A new mixed potential representation for the equations of unsteady, incompressible flow
This work provides a novel numerical method for solving unsteady incompressible flow problems, offering high-order accuracy and well-conditioned equations for boundary integral formulations.
The paper introduces a new integral representation for unsteady, incompressible Stokes and Navier-Stokes equations, leading to a well-conditioned coupled system of integral equations that enables high-order accurate solvers when combined with spectral deferred correction.
We present a new integral representation for the unsteady, incompressible Stokes or Navier-Stokes equations, based on a linear combination of heat and harmonic potentials. For velocity boundary conditions, this leads to a coupled system of integral equations: one for the normal component of velocity and one for the tangential components. Each individual equation is well-condtioned, and we show that using them in predictor-corrector fashion, combined with spectral deferred correction, leads to high-order accuracy solvers. The fundamental unknowns in the mixed potential representation are densities supported on the boundary of the domain. We refer to one as the vortex source, the other as the pressure source and the coupled system as the combined source integral equation.