An Embedded Boundary Adaptive Mesh Refinement Method for Environmental Flows

Michael Barad, University of California, Davis

I will present our block-structured adaptive mesh refinement (AMR) computational fluid dynamics model. The model is based on the solution of the unsteady, variable density, incompressible, Navier-Stokes equations in two or three dimensions, including air/water and fluid/solid interfaces and the transport of scalars. The methodology is based on a second-order accurate projection method with high-order accurate Godunov finite differencing including slope limiting and a stable differencing of the nonlinear convection terms.

This is a proven methodology for hyperbolic problems that yields accurate transport with low phase error while minimizing the numerical diffusion at steep gradients typically found in ~classical~ high order finite difference methods.

This methodology is combined with finite volume AMR discretizations based on flux matching at refinement boundaries to obtain a conservative method that is second-order accurate in solution error for environmental flows.

The control volumes are formed by the intersection of the irregular embedded boundary with Cartesian grid cells. Unlike typical discretization methods, these control volumes naturally fit within easily parallelized disjoint block data structures, and permit dynamic AMR coarsening and refinement as a simulation progresses.

AMR allows the simulation of a range of spatial and temporal scales. Capturing these ranges is critical to accurately modeling multi-scale transport complexities such as boundaries, fronts, and mixing zones that exist in natural environments.

Abstract Author(s): Michael Barad