Abstract: In the context of expensive numerical experiments, a promising solution to alleviate the computational costs consists of using partially converged simulations instead of exact solutions. The gain in computational time is at a price of precision in the response. This work addresses the issue of fitting a Gaussian process metamodel to partially converged simulation data, for further use in prediction and optimization. The main challenge consists in the adequate approximation of the error due to partial convergence, which is correlated in both design variables and time directions. Here, we propose to fit a Gaussian process in the joint space of design parameters and computational time. The model is constructed by building a covariance function that reflects accurately the actual structure of the error. Practical solutions are proposed to solve the learning issues associated with the model. The method is applied to a CFD simulator test-case, and shows significant improvement in prediction compared to a classical kriging model.