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This error consists of a long wavelength noise in the downstream running wave families that is not effectively damped by the dissipation of the scheme.
γ and β are constants that control the accuracy and numerical dissipation of the scheme.
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Irreversible energy dissipation of the system.
Despite the efficiency and low dissipation of the stream-collide scheme of the discrete-velocity Boltzmann equation, which is nowadays implemented in many lattice Boltzmann solvers, a major drawback exists over alternative discretization schemes, i.e. finite-volume or finite-difference, that is the limitation to Cartesian uniform grids.
The derived hybrid central-WENO scheme is written as a combination of the central flux scheme and the numerical dissipation of the fifth order WENO scheme, which is controlled adaptively by a weighting function.
They also demonstrate that the upwinding inherent in the Godunov scheme, which provides dissipation of the appropriate form, stabilizes the FOS scheme.
The analysis demonstrates that the dissipation of AP schemes has to be properly controlled in the continuum flow regime through a delicate numerical treatment of collision and convection of the kinetic equation.
Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed.
to topics of a more numerical nature such as the spurious mixing and dissipation of advection schemes, and direct numerical simulations of surface waves at the air-sea interface.
The dissipation properties of the above schemes were then compared with existing flux formulations (local discontinuous Galerkin, Penalty and BR2).
The monotonicity of the scheme is achieved with the explicit adaptive dissipation.
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