An Embedded Boundary Adaptive Mesh Refinement Method for Highly Nonlinear Internal Waves

Michael Barad, University of California, Davis

I will present our block-structured adaptive mesh refinement (AMR) computational fluid dynamics model and its application to the study of highly nonlinear environmental flows. AMR allows researchers to &#lsquo;zoom in&#rsquo; on important flow features by dynamically tracking them with recursively nested finer grids. For example, this permits the simulation of oceanic internal wave generation at the meter scale, propagation and interaction over hundreds of kilometers, and subsequent dissipation at the meter scale, all in the same calculation.

The model is based on the solution of the variable density, incompressible, Navier-Stokes equations in two or three dimensions, including air/water and fluid/solid interfaces and the transport of scalars. The model uses a second-order accurate nonhydrostatic, non-Boussinesq, projection method with high-order accurate Godunov finite differencing including slope limiting. 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. We discretize irregular domains as a collection of control volumes formed by the intersection of the domain with Cartesian grid cells. The control volumes naturally fit within disjoint block data structures, and permit dynamic AMR coarsening and refinement of arbitrarily complex domains as a simulation progresses. 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.

Abstract Author(s): Michael Barad