Equilibrium real gas computations using Marquina's scheme

Stiriba, Youssef; Marquina, Antonio; Donat, Rosa

doi:10.1002/fld.432

Cited by 9 publications

(9 citation statements)

References 16 publications

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“…The results shown in [36] on the same test problem with a second-and a thirdorder scheme show no spurious oscillations. Again, it is not surprising that an ad hoc scheme can exhibit better results on a specific problem than those obtained with our multipurpose scheme.…”

Section: Black-box Approachmentioning

confidence: 76%

“…Even upwind schemes based on projection along characteristic directions require a considerable amount of extra work to deal with such a simple change; see, for instance, [36]. Here we need only to change one line in the function that computes the fluxes.…”

Section: Black-box Approachmentioning

confidence: 99%

“…As in [36], we pick γ = 1.4, a = 0.03412, and b = 0.23 for the parameters appearing in (4.1). We compute the solution up to T = 0.1386, with λ = 0.2 and N = 200.…”

Section: Black-box Approachmentioning

confidence: 99%

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A Fourth-Order Central WENO Scheme for Multidimensional Hyperbolic Systems of Conservation Laws

Levy¹,

Puppo²,

Russo³

2002

SIAM J. Sci. Comput.

129

121

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Abstract. We present the first fourth-order central scheme for two-dimensional hyperbolic systems of conservation laws. Our new method is based on a central weighted nonoscillatory approach. The heart of our method is the reconstruction step, in which a genuinely two-dimensional interpolant is reconstructed from cell averages by taking a convex combination of building blocks in the form of biquadratic polynomials.Similarly to other central schemes, our new method enjoys the simplicity of the black-box approach. All that is required in order to solve a problem is to supply the flux function and an estimate on the speed of propagation. The high-resolution properties of the scheme as well as its resistance to mesh orientation, and the effectiveness of the componentwise approach, are demonstrated in a variety of numerical examples.Key words. hyperbolic systems, central difference schemes, high-order accuracy, nonoscillatory schemes, weighted essentially nonoscillatory reconstruction, central weighted essentially nonoscillatory reconstruction AMS subject classification. 65M06 PII. S10648275013858521. Introduction. The integration of hyperbolic systems of conservation laws has initially been approached in the framework of upwind schemes, generalizing the firstorder upwind Godunov scheme. Effective high-order methods based on the upwind approach are the essentially nonoscillatory (ENO) schemes [7,32] and more recently the weighted ENO (WENO) schemes [26,8]. For a thorough review of the schemes obtained with the upwind approach, see [31] and [6].More recently high-order central schemes have appeared. These schemes can be viewed as extensions of the first-order Lax-Friedrichs scheme [5]. They are characterized by a very simple formulation, which, unlike traditional upwind schemes, requires neither Riemann solvers (exact or approximate) nor projection of the equations along characteristic directions.The first high-order central method obtained following these lines is the secondorder Nessyahu-Tadmor scheme [28]. This scheme was based on a MUSCL-type interpolant in space (see [17]) and a midpoint quadrature to approximate the timeintegrals of the fluxes. For a related approach see [30]. Motivated by the simplicity and robustness of the second-order method, various high-order schemes, multidimensional extensions, and semidiscrete schemes have been suggested in the literature; see, e.g., [2,27,9,10,13,18,3,19,22,11,12,37] and the references therein. Central schemes have been used also for hyperbolic systems with source terms. We mention here the

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Section: Black-box Approachmentioning

confidence: 76%

Section: Black-box Approachmentioning

confidence: 99%

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A Fourth-Order Central WENO Scheme for Multidimensional Hyperbolic Systems of Conservation Laws

Levy¹,

Puppo²,

Russo³

2002

SIAM J. Sci. Comput.

129

121

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“…the physical flux no longer possesses the homogeneity property and we cannot find a natural real-gas extension of SW FVS and other FVS and FDS methods [13,23]. This method extends easily to nonhomogeneous fluxes and especially to real gases without using additional assumptions or approximations.…”

Section: Extension To Higher Dimensionmentioning

confidence: 96%

“…We use the numerical treatment of [27,3,23] near the corner to fix the errors generated: a boundary layer in density of about one to two zones, the decrease of the two components of the velocity, as well as a spurious Mach steam at the bottom wall (see [23] for corner treatment using equilibrium equations of state).…”

Section: Two-dimensional Testsmentioning

confidence: 99%

A Nonlinear Flux Split Method for Hyperbolic Conservation Laws

Stiriba¹

2002

Journal of Computational Physics

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We present and analyze the performance of a nonlinear, upwind flux split method for approximating solutions of hyperbolic conservation laws. The method is based on a new version of the single-state-approximate Riemann solver devised by Harten, Lax, and van Leer (HLL) and implemented by Einfeldt. It makes use of two-sided local characteristic variables to reduce the dissipation of HLL by introducing the flavor of HLL into the Steger-Warming flux vector splitting scheme. We use the characteristic decomposition and the method-of-lines approach to construct high-order versions of the first-order scheme and demonstrate their efficiency and robustness in several numerical tests.

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