A New Level-Set Model for the Representation of Non-Smooth Geometries

Semi-implicit second order schemes for numerical solution of level set advection equation on Cartesian grids

“…If C ij < 0 then the value U n+1 i+1j is required by (40). In this case the solution shall be given at the boundary node (x i+γ , y j ), namely u(x i+γ , y j , t n+1 ) = u D (x i+γ , y j , t n+1 ), where the function u D is given.…”

“…We consider two typical initial level set functions -the first one representing implicitly a smooth interface (e.g. a circle [33,12,36,22,46,38,40]), and the second one representing a piecewise smooth interface [37,33,12,36,40] (e.g. a square).…”

“…the distance function in the maximum metric. It can be viewed as an example of the level set function representing a squared interface [37,33,12,36,40] (i.e. a piecewise smooth interface in this case).…”

“…In the last section on numerical experiments we present two standard benchmark examples for the tracking of moving interfaces -the rotation of Zalesak's disc [37,12,19,21,22,46,38,40] and the single vortex example [37,33,12,19,21,22,46,38,40] Note that in a standard setting of these examples there is no need to use a implicit or a semi-implicit scheme, nevertheless we compute these benchmark examples to show a satisfactory accuracy of the proposed semi-implicit κ-scheme.…”

“…Furthermore, if C ij > 0 then the value U n i+1j is required by (40). This situation corresponds to the outflow boundary, when we apply the standard linear extrapolation [26,14,13] to use the substitution…”