Boundary integral solutions of coupled Stokes and Darcy flows

  • Authors:

  • Svetlana Tlupova;Ricardo Cortez

  • Affiliations:

  • Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, 323 Dr. Martin Luther King, Jr. Boulevard, University Heights, Newark, NJ ...;Department of Mathematics, Tulane University, 6823 St. Charles Avenue, New Orleans, LA 70118, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

An accurate computational method based on the boundary integral formulation is presented for solving boundary value problems for Stokes and Darcy flows. The method also applies to problems where the equations are coupled across an interface through appropriate boundary conditions. The adopted technique consists of first reformulating the singular integrals for the fluid quantities as single and double layer potentials. Then the layer potentials are regularized and discretized using standard quadratures. As a final step, the leading term in the regularization error is eliminated in order to gain one more order of accuracy. The numerical examples demonstrate the increase of the convergence rate from first to second order and show a decrease in magnitude of the error. The coupled problems require the computation of the gradient of the Stokes velocity at the common interface. This boundary condition is also written as a combination of single and double layer potentials so that the same approach can be used to compute it accurately. Extensive numerical examples show the increased accuracy gained by the correction terms.