Semi-implicit second order schemes for numerical solution of level set advection equation on Cartesian grids
arXiv:1803.05332 · doi:10.1016/j.amc.2018.01.065
The paper introduces a class of semi‑implicit numerical schemes for solving the level set advection equation on Cartesian grids, providing second‑order accuracy in space and time generally and third‑order accuracy for constant velocity, with unconditional stability demonstrated via von Neumann analysis.
Abstract
A new parametric class of semi-implicit numerical schemes for a level set advection equation on Cartesian grids is derived and analyzed. An accuracy and a stability study is provided for a linear advection equation with a variable velocity using partial Lax-Wendroff procedure and numerical von Neumann stability analysis. The obtained semi-implicit kappa-scheme is 2nd order accurate in space and time in any dimensional case when using a dimension by dimension extension of the one-dimensional scheme that is not the case for analogous fully explicit or fully implicit kappa-schemes. A further improvement is obtained by using so-called Corner Transport Upwind extension in two-dimensional case. The extended semi-implicit kappa-scheme with a specific (velocity dependent) value of kappa is 3rd order accurate in space and time for a constant advection velocity, and it is unconditional stable according to the numerical von Neumann stability analysis for the linear advection equation in general.
arXiv admin note: substantial text overlap with arXiv:1611.04153 Comment from the authors - this is a corrected paper where typesetting error in formula (37) is removed