Weighted essentially non-oscillatory schemes on triangular meshes. (English) Zbl 0926.65090

For 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.
Reviewer: E.Emmrich (Berlin)


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
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