LEAPS-MPS: Robust and High Order Numerical Simulation for Phase Field Modeling

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This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).The phase-field method is an established theoretical approach used to study the interfacial dynamics of the mixture of different fluids, solids, and gas. This project will investigate an efficient numerical framework for its numerical simulation. The algorithms developed will be applicable to a large class of physical problems, and thus will contribute to the understanding of fundamental mechanisms in materials science, biology, and other related fields. The project will also provide training and outreach opportunities to K-12 students, undergraduates, and graduate students, with a focus in mathematical modeling, numerical analysis, and engineering applications, and special attention to promoting the participation of members of groups underrepresented in STEM. This project is devoted to designing, analyzing, and implementing a fully discrete numerical framework for phase-field models in high dimensional spaces and arbitrary computational geometries. Under the scalar auxiliary variable framework, high order symplectic Runge-Kutta methods will be carefully constructed and studied to ensure energy stability. To efficiently capture the sharp gradient and easily handle the complex boundary conditions, the discontinuous Galerkin (DG) method will be employed as the spatial discretization technique. Investigation and comparison of high dimensional computational efficiency between classical modal DG and multiresolution DG methods will be carried out.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.