非圧縮性粘性流れに対する射影法と圧力を含む境界条件

Abstract

We consider a projection method for time-dependent incompressible Navier—Stokes equations with pressure boundary conditions. The projection method is one of the numerical calculation methods for incompressible viscous fluids often used in engineering. In general, the projection method needs additional boundary conditions to solve a pressure-Poisson equation, which does not appear in the original Navier—Stokes problem. On the other hand, many mechanisms generate flow by creating a pressure difference, such as water distribution systems and blood circulation. Traction and open boundary conditions are often used to impose pressure boundary conditions. We review recent studies on these boundary conditions and propose a new additional boundary condition for the projection method with a Dirichlet-type pressure boundary condition and no tangent flow. We show stability for the scheme and error estimates for the velocity and pressure under suitable norms.