Lean combustion is an attractive alternative to limit pollutants levels in order to meet the imposed limitations for the next generation of civil aero-engines. However, its implementation involves important technological questions related to the augmentation of the air dedicated to the combustion process. An effort on the injection system design is required and large eddy simulation (LES) can be a useful tool in order to explore the design of novel concepts. At the state of the art, the validation of LES in high-pressure reactive conditions and in presence of the liquid phase is still limited. This shrinks the understanding and optimization of lean devices. The industrial project PERCEVAL, between Safran Tech and the CORIA laboratory, aims at extending the actual knowhow on lean combustion. Novel optical experimental techniques have been developed at CORIA to gain detailed information on industrial injection systems at high-pressure conditions. Within PERCEVAL, Safran Tech is in charge of the assessment of LES by using the experimental dataset collected at CORIA. In this framework, a novel automatic mesh convergence (AMC) procedure, based on adaptive mesh refinement, has been developed in the YALES2 platform to speed-up the calculation process. In the present paper, the AMC framework is described and then applied on the lean injection system designed at Safran Tech and tested during PERCEVAL. An analysis is carried out to evaluate the interest and gains offered by the AMC framework.