Abstract:
For the three-dimensional Euler equations, a locally one-dimensional bicompact scheme having the fourth order of approximation in space and the second order of approximation in time is considered. The scheme is used in the Taylor–Green vortex problem in an inviscid perfect gas to examine the degree to which a conservative limiting (monotonization) method applied to bicompact schemes affects their theoretically high spectral resolution. Two parallel computational algorithms for locally one-dimensional bicompact schemes are proposed. One of them is used for carrying out computations. It is shown that, in the case of monotonization, the chosen bicompact scheme resolves 70–85% of the kinetic energy spectrum of the fluid. The scheme is compared with high-order accurate WENO$_5$ schemes in terms of the behavior of kinetic energy and enstrophy. It is demonstrated that the bicompact scheme has noticeably lower dissipation and more weakly suppresses medium-scale eddies.
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