We present a new formulation of the incompressible Navier-Stokes equation in terms of an auxiliary field that differs from the velocity by a gauge transformation. The gauge freedom allows us to assign simple and specific boundary conditions for both the auxiliary field and the gauge field, thus eliminating the issue of pressure boundary condition in the usual primitive variable formulation. The...

In this paper, we propose a new paradigm for solving Navier–Stokes equations. The proposed methodology is based on a streamfunction–velocity formulation of the two-dimensional steady-state Navier–Stokes equations representing incompressible fluid flows in two-dimensional domains. Similar formulations are also possible for three-dimensional fluid flows. The main advantage of our formulation is t...

A new multicomponent formulation, appropriate for use with the finite-volume method, has been developed to describe mass diffusion velocities accurately. The new formulation is applied in a quasi-steady numerical model for n-heptane fuel droplet combustion in a forced-convection environment. Results obtained using the complete formulation are compared to the results obtained under various assum...

We present a rigorous numerical analysis and computational tests for the Galerkin finite element discretization of the velocity-vorticity-helicity formulation of the equilibrium Navier-Stokes equations (NSE). This formulation was recently derived by the authors, is the first NSE formulation that directly solves for helicity, the first velocityvorticity formulation to naturally enforce incompres...

In this paper we consider the steady water wave problem for waves that possess a merely Lr−integrable vorticity, with r ∈ (1,∞) being arbitrary. We rst establish the equivalence of the three formulations the velocity formulation, the stream function formulation, and the height function formulation in the setting of strong solutions, regardless of the value of r. Based upon this result and using...

The classical formulation of the coupled hydroelectrical flow in porous media is based on a linear formulation of two coupled constitutive equations for the electrical current density and the seepage velocity of the water phase and obeying Onsager’s reciprocity. This formulation shows that the streaming current density is controlled by the gradient of the fluid pressure of the water phase and a...