Multiscale finite element methods were introduced to solve stationary (elliptic) or quasi-stationary (parabolic) equations involving subgrid-scale features (see [1]). This method was extended by a Lagrangian ap- proach to be applicable for hyperbolic transport-dominated equations in [2]. Further refinement of the method for multi-dimensional and arbitrary flow simulations was introduces in [3]. This latter method is based on a semi-Lagrangian subgrid reconstruction (SLMsR) algorithm. The idea of the method is simple: By augmenting the finite element basis function with subgrid infor- mation, maintaining its main property of element compatibility, a coarse scale finite element problem is informed with subgrid information. Interestingly, the subgrid information alters the solution of transport- dominated equations, because – as an example – small-scale riding waves may change the phase speed of their large-scale hosting waves. In this presentation we extend the SLMsR method to nonlinear systems of equations [4]. A Saint- V enant system is computed on two widely differing meshes, a fine-scale momentum equation and a coarse-scale continuity equation. To demonstrate the ability of SLMsR to inform the coarse equation of subgrid features, a (discontinuous) dam break problem is solved. By comparing the solution to a fine-grid reference accuracy and convergence can be demonstrated.