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Computer Physics Communications, Volume 184, Issue 6, June 2013, Pages 1547-1554
Haruhiko Kohno, Jean-Christophe Nave.
Plasma Science and Fusion Center, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.
The Department of Mathematics and Statistics, McGill University, 805 Sherbrooke W., Montreal, QC, H3A 2K6, Canada.
Abstract
We present a novel numerical method for solving the advection equation for a level set function. The new method uses hierarchical-gradient truncation and remapping (H-GTaR) of the original partial differential equation (PDE). Our strategy reduces the original PDE to a set of decoupled linear ordinary differential equations with constant coefficients. Additionally, we introduce a remapping strategy to periodically guarantee solution accuracy for a deformation problem. The proposed scheme yields nearly an exact solution for a rigid body motion with a smooth function that possesses vanishingly small higher derivatives and calculates the gradient of the advected function in a straightforward way. We will evaluate our method in one- and two-dimensional domains and present results to several classical benchmark problems.
