Abstract
Flux-based level set method is a finite volume method for the numerical solution of advective level set equation which describes the transport of level lines by an external velocity field and by a speed in normal direction. The method is introduced for rectangular grids without using any dimensional splitting. The second order accurate discretization scheme is derived with one free parameter in the definition of piecewise linear reconstruction. A significant improvement of the accuracy can be obtained by special choices of this parameter for two benchmark examples of linear conservation laws. Moreover, the flux-based level set method can be used for computation of first arrival time functions in the class of problems such as “boat sailing” or “fire spread” where some external velocity field (e.g., a water or wind flow) must be considered additionally to the speed of boat or fire. Numerical experiments confirm very good performance of the method for this type of problems.
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