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This is because that the simulation of a gas-solid flow with a moving boundary requires an extremely complex algorithm.
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As the investigation involves three-dimensional computational fluid dynamics (CFD) simulation with moving boundary requiring significant computing resources, it was executed on a Silicon Graphics (SGI) Supercomputer using parallel processing technique.
But some additional conditions on the moving boundary were required, which render the method used in [1] and [3] inapplicable to the controllability problems of (1.2).
But some additional conditions on the moving boundary were required, which entail the method used in [1] and [3] not to be applicable to the controllability problems of (1.2).
The nature of the two-material problem is such that shocks and expansion waves can develop at this interface and thus special numerical treatment of the moving boundary is required; this is achieved by using a lower order approximation in this localised region.
To estimate the interfacial velocity in a multicomponent moving boundary problem, existing procedures require an interative technique to be used if a sharp interface method is employed.
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).
We need not transform the moving boundary into a fixed boundary as in prior research.
This algorithm requires the hyperbolic conservation law to be solved on a moving mesh since the interface between the materials is numerically treated as a moving boundary.
Some benefits of adopting moving boundary method are illustrated by comparing with the fixed boundary method.
A moving boundary method is used to describe the movement of boundaries across these regions.
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