  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.
