Time-splitting framework for Godunov-type finite- volume non-hydrostatic atmospheric models
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چکیده
Highorder extensions of the classical Godunov scheme offer computationally attractive features including inherent conservation, geometric flexibility, and accuracy for solving hyperbolic conservation laws. The Godunov-type methods typically do not rely on staggered grids, and the cellaveraged solution is not assumed to be continuous across the cell (control volume) edges. The discontinuity of the fluxes at the cell interface is resolved by a Riemann solver (numerical flux). We consider an upwindbased Godunov-type FV method for solving nonhydrostatic (NH) atmospheric flows (fully compressible Euler system of equations) on a rectangular 2D (x, z)-domain. The fluxes at the cell interface are reconstructed by the fifth-order accurate Piecewise Quartic Method (PQM), in a dimension-split manner. The AUSM+-up numerical flux is used for the FV model, which is particularly effective for low Mach number problems such as the NH atmospheric modeling.
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