An a posteriori-implicit turbulent model with automatic dissipation adjustment for Large Eddy Simulation of compressible flows

•A high-order finite volume scheme with adaptive dissipation is presented for the computation of compressible turbulent flows.•The dissipation added by the numerical flux is modified to act as an implicit SGS term.•The a posteriori detection paradigm is used to preserve the stability of the scheme.•Compared with the regular FV scheme we obtain important gains in accuracy. In this work we present an a posteriori high-order finite volume scheme for the computation of compressible turbulent flows. An automatic dissipation adjustment (ADA) method is combined with the a posteriori paradigm, in order to obtain an implicit subgrid scale model and preserve the stability of the numerical method. Thus, the numerical scheme is designed to increase the dissipation in the control volumes where the flow is under-resolved, and to decrease the dissipation in those cells where there is excessive dissipation. This is achieved by adding a multiplicative factor to the dissipative part of the numerical flux. In order to keep the stability of the numerical scheme, the a posteriori approach is used. It allows to increase the dissipation quickly in cells near shocks if required, ensuring the stability of the scheme. Some numerical tests are performed to highlight the accuracy and robustness of the proposed numerical scheme.