Unified conservative numerical framework for interfacial flows of incompressible and compressible fluids at all speeds

• Applicant: Professor Dr. Berend van Wachem
• Subject Area: Fluid Mechanics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 452036112

When considering the simulation of the fluid dynamics of flows with interfaces, the majority of numerical methods that have been developed so far are either for compressible fluids or for incompressible fluids, limiting their performance and limiting the range of systems and applications that can be researched. In addition, open questions relating to the conservation of mass, momentum and energy of numerical schemes applied to interfacial flows at all flow speeds further complicate the application of contemporary numerical algorithms for research and product development, in areas ranging from fuel injection in aircraft engines to shock wave lithotripsy for the treatment of kidney stones. The primary objective of this project is the development of a new unified numerical framework to enable, for the first time, the simulation of interfacial flows at all speeds, with Mach numbers ranging from M=0 to M >> 1, including interfacial flows in which compressible and incompressible fluids directly interact with each other, with the same conservative discretization.The proposed research will focus on key algorithmic aspects, novel numerical schemes and the conservation errors, closing important current gaps in the literature with respect the conservation mass, momentum and energy of interfacial flows, also in the presence of surface tension, and the definition of thermodynamic properties in compressible incompressible interfacial flows. Furthermore, a systematic study of the influence and importance of the compressibility of liquids for the simulation of interfacial flows and a comprehensive assessment of the performance of the new algorithm will be conducted. Finally, verification and validation of the newly developed methods will be an important aspect of the proposed project.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr. Fabian Denner