# Fifth-order weighted essentially non-oscillatory schemes with new Z-type nonlinear weights for hyperbolic conservation laws

@inproceedings{Gu2021FifthorderWE, title={Fifth-order weighted essentially non-oscillatory schemes with new Z-type nonlinear weights for hyperbolic conservation laws}, author={Jiaxi Gu and Xinjuan Chen and Jae-Hun Jung}, year={2021} }

. In this paper we propose new Z-type nonlinear weights of the ﬁfth- order weighted essentially non-oscillatory (WENO) ﬁnite diﬀerence scheme for hyperbolic conservation laws. Instead of employing the classical smoothness indicators for the nonlinear weights, we take the p th root of the smoothness indicators and follow the form of Z-type nonlinear weights, leading to ﬁfth order accuracy in smooth regions, even at the critical points, and sharper approximations around the discontinuities. We…

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## References

SHOWING 1-10 OF 14 REFERENCES

### Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws

- Mathematics
- 1998

In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation…

### Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points

- Mathematics
- 2005

### Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy

- Mathematics
- 2000

In this paper we design a class of numerical schemes that are higher-order extensions of the weighted essentially non-oscillatory (WENO) schemes of G.-S. Jiang and C.-W. Shu (1996) and X.-D. Liu, S.…

### A RBF-WENO finite volume method for hyperbolic conservation laws with the monotone polynomial interpolation method

- Mathematics, Computer Science
- 2017

### Weighted essentially non-oscillatory schemes

- Computer Science
- 1994

A new version of ENO (essentially non-oscillatory) shock-capturing schemes which is called weighted ENO, where, instead of choosing the "smoothest" stencil to pick one interpolating polynomial for the ENO reconstruction, a convex combination of all candidates is used.

### Efficient Implementation of Weighted ENO Schemes

- Computer Science
- 1996

A new way of measuring the smoothness of a numerical solution is proposed, emulating the idea of minimizing the total variation of the approximation, which results in a fifth-order WENO scheme for the caser= 3, instead of the fourth-order with the original smoothness measurement by Liuet al.

### Solution of two‐dimensional Riemann problems for gas dynamics without Riemann problem solvers

- Physics
- 2002

We report here on our numerical study of the two‐dimensional Riemann problem for the compressible Euler equations. Compared with the relatively simple 1‐D configurations, the 2‐D case consists of a…

### Radial Basis Function ENO and WENO Finite Difference Methods Based on the Optimization of Shape Parameters

- Computer ScienceJ. Sci. Comput.
- 2017

These methods slightly perturb the polynomial reconstruction coefficients with RBFs as the reconstruction basis and enhance accuracy in the smooth region by locally optimizing the shape parameters to provide more accurate reconstructions and sharper solution profiles near the jump discontinuity.

### Efficient implementation of essentially non-oscillatory shock-capturing schemes, II

- Computer Science, Mathematics
- 1989