Developing a second order accurate level-set method for solving the one-dimensional Stefan problem
C. Verburg (TU Delft - Applied Sciences)
Kees Vuik – Mentor (TU Delft - Numerical Analysis)
Danny Lathouwers – Mentor (TU Delft - RST/Reactor Physics and Nuclear Materials)
S. Kenjeres – Graduation committee member (TU Delft - ChemE/Transport Phenomena)
J.L.A. Dubbeldam – Mentor (TU Delft - Mathematical Physics)
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Abstract
This work aims at finding a second order accurate level-set method which solves the Stefan problem with non-homogeneous Dirichlet boundary conditions in one dimension. The numerical accuracy of the FTCS-scheme, BTCS-scheme and Crank-Nicolson scheme for the discretization of the heat equation was considered, as well as the accuracy of the first order Upwind method, Leapfrog method and the Lax-Wendroff method for the discretization of the advection equation. A level-set method was developed using a finite volume Crank-Nicolson scheme for the discretization of the moving boundary. A second order accurate scheme for solving the advection equation was developed using Lagrange extrapolation polynomials. The moving boundary velocity was estimated using second order Lagrange polynomials. The developed method was found to be second order accurate for a specific range of ratios between time step size and spatial step size.