Monotone approximation of a scalar conservation law based on the CABARET scheme in the case of a sign-changing characteristic field

Zyuzina, N. A.; Остапенко, В. В.

doi:10.1134/s1064562416050185

Cited by 7 publications

(2 citation statements)

References 9 publications

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“…The results of the oblique wave propagation test are summarised in Figs. [23][24][25]. First, in case of the CABARET with the full baseline correction (10), even a twice higher grid resolution in the x-direction compared to the normal wave propagation leads to a similar strong dissipation of the wave amplitude (compare Fig.…”

Section: D and 2d Isothermal Gas Dynamicsmentioning

confidence: 99%

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Flux-corrected dispersion-improved CABARET schemes for linear and nonlinear wave propagation problems

2018

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The new two-time-level dispersion improved CABARET scheme is developed as an upgrade of the original CABARET for improved wave propagation modelling in multiple dimensions and for nonlinear conservation laws including gas dynamics. The new upgrade retains many attractive features of the original CABARET scheme such as shock-capturing and low dissipation. It is simple for implementation in the existing CABARET codes and leads to a greater accuracy for solving linear wave propagation problems. A non-linear version of the dispersion-improved CABARET scheme is introduced to efficiently deal with contact discontinuities and shocks. The properties of the new linear and nonlinear CABARET schemes are analysed for numerical dissipation and dispersion error based on Von Neumann analysis and Pirrozolli's method. Numerical examples for one-dimensional and two-dimensional linear advection, the one-dimensional inviscid Burger's equation, and the isothermal gas dynamics problems in one and two dimensions are presented.

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Section: D and 2d Isothermal Gas Dynamicsmentioning

confidence: 99%

“…where the sonic point 0  f du d generally requires a special consideration, e.g. as discussed in [24],  Corrector step, conservative variables at the new time level are computed based on updated values of flux variables…”

Section: Linear Cabaret Schemes For One-dimensional Scalar Conservatimentioning

confidence: 99%

Flux-corrected dispersion-improved CABARET schemes for linear and nonlinear wave propagation problems

2018

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Decay of Unstable Strong Discontinuities in the Case of a Convex-Flux Scalar Conservation Law Approximated by the CABARET Scheme

Zyuzina

Остапенко

2018

Comput. Math. and Math. Phys.

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Monotonicity of the CABARET Scheme Approximating a Hyperbolic System of Conservation Laws

Ковыркина

Остапенко

2018

Comput. Math. and Math. Phys.

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Monotone approximation of a scalar conservation law based on the CABARET scheme in the case of a sign-changing characteristic field

Cited by 7 publications

References 9 publications

Flux-corrected dispersion-improved CABARET schemes for linear and nonlinear wave propagation problems

Flux-corrected dispersion-improved CABARET schemes for linear and nonlinear wave propagation problems

Decay of Unstable Strong Discontinuities in the Case of a Convex-Flux Scalar Conservation Law Approximated by the CABARET Scheme

Monotonicity of the CABARET Scheme Approximating a Hyperbolic System of Conservation Laws

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