Adaptive volume penalization for ocean modeling

Abstract

The development of various volume penalization techniques for use in modeling topographical features in the ocean is the focus of this paper. Due to the complicated geometry inherent in ocean boundaries, the stair-step representation used in the majority of current global ocean circulation models causes accuracy and numerical stability problems. Brinkman penalization is the basis for the methods developed here and is a numerical technique used to enforce no-slip boundary conditions through the addition of a term to the governing equations. The second aspect to this proposed approach is that all governing equations are solved on a nonuniform, adaptive grid through the use of the adaptive wavelet collocation method. This method solves the governing equations on temporally and spatially varying meshes, which allows higher effective resolution to be obtained with less computational cost. When penalization methods are coupled with the adaptive wavelet collocation method, the flow near the boundary can be well-resolved. It is especially useful for simulations of boundary currents and tsunamis, where flow near the boundary is important. This paper will give a thorough analysis of these methods applied to the shallow water equations, as well as some preliminary work applying these methods to volume penalization for bathymetry representation for use in either the nonhydrostatic or hydrostatic primitive equations.

Adaptive wavelet simulation of global ocean dynamics using a new Brinkman volume penalization

“…The Reckinger et al (2012) penalization also has the property that inertia-gravity wave speeds are 1/ √ α times faster in the porous medium. This introduces a stiffness in time associated with the small porosity α that enforces an artificially small time step.…”

“…In vector-invariant form, Reckinger et al (2012) proposed the following set of penalized shallow water equations with a flat bottom:…”

“…The shallow water penalization method we propose is a modification of the one proposed by Reckinger et al (2012) to ensure that mass and energy are conserved and that the wave speed is the same in both the solid and fluid parts of the domain. We also modify the velocity penalization (i.e.…”

“…Since its introduction, Brinkman penalization has been applied to a wide range of fluid flow problems and numerical schemes, including spectral methods (Kevlahan and Ghidaglia, 2001), moving boundaries (Kevlahan and Wadsley, 2005;Kolomenskiy and Schneider, 2009), the wave equation (Paccou et al, 2005), the compressible Euler equations (Liu and Vasilyev, 2007), and the shallow water equations (Perret et al, 2003;Reckinger et al, 2012). The shallow water penalization method we propose is a modification of the one proposed by Reckinger et al (2012) to ensure that mass and energy are conserved and that the wave speed is the same in both the solid and fluid parts of the domain.…”

Multiscale modeling of coastal, shelf, and global ocean dynamics

“…Examples are provided for the Aegean Sea, Indonesian Archipelago and Canadian Arctic Archipelago. Reckinger et al (2012) develop several adaptive volume penalization techniques to represent topographic effects in ocean models that use a stair-step representation of the geometry. Such stair-steps can cause accuracy and numerical stability problems.…”