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

Zyuzina, N. A.; Остапенко, В. В.

doi:10.1134/s0965542518060155

Cited by 2 publications

(1 citation statement)

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“…Upwind Leapfrog schemes were used to solve aeroacoustics problems [17,18]. The monotonicity of difference schemes is researched in [19][20][21], including the Upwind Leapfrog schemes for the transport problem. A number of papers were devoted to the consideration of various modifications of the Upwind Leapfrog scheme, including [22], in which it was proposed to use weight multipliers to eliminate oscillations when solving a nonlinear transport problem.…”

Section: Introductionmentioning

confidence: 99%

Development and Research of a Modified Upwind Leapfrog Scheme for Solving Transport Problems

et al. 2022

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Modeling complex hydrodynamic processes in coastal systems is an important problem of mathematical modeling that cannot be solved analytically. The approximation of convective terms is difficult from the point of view of error reduction. This paper proposes a difference scheme based on a linear combination of the Upwind Leapfrog scheme with 2/3 weight coefficient, and the Standard Leapfrog scheme with 1/3 weight coefficient. The weight coefficients are obtained as a result of solving the problem of minimizing the approximation error. Numerical experiments show the advantage of the developed scheme in comparison with other modifications of the Upwind Leapfrog scheme in the case when the convective transport prevails over the diffusion one. The proposed difference scheme solves transport problems more effectively than classical difference schemes in the case when the Péclet number falls in the range from 2 to 20. It follows that the considered difference scheme allows hydrodynamic problems to be solved in regions of complex shape effectively.

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