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The accuracy and the limits of validity of the discontinuous pressure model, which describes fluid flow inside a fracture using a subgrid scale approach, is assessed by comparing simulation results with those from direct simulation using Stokes flow. While the subgrid scale approach assumes a unidirectional flow, the Stokes model includes both velocity components. This is at the cost of meshing the interior of the fracture, which is here achieved through a spline-based mesh generation scheme. This scheme explicitly couples the spline representing the discontinuity to the fracture mesh and thereby alleviates the (re)meshing requirements for the interior of the fracture. The subgrid model and the direct simulation of Stokes flow approaches are compared by simulating a typical case containing a pressurised fracture, highlighting the advantages of using a subgrid model for the range in which its assumptions are valid, and showing its capabilities to accurately include the influence of the fracture on the porous material even outside this range. [ABSTRACT FROM AUTHOR]