Semi-implicit Second Order Accurate Finite Volume Method for Advection-Diffusion Level Set Equation

We present a second order accurate finite volume method for level set equation describing the motion in normal direction with the speed depending on external properties and curvature. A convenient combination of a Crank-Nicolson type of the time discretization for diffusion term [1] and an Inflow Implicit and Outflow Explicit scheme [6] for advection term is used. Numerical experiments for an example with the exact solution derived in this paper and for examples motivated by modeling of fire propagation in forests are presented.