Rami Masri - Pressure correction discontinuous Galerkin methods for Navier-Stokes and Cahn-Hilliard-Navier-Stokes systems
We combine a pressure correction scheme with interior penalty discontinuous Galerkin (dG) discretisation to solve the time-dependent Navier–Stokes equations. We prove unconditional energy stability and a priori error estimates for the velocity. With duality arguments, optimal L2 error rates are obtained. Convergence of the discrete pressure is also established. Further, we propose a splitting scheme, integrating the pressure correction approach, for the Cahn–Hilliard–Navier–Stokes system The numerical analysis of dG combined with this scheme is discussed. Namely, we show well--posedness, stability, and error estimates. Numerical results with manufactured solutions display our theoretical findings, and a spinodal decomposition example portrays the robustness of our approach.
Published Nov. 14, 2023 7:07 PM
- Last modified Nov. 14, 2023 7:10 PM