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We find that, in the moving boundary case, the use of Crank Nicolson time discretization is unstable, requiring us to use the L0-stable implicit Runge Kutta method of Twizell, Gumel, and Arigu (1996, Adv. Comput. Math.6, 333).
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The present numerical approach provides simplicity, computational efficiency and accuracy for solving moving boundary cases.
Predictions are compared with available experimental and numerical data for several fixed and moving boundary cases.
To justify the proposed method, a series of test cases, including fixed boundary cases and moving boundary cases, are invested.
At last, the applied numerical method is validated by stationary and moving boundary cases and an excellent agreement is obtained with good accuracy, efficiency and conservation.
The interpolation-free models are then applied to the case of moving boundary problems in which a square block and a cylindrical block, respectively, move with a constant speed along a channel containing stationary flows.
The third example presents the case of a moving boundary condition problem which models a cable entangled by fishing boat-trawling equipment.
The moving boundary effect can help prevent the case wherein a certain UE is located at the edge of the cell during the whole transmission time.
Most numerical methods developed for moving boundary or Stefan problems deal with the case of a single moving boundary (MB) separating two different media.
In the present work, moving boundary diffusion problems have been simulated for two cases.
Carin, M. Numerical Simulation of Moving Boundary Problems with the ALE Method: Validation in the Case of a Free Surface and a Moving Solidification Front.
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