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We present two new algorithms for maintaining high-resolution and sharp computational boundaries in computations of these types of problems: a discontinuous Galerkin method with a bound preserving limiter and a Volume-of-Fluid interface tracking algorithm.
The key idea is to derive approximate boundary values or normal derivatives on computational boundaries, with second-order accuracy, by using the prescribed boundary condition.
They are used to absorb and minimize reflections from computational boundaries and as forcing sponges to introduce prescribed disturbances into a calculation.
According to the classical theory, these terms play an important role to damp and minimize the acoustic wave reflections from computational boundaries.
These methods have very low dispersion errors and require precise boundary conditions to avoid numerical instabilities and to control spurious wave reflections at the computational boundaries.
The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries.
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Then we display the implementation of this method, while the computational boundary is complex and less boundary points need to be handled.
However, unlike other methods based on the Godunov numerical Hamiltonian, some computational boundary conditions are needed in the implementation.
Furthermore, it can be applied to any type of computational boundary, either inflow or outflow, either subsonic or supersonic.
The nonlocal Dirichlet-to-Neumann (DtN) map is used as a nonreflecting condition on the outer computational boundary.
Suppose that the medium consists of homogeneous layers separated by parallel horizontal interfaces, and suppose that absorbing boundary conditions are needed along a vertical computational boundary.
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