Marker ReDistancing/Level Set Method for High-Fidelity Implicit Interface Tracking
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 PDE-based re-distancing. We have demonstrated that the method is 3rd-order accurate in space, near the markers, and therefore 1st-order convergent in curvature; in contrast to traditional PDE-based re-initialization algorithms, which tend to slightly relocate the zero Level Set and can be shown to be non-convergent in curvature. The implicit pseudo-time discretization of the re-distancing equation is implemented within the Jacobian-Free Newton Krylov (JFNK) framework combined with ILU(k) preconditioning. We have demonstrated that the steady-state solutions in pseudo-time can be achieved very efficiently, with iterations (CFL ), in contrast to the explicit re-distancing which requires 100s of iterations with CFL . The most cost-effective algorithm is found to be a hybrid of explicit and implicit discretizations, in which we apply first 10-15 iterations with explicit discretization (to bring the initial guess to the ball of convergence for the Newton’s method) and then finishing with 2-3 implicit steps, bringing the re-distancing equation to a complete steady-state. The eigenscopy of the JFNK-ILU(k) demonstrates the efficiency of the ILU(k) preconditioner, which effectively cluster eigenvalues of the otherwise extremely ill-conditioned Jacobian matrices, thereby enabling the Krylov (GMRES) method to converge with iterations, with only a few levels of ILU fill-ins. Importantly, due to the Level Set localization, the bandwidth of the Jacobian matrix is nearly constant, and the ILU preconditioning scales as , which implies efficiency and good scalability of the overall algorithm. The numerical examples include the well-established tests for interface kinematics under translational, rotational and tearing/stretching motion. We have shown that the mass conservation is not an issue anymore, as demonstrated using the Rider&Kothe’s time-reversed tests with extreme deformation. We are able to stretch interface structures to the under-resolved/subgrid (on the chosen Eulerian mesh) scales, and recover them back without any change in shape/loss of mass.
- Research Organization:
- Idaho National Lab. (INL), Idaho Falls, ID (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- DE-AC07-05ID14517
- OSTI ID:
- 974429
- Report Number(s):
- INL/JOU-08-14433; SJOCE3; TRN: US201007%%707
- Journal Information:
- SIAM Journal on Scientific Computing, Vol. 32, Issue 1; ISSN 1064-8275
- Country of Publication:
- United States
- Language:
- English
Similar Records
Enhanced nonlinear iterative techniques applied to a nonequilibrium plasma flow
A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems