Project R-9426

PhaseFlow: Efficient numerical solver for the Cahn-Hilliard/Navier-Stokes system (Research)

In this project, we develop efficient mathematical algorithms for the simulation of flows involving two different substances. These flows occur in a variety of applications and a typical example could be the mixture of fuel with air in the engine of a car. Also, the process of carbon sequestration to capture carbon dioxide in the subsurface involves the flow of two substances as the gas is injected into the ground thereby coming into contact with water. Having an efficient algorithm to simulate these flows at one's disposal is of extreme interest to the practitioner, because it allows for making predictions of reality without having to rely on costly, possibly non-conclusive and potentially dangerous experiments. One way of theoretically describing the considered flows is via so-called phase-field approaches. Mathematically speaking, this leads to the coupling of two well-known equations, namely the Cahn- Hilliard equation for the interplay between the two substances, and the Navier-Stokes equation describing the flow. Based on recent results, we propose a numerical method for the coupling of these two equations and apply appropriate measures to analyze the method and to increase its efficiency. Upon completion of the project, we will have a method at our disposal that can be used for engineering applications.

01 January 2019 - 31 December 2022