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Partially implicit peer methods for the compressible Euler equations. (English) Zbl 1416.76178

Summary: When cut cells are used for the representation of orography in numerical weather prediction models this leads to very small cells. On one hand this results in very harsh time step restrictions for explicit methods due to the CFL criterion. On the other hand cut cells only appear in a small region of the domain. Therefore we consider a partially implicit method: In cut cells the Jacobian incorporates advection, diffusion and acoustics while in the full cells of the free atmosphere only the acoustic part is used, i.e. the method is linearly implicit in the cut cell regions and semi-explicit in the free regions and computes with time step sizes restricted only by the CFL condition in the free atmosphere. Furthermore we use a simplified Jacobian in the cut cell regions in order to save storage and gain computational efficiency. While the method retains the order independently of the Jacobian we present a linear stability theory which takes the effects of the simplifications of the Jacobian on stability into account. The presented method is as stable and accurate as the underlying split-explicit method but furthermore it can compute with cut cells with nearly no additional effort.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76N99 Compressible fluids and gas dynamics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs

Software:

ROS3P
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Full Text: DOI

References:

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