Geodesic
Development of unstructed code for rotating zones based on the CABARET method with improved spectral properties
Matematičeskoe modelirovanie, Tome 34 (2022) no. 7, pp. 73-92

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In this study we develop modification of the high-resolution CABARET scheme for rotating meshes surrounded by an external fixed zone. CABARET is second-order in space and time conservative/characteristic scheme with compact stencil which has lowdissipative and low-dispersive properties and is non-oscillatory for calculations involving non-linear flow problems with a wide range of frequencies in computational aeroacoustics. To expand this method for rotor-stator interaction problem, an approximation of non-inertial terms in rotating zones for conservative steps is added, and appropriate modification of characteristic step on the sliding interface is developed. An evolutionary approach, which ensures the preservation of the fluxes of conservative variables through the contact surface is implemented. The dispersion-improved version of the scheme with an added anti-dispersion term expressed via a flux derivative is added as well as a modification of the non-linear flux correction algorithm with reduced dissipation. For testing, the problem of acoustic wave propagation through rotating zones and sliding interfaces is considered. It is shown that the developed CABARET method for rotating zones retains the main characteristics of the baseline CABARET algorithm on fixed meshes.
Keywords: CABARET conservative scheme, non-inertial terms, sliding interface. 
@article{MM_2022_34_7_a5,
     author = {I. A. Solntsev and S. A. Karabasov},
     title = {Development of unstructed code for rotating zones based on the {CABARET} method with improved spectral properties},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {73--92},
     publisher = {mathdoc},
     volume = {34},
     number = {7},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2022_34_7_a5/}
}
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I. A. Solntsev; S. A. Karabasov. Development of unstructed code for rotating zones based on the CABARET method with improved spectral properties. Matematičeskoe modelirovanie, Tome 34 (2022) no. 7, pp. 73-92. http://geodesic.mathdoc.fr/item/MM_2022_34_7_a5/