Consistent Semi-Lagrangian Method for Accurate Simulations of Gas-Liquid Flows in Complex Geometries

About This Grant

Gas-liquid flows occur in many natural processes and engineered devices, including breaking waves, painting, fuel injection, and fire suppression. Understanding these processes and improving device design require accurate predictions of these flows. A leading numerical method for simulating gas-liquid flows is called the volume-of-fluid (VoF) method. This project will reformulate the VoF method to improve its accuracy and reduce computational costs. The reformulation will also eliminate the need for correction factors in the method and improve its performance near solid boundaries. The project will create a hands-on laboratory for undergraduate students in numerical methods courses. The research team will help high-school teachers acquaint students with computational fluid dynamics and inspire them to pursue STEM careers through the Montana GEAR-Up program. The project will improve software used in many technological areas such as energy conversion systems and advanced manufacturing. This project will modify the discretization of the Navier-Stokes equations applied to gas-liquid flows to address two major flaws with the geometric VoF method. The first flaw is that to achieve exact conservation, flux corrections have been added to the transport scheme, decreasing the accuracy of the method and increasing computational cost. The second flaw is that the geometric volume-of-fluid scheme has not been formulated to work well near solid boundaries. Removing these flaws by fundamentally changing the discretization of the Navier-Stokes equations using a semi-Lagrangian formulation will elevate the numerical methods and provide a tool that will dramatically enhance capabilities for simulating and engineering gas-liquid flows in complex geometries. The project will address core limitations in existing numerical approaches and will advance computational fluid dynamics for multiphase flows by providing new tools for studying and engineering gas–liquid systems. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.