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A Numerical Framework for Wall Dissolution Modeling

Analysis of Flute Formation

Abstract

Scallops and flutes are common dissolution rock forms encountered in karst caves and surface streams. Their evolution is only partially understood and no numerical model that simulates their formation has been presented. This work at least partially fills the gap by introducing a numerical approach to simulate the evolution of different initial forms of soluble surfaces embedded in a turbulent fluid. The aim is to analyze wall dissolution phenomena from basic principles and to identify stable profiles. The analysis is based on a finite volume moving boundary method. The underlying mathematical model is a \(k-\epsilon \) turbulent model for fluid flow coupled with turbulent scalar transport. The rock wall is treated as a moving boundary, where the normal wall retreat velocity is proportional to the under-saturation of the boundary fluid cells with respect to the mineral comprising the wall. As the flow time scale is several orders of magnitude smaller than the dissolution time scale, stationary flow field, concentration field and wall propagation velocity are calculated for each iteration. The boundary at all points is then moved by distracting minimal velocity along the entire boundary from the actual velocity at a certain location, and then normalized to the maximum allowed shift, which is equal to half the height of the boundary cell. In this way only deformation of the initial wall is calculated. The method was applied to several different initial profiles. During the evolution, the profiles progressively converged towards stable forms. In this work, a framework is proposed for a computation of the moving boundary problem related to slow dissolution of a soluble surface.

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Acknowledgments

This research has been supported by the Grant J2-4093 of Slovenian Research Agency (ARRS).

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Correspondence to Aleksander Grm.

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Grm, A., Šuštar, T., Rodič, T. et al. A Numerical Framework for Wall Dissolution Modeling. Math Geosci 49, 657–675 (2017). https://doi.org/10.1007/s11004-016-9641-2

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  • DOI: https://doi.org/10.1007/s11004-016-9641-2

Keywords

  • Moving boundary problem
  • Quasi-stationary turbulent flow and turbulent transport
  • Finite volume
  • Soluble surface