Several numerical methods for the Navier-Stokes problem with Signorini's boundary condition (The State of the Art in Numerical Analysis : Theory, Methods, and Applications)

Abstract

We propose the outflow boundary condition of Signorini's type to ensure the energy inequality for the Navier-Stokes problem with an open outflow boundary. Since the Signorini's boundary condition involves the variational inequality, wc propose several efficient numerical schemes to obtain the stable discrete solutions, including the penalty method and Lagrange multiplier approach. To evaluate the appropriateness of this artificial boundary condition, we carry out the numerical simulations using our schemes, and compare the simulation results with the data from physical experiments.