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In this contribution we present the use of local one-dimensional boundary value problems (BVPs) to compute the interface velocities in the convective terms of the incompressible Navier-Stokes equations. This technique provides us with a better estimate for the interface velocities than linear interpolants.

Abstract. We present a flux approximation scheme for the incompressible NavierStokes equations, that is based on a flux approximation scheme for the scalar advection-diffusion-reaction equation that we developed earlier. The flux is computed from local boundary value problems (BVPs) and is expressed as a sum of a homogeneous and an inhomogeneous part. The homogeneous part depends on the balance of the convective and viscous forces and the inhomogeneous part depends on source terms included in the local BVP.

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We present a novel flux approximation scheme for the viscous Burgers equation. The numerical flux is computed from a local two-point boundary value problem for the stationary equation and requires the iterative solution of a nonlinear equation depending on the local boundary values and the viscosity. In the inviscid limit the scheme reduces to the Godunov numerical flux.