Journal
INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS
Volume 27, Issue 4-5, Pages 210-227Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/10618562.2013.813491
Keywords
fluctuation splitting; residual distribution; compressible flows; unsteady flows; mass matrix; low Mach number; linearisation; parameter vector
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A mass-matrix formulation of the fluctuation splitting schemes for solving compressible, unsteady flows is proposed. This formulation is consistent with the conservative linearisation based on parameter vector and allows to extend to unsteady flows the invariance under similarity transformations' property that had been shown to hold for the steady version of the schemes. Second-order time accuracy is achieved using a Petrov-Galerkin finite element interpretation of the fluctuation splitting schemes. The approach may however be readily applicable to all other time-accurate fluctuation splitting formulations that have been so far proposed in the literature. Applications of the proposed methodology to two- and three-dimensional, inviscid and viscous compressible flows are reported and discussed in the paper.
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