Inexact Newton-Krylov for Fractional Step Method in Incompressible Flow Solver based on the Adaptive Mesh Refinement for Exascale (AMReX) Framework

We present a novel approach for simulating incompressible flows with moving boundaries. Our method uniquely combines staggered/non-staggered grid layouts with a projection method, storing fluxes at volume faces and pressure fields at volume centers. This hybrid approach allows flexible boundary condition prescription on moving bodies while maintaining exact incompressibility. A key innovation is our momentum equation solver, which employs an Inexact Newton method, offering improved convergence and efficiency over traditional iterative schemes such as the Runge-Kutta method. The Adaptive Mesh Refinement for Exascale (AMReX) framework continues to be integrated for leveraging fast linear solvers, extensibility to AMR, and parallelization in multi-GPU HPC clusters. The accuracy of our schemes has been validated through two standard 2D problems: (i) lid-driven cavity flow; and (ii) Taylor-Green vortex. The large-scale performance of our code is important in many problems in fluid-structure interaction of biological flows. Finally, our scaling tests are performed to benchmark performance improvements across various grid sizes and heterogeneous computing infrastructures. This work is supported by the NSF grant number 1946202 ND-ACES and a start-up package of Trung Le from North Dakota State University. The authors acknowledge the use of computational resources at the Center for Computationally Assisted Science and Technology CCAST-NDSU, which is supported by the NSF MRI 2019077.