2014
DOI: 10.1002/fld.3903
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Roe‐type Riemann solvers for general hyperbolic systems

Abstract: SUMMARYWe present a Roe‐type weak formulation Riemann solver where the average coefficient matrix is computed numerically. The novelty of this approach is that it is general enough that can be applied to any hyperbolic system while retaining the accuracy of the original Roe solver. We show applications to the compressible Euler equations with general equation of state. An alternative version of the method uses directly the eigenvectors in the averaging process, simplifying the algorithm. These new solvers are … Show more

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Cited by 10 publications
(6 citation statements)
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References 41 publications
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“…The first alternative, that yields characteristic-wise numerical schemes, gives better resolution than the second, since the amount of numerical viscosity is much smaller. The prototype method of this kind of is Roe's method [1] (see also [2]), for which the first-order numerical flux, specified here for two adjacent states L and R to the left and right of a cell boundary, is given bŷ…”
Section: A Scopementioning
confidence: 99%
See 1 more Smart Citation
“…The first alternative, that yields characteristic-wise numerical schemes, gives better resolution than the second, since the amount of numerical viscosity is much smaller. The prototype method of this kind of is Roe's method [1] (see also [2]), for which the first-order numerical flux, specified here for two adjacent states L and R to the left and right of a cell boundary, is given bŷ…”
Section: A Scopementioning
confidence: 99%
“…The first alternative, that yields characteristic‐wise numerical schemes, gives better resolution than the second, since the amount of numerical viscosity is much smaller. The prototype method of this kind of is Roe's method (see also ), for which the first‐order numerical flux, specified here for two adjacent states Φ normalL and Φ normalR to the left and right of a cell boundary, is given by bold-italicf true^ ( Φ normalL , Φ normalR ) = 1 2 ( f ( Φ normalL ) + f ( Φ normalR ) | A ( Φ normalL , Φ normalR ) | ( Φ normalR Φ normalL ) ) , where A ( Φ normalL , Φ normalR ) is a Roe matrix (related to the flux Jacobian scriptJ bold-italicf = ( f i / ϕ j ) 1 i , j N ) for the flux bold-italicf and | A | N × N denotes a real diagonalizable matrix that is computed through the eigenvectors and eigenvalues of bold-italicA (not to be confused with the matrix of absolute values of the entries of bold-italicA ). Conversely, the second alternative, which gives rise to component‐wise schemes, tends to yield faster methods.…”
Section: Introductionmentioning
confidence: 99%
“…Integrating the matrices d U / d Z and d F / d Z in ξ , for each state φ ( ξ , u L , u R ) reaches φ ( z L + ξ ( z R − z L )) to obtain trueB^ and Ĉ , see . Except the first and second lines of d U / d Z matrix and the first line of d F / d Z , all other terms were integrated numerically using a Gauss–Legendre quadrature with three points, employing a procedure similar to one found in .…”
Section: Mathematical Formulationmentioning
confidence: 99%
“…The schemes provide the intercell fluxes by a family of waves which propagates through the cell's interface. For two‐phase flows the resultant non‐linear hyperbolic system of the conservative laws is frequently solved employing Roe linearization , see for example .…”
Section: Introductionmentioning
confidence: 99%
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