This presents the idea of xfem for 1d stefan problem

1. Simulation of 1-d Stefan Problem using XFEM V. S. S. Srinivas

3. Stefan problem T=T 0 0 °C Initial Temperature = 0°C h(t) Governing equations Initial and boundary conditions

4. Analytical solution Solve the transcendental equation, get Transcendental equation: Temperature profile: Interface position:

7. Enriched shape function Level set function in 1d: Interface position: x b , Element length: l e =1 X b =0.5 X b =0.3

8. Contd.. X b =0.5 X b =0.3

13. A peep into the matrices Governing equation after applying weighted residuals Discretized equation: Unsymmetric Symmetric

14. Validation: Numerical against Analytical

15. Convergence check

16. T versus x at different times

22. Thank you