Weighted essentially non-oscillatory schemes on triangular meshes.

*(English)*Zbl 0926.65090For the two-dimensional system of conservation laws
\[
u_t+ f(u)_x+ g(u)y= 0
\]
with prescribed initial data, third- and fourth-order weighted essentially non-oscillating (WENO) schemes using a combination of 2D linear and quadratic polynomials, respectively, are constructed. WENO schemes have been proposed in the mid 90’s to improve ENO schemes by smoothing the numerical flux, better steady-state convergence and accuracy. The main part in such a scheme is the reconstruction from cell averages to point values by using polynomials.

The authors describe this technique in detail and illustrate it by some examples including the Burgers equation and the Euler system of gas dynamics. Finally, numerical tests demonstrate the accuracy of the method and its improvements.

The authors describe this technique in detail and illustrate it by some examples including the Burgers equation and the Euler system of gas dynamics. Finally, numerical tests demonstrate the accuracy of the method and its improvements.

Reviewer: E.Emmrich (Berlin)

##### MSC:

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |

35Q53 | KdV equations (Korteweg-de Vries equations) |

76N15 | Gas dynamics (general theory) |

35L65 | Hyperbolic conservation laws |

##### Keywords:

weighted essentially non-oscillatory schemes; finite volume method; numerical examples; system of conservation laws; WENO schemes; convergence; Burgers equation; Euler system of gas dynamics
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\textit{C. Hu} and \textit{C.-W. Shu}, J. Comput. Phys. 150, No. 1, 97--127 (1999; Zbl 0926.65090)

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