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**Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids.**
*(English)*
Zbl 1392.76048

Summary: In this paper the weighted ENO (essentially non-oscillatory) scheme developed for the one-dimensional case by Liu, Osher, and Chan is applied to the case of unstructured triangular grids in two space dimensions. Ideas from Jiang and Shu, especially their new way of smoothness measuring, are considered. As a starting point for the unstructured case we use an ENO scheme like the one introduced by Abgrall. Beside the application of the weighted ENO ideas the whole reconstruction algorithm is analyzed and described in detail. Here we also concentrate on technical problems and their solution. Finally, some applications are given to demonstrate the accuracy and robustness of the resulting new method. The whole reconstruction algorithm described here can be applied to any kind of data on triangular unstructured grids, although it is used in the framework of compressible flow computation in this paper only.

### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

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\textit{O. Friedrich}, J. Comput. Phys. 144, No. 1, 194--212 (1998; Zbl 1392.76048)

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### References:

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[2] | Test Cases for Inviscid Flow Field Methods |

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[10] | Sonar, Th., On the construction of essentially non-oscillatory finite volume approximations to hyperbolic conservation laws on general triangulations: polynomial recovery, accuracy and stencil selection, Comput. Methods Appl. Mech. Engrg., 140, 157, (1997) · Zbl 0898.76086 |

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