A hybrid staggered/non-staggered formulation for simulating incompressible flows with block-structured mesh refinement

We present a novel approach for simulating incompressible flows with local mesh refinement. In many biological problems such as simulations of cells, it is highly desirable to accommodate high-resolution regions near the surface of moving bodies in flows. In this work, we present a new approach for local mesh refinement with the dual use of staggered and non-staggered grid layouts. Our finite volume solver for incompressible flows is based on a fractional step method. The fluxes are stored at the surface centers whereas the pressure field and the Cartesian velocity components are at the volume centers. This hybrid staggered – non-staggered approach allows the flexibility of prescribing the boundary conditions on the moving bodies while satisfying the incompressibility constraint exactly. We use the Adaptive Mesh Refinement for Exascale (AMReX) framework for designing our grid infrastructure. The momentum equation is solved iteratively with an implicit Runge-Kutta method. The native Poisson solver of AMReX is utilized for the projection step. Our preliminary work includes two benchmark simulations: (a) lid-driven flow; and (b) Taylor-Green Vortex to demonstrate the feasibility of our approach. We will report on the efficiency and scalability of this approach for different grid sizes in different heterogenous computing infrastructures.