Applied & Computational Mathematics seminar: Towards efficient and robust methods for immiscible incompressible multiphase flows with variable density

Speaker:  Loic Cappanera, University of Houston

Title:  Towards efficient and robust methods for immiscible incompressible multiphase flows with variable density

Abstract:   The development of numerical methods for incompressible multiphase flows is important for many applications in engineering and geophysics (e.g. aluminum production, mantle convection). We will present two methods that are suitable for spectral and high order finite element methods. Moreover, these methods use time-independent stiffness matrices so they can be assembled and preconditioned at initialization. The interface between the fluids is tracked using a level set techniques and the momentum, equals to the density times the velocity, is used as primary unknown. The main novelty of these methods lies on how the incompressibility condition of the flow is enforced. First, we present a projection-based method that leads to the resolution of a Poisson problem with constant coefficient. After establishing the stability and convergence properties of a semi-implicit version of the scheme, the fully explicit version is studied numerically on various setups using a pseudo-spectral code. Then, we present a method based on artificial compressibility techniques that only requires to solve a parabolic type problem. The robustness of both methods is compared on a two-phase setup similar to aluminum production cell where magnetohydrodynamics instabilities arises and leads to a tilting and rotating motion of the fluids' interface.

Time:  Friday, October 6, 2023 - 10:00am-11:00am

Place:  Exploratory Hall, Room 4106