A second-order discretization of the nonlinear Poisson-Boltzmann equation over irregular geometries using non-graded adaptive Cartesian grids

  • Authors:

  • Mohammad Mirzadeh;Maxime Theillard;Frédéric Gibou

  • Affiliations:

  • Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106-5070, USA;Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106-5070, USA and Ecole Polytechnique, 91120 Palaiseau, France;Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106-5070, USA and Department of Computer Science, University of California, Santa Barbara, CA 93106, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

In this paper we present a finite difference scheme for the discretization of the nonlinear Poisson-Boltzmann (PB) equation over irregular domains that is second-order accurate. The interface is represented by a zero level set of a signed distance function using Octree data structure, allowing a natural and systematic approach to generate non-graded adaptive grids. Such a method guaranties computational efficiency by ensuring that the finest level of grid is located near the interface. The nonlinear PB equation is discretized using finite difference method and several numerical experiments are carried which indicate the second-order accuracy of method. Finally the method is used to study the supercapacitor behaviour of porous electrodes.