A moving-mesh finite element method and its application to the numerical solution of phase-change problems

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Hubbard, M.E. ; Baines, Michael ; Jimack, P.K. ; Mahmood, R. (2009)
  • Publisher: Global Science Press

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a generalization of the original algorithm presented in Applied Numerical Mathematics, 54:450--469 (2005). Having described the details of the generalized algorithm it is validated on two test cases from the original paper and is then applied to one-phase and, for the first time, two-phase Stefan problems in one and two space dimensions, paying particular attention to the implementation of the interface boundary conditions. Results are presented to demonstrate the accuracy and the effectiveness of the method, including comparisons against analytical solutions where available.
  • References (4)

    [1] Baines MJ, Hubbard ME, Jimack PK. A moving mesh nite element algorithm for the adaptive solution of time-dependent partial di erential equations with moving boundaries. Appl Numer Math, to appear.

    [2] Baines MJ, Hubbard ME, Jimack PK. A moving mesh nite element algorithm for uid ow problems with moving boundaries. Int J Numer Meth Fl, to appear.

    [3] Baines MJ, Hubbard ME, Jimack PK, Jones AC. Scale-invariant moving nite elements for nonlinear partial di erential equations in two dimensions. Appl Numer Math, submitted.

    [4] Murray JD, Mathematical Biology: An Introduction (3rd edition), Springer (2002).

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