2017
DOI: 10.1088/1757-899x/243/1/012007
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Comparative study of Roe, RHLL and Rusanov fluxes for shock-capturing schemes

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Cited by 5 publications
(5 citation statements)
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“…The standard semi-discrete conservative formulation of the Euler equations is given by where is the vector of the conserved quantities as stated in Equation (15). The numerical flux of the conserved gas-dynamic quantities here chosen is the one proposed by Rusanov [ 44 ] with piecewise linear reconstruction (TVD—Van Albada’s slope limiter [ 32 ]) at the volume boundaries: where and …”
Section: Numerical Methodsmentioning
confidence: 99%
“…The standard semi-discrete conservative formulation of the Euler equations is given by where is the vector of the conserved quantities as stated in Equation (15). The numerical flux of the conserved gas-dynamic quantities here chosen is the one proposed by Rusanov [ 44 ] with piecewise linear reconstruction (TVD—Van Albada’s slope limiter [ 32 ]) at the volume boundaries: where and …”
Section: Numerical Methodsmentioning
confidence: 99%
“…Gottlieb [63] proved that RBM is unconditionally unstable, especially in higher dimension problem. Simulation work by Darwis et al, [64] also illustrated that RBM method could not suppress shock instability. The complexity of RBM method is futile [9].…”
Section: Average Numerical Errormentioning
confidence: 99%
“…However, it is dissipative compared to other schemes. 36 As a slope-limited TVD scheme is used, the left and right cell values for each cell are extrapolated by the set of equations below The slope is limited by ϕ ( r i ) , which is calculated using a slope limiter. Consequently, large gradients are not allowed, which reduces fluctuations occurring in the solution at discontinuities.…”
Section: Nomenclaturementioning
confidence: 99%
“…However, it is dissipative compared to other schemes. 36 As a slope-limited TVD scheme is used, the left and right cell values for each cell are extrapolated by the set of equations below…”
Section: Nomenclaturementioning
confidence: 99%