The Roe-type Scheme in the Scalar Conservation Form

Details The Roe-type Scheme in the Scalar Conservation Form The Roe-type Scheme in the Scalar Conservation Form

2012-01-07

arxiv.org/abs/1201.1553v1

Physics

Computational Physics

Scientific paper

The Roe-type schemes are usually expressed as the vector forms. In this paper, three-dimension finite-volume scalar conservation forms of the Roe, preconditioned Roe, All-Speed Roe, Thornber's Roe and LM Roe schemes are deduced. The possible added NS-type equation is also considered such as the turbulence model. Such the scalar forms are very simple, easy for coding, low computational cost and valuable for theoretical analysis. Simultaneously, the conservation character makes the forms strictly equal to their vector forms, which was also validated by the numerical experiment. Thus, the scalar conservation forms of the Roe-type schemes will be very useful, and can replace the traditional vector forms without any hidden trouble.

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