MARKER REDISTANCING/LEVEL SET METHOD FOR HIGH-FIDELITY IMPLICIT INTERFACE TRACKING


Nourgaliev R., Kadioglu S. Y. , Mousseau V.

SIAM JOURNAL ON SCIENTIFIC COMPUTING, vol.32, no.1, pp.320-348, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 1
  • Publication Date: 2010
  • Doi Number: 10.1137/080727439
  • Title of Journal : SIAM JOURNAL ON SCIENTIFIC COMPUTING
  • Page Numbers: pp.320-348

Abstract

A hybrid of the front tracking (FT) and the level set (LS) methods is introduced, combining advantages and removing drawbacks of both methods. The kinematics of the interface is treated in a Lagrangian (FT) manner, by tracking markers placed at the interface. The markers are not connected-instead, the interface topology is resolved in an Eulerian (LS) framework, by wrapping a signed distance function around Lagrangian markers each time the markers move. For accuracy and efficiency, we have developed a high-order "anchoring" algorithm and an implicit PDEbased redistancing. We have demonstrated that the method is 3rd-order accurate in space, near the markers, and therefore 1st-order convergent in curvature; this is in contrast to traditional PDE-based reinitialization algorithms, which tend to slightly relocate the zero level set and can be shown to be nonconvergent in curvature. The implicit pseudo-time discretization of the redistancing equation is implemented within the Jacobian-free Newton-Krylov (JFNK) framework combined with ILU(k) preconditioning. Due to the LS localization, the bandwidth of the Jacobian matrix is nearly constant, and the ILU preconditioning scales as similar to N log(root N) in two dimensions, which implies efficiency and good scalability of the overall algorithm. We have demonstrated that the steady-state solutions in pseudo-time can be achieved very efficiently, with approximate to 10 iterations (CFL approximate to 10(4)), in contrast to the explicit redistancing which requires hundreds of iterations with CFL <= 1.