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We also validate the accuracy of the proposed method of moments by utilizing a known numerical moving grid discretization method as a reference.
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First, the mathematical model is numerically solved by the method of lines (MOL) using a space discretization with moving grid points (r-adaptivity).
A self-adaptive moving grid method is implemented for MOL discretization by means of finite-difference and finite-volume schemes.
Unlike previous approaches which bootstrap the moving grid from a lower-order, finite-difference discretization, this work uses a consistent spectral collocation discretization for both the grid movement problem and the underlying, physical partial differential equation.
Several examples are given, some of which include moving grids.
This permits very long time-steps on rapidly moving grids.
The coarse grid discretization is of spectral accuracy.
The numerical method consists in a finite volume staggered grid discretization of the governing equations.
Possible extension of these results to a real-space (grid) discretization is discussed.
Apart from the approximations of material dispersions and grid discretization, these calculation methods are exact.
This grid discretization represents a trade-off between the conflicting goals of achieving reasonable computing times (with a coarser grid) and preventing loss of relevant details (with a finer grid) while maintaining numerical stability (Fig. 3).
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