AbstractA method for modelling of flow discontinuities based on deconvolution with a relaxation regularization (DDM) is compared with an essentially non‐oscillatory scheme (ENO) without further modelling and with a dynamic Smagorinsky subgrid‐scale model (DSM). For the DDM approach, a sufficiently accurate representation of the filtered non‐linear combination of discontinuous solution components which arise from the convection term is obtained by regularized deconvolution applied to the filtered solution. For stable integration the evolution equations are supplemented by a relaxation regularization based on a secondary filter operation and a relaxation parameter. We apply the above method to the generic test case of a two‐dimensional solenoidal velocity fluctuation field interacting with a normal shock. The results demonstrate a good agreement of DDM with a reference computation, while DDM significantly reduces computational cost. Predictions with DDM are found to provide a more accurate representation of the shock–vorticity–wave interaction phenomena than that which can be accomplished using the ENO scheme with or without subgrid‐scale model. Copyright © 2002 John Wiley & Sons, Ltd.