Dr. Lili Ju received a research grant from the NSF Division of Mathematical Sciences (DMS-2409634) on “Structure-Preserving Linear Schemes for the Diffuse-Interface Models of Incompressible Two-Phase Flows with Matched Densities". The total amount of the award is $294,473 for the period of three years from August 1, 2024 to July 31, 2027.

As a fundamental example of multi-phase flows, two-phase flows are frequently encountered in natural and industrial processes, such as the mixing of the fresh water and seawater at the estuaries in marine science, the oil and gas transportation in the petroleum industry, the solidification of binary alloys in materials science and so on. The interfaces between the two immiscible fluids play a crucial role in these phenomena, and the diffusive-interface approach have been widely used for their modeling due to its significant advantages in handling topological changes and easiness of implementation. These two-phase flow systems also often possess some crucial physical structures, such as energy stability, bound preservation, and mass conservation. Preservation of these structures is not only a desirable attribute of numerical schemes for their high-fidelity simulations in scientific and engineering applications but also plays a pivotal role in stability and error analysis of the numerical schemes. The primary goal of the project is to develop and analyze efficient, robust, and accurate structure-preserving linear schemes for simulating diffuse-interface models of incompressible two-phase flows with matched densities.  The project involves diverse research work in computational and applied mathematics, ranging from algorithm design, numerical analysis, to computer implementation. 

Congratulations Dr Ju!