Vortex methods were initially conceived as a tool to simulate the inviscid dynamics of vortical flows. The vorticity carried by the fluid elements is conserved in inviscid flows and simulating the flow amounts to the computation of the velocity field. In bounded domains the velocity field is constrained by the conditions imposed by the type and the motions of the boundaries. For an inviscid flow, it is not possible to enforce boundary conditions for all three velocity components as we have lost the highest-order viscous term from the set of governing Navier–Stokes equations. Usually for inviscid flows past solid bodies we impose conditions on the velocity component locally normal to the boundary.

The description of an inviscid flow can be facilitated when the velocity field is decomposed into two components that have a kinematic significance. In this decomposition, a rotational component accounts for the velocity field due to the vorticity in the flow whereas a potential component is used in order to enforce the boundary conditions and to ensure the compatibility of the velocity and the vorticity field in the presence of boundaries. This is the well-known Helmholtz decomposition.

Alternatively the evolution of the inviscid flow can be described in terms of an extended vorticity field. The enforcement of a boundary condition for the velocity components normal to the boundary does not constrain the wall-parallel velocity components. This allows for velocity discontinuities across the interface that may be viewed as velocity gradients over an infinitesimal region across the boundary.