Ocean Dynamics

, Volume 62, Issue 8, pp 1201–1215 | Cite as

Adaptive volume penalization for ocean modeling

  • Shanon M. ReckingerEmail author
  • Oleg V. Vasilyev
  • Baylor Fox-Kemper
Part of the following topical collections:
  1. Topical Collection on Multi-scale modelling of coastal, shelf and global ocean dynamics


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.


Immersed boundary methods Shallow water equations Adaptive mesh refinement Wavelet collocation Complex geometry 



This work was supported by DOE-CCPP (DE-FG02-07ER64468). BFK was supported by NSF FRG 0855010. Also, thanks to Scott Reckinger.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Shanon M. Reckinger
    • 1
    Email author
  • Oleg V. Vasilyev
    • 2
  • Baylor Fox-Kemper
    • 3
  1. 1.School of Engineering, Department of Mechanical EngineeringFairfield UniversityFairfieldUSA
  2. 2.Department of Mechanical Engineering, UCB 427University of Colorado at BoulderBoulderUSA
  3. 3.Department of Cooperative Institute for Research in Environmental Sciences (CIRES), and Department of Atmospheric and Oceanic Sciences, UCB 216University of Colorado at BoulderBoulderUSA

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