamics and secondary effects at play. This paper is the first of a series in which all gravitational lensing corrections known so far will be implemented in the same set of simulations, using realistic mock catalogues and non‐Gaussian statistics. In this first paper, we present the  tcs  simulation suite and we compute basic statistics, such as the second‐ and third‐order convergence and shear correlation functions. These simple tests set the range of validity of our simulations, which are resolving most of the signals at the subarcminute level (or ℓ ∼ 10 4 ). We also compute the non‐Gaussian covariance matrix of several statistical estimators, including many that are used in the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS). From the same realizations, we construct halo catalogues, computing a series of properties that are required by most galaxy population algorithms.

Gravitational lensing simulations – I. Covariance matrices and halo catalogues