# Third order nonoscillatory central scheme for hyperbolic conservation laws

@article{Liu1998ThirdON, title={Third order nonoscillatory central scheme for hyperbolic conservation laws}, author={Xu-Dong Liu and Eitan Tadmor}, journal={Numerische Mathematik}, year={1998}, volume={79}, pages={397-425} }

Summary. A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: 1. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given cell averages; and 2. A central differencing based on staggered evolution of the reconstructed cell averages. This results in a third-order central scheme, an extension along the lines of the second-order central scheme of Nessyahu and…

## 187 Citations

### Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws

- Computer ScienceSIAM J. Sci. Comput.
- 1998

A new nonoscillatory high-resolution scheme for two-dimensional hyperbolic conservation laws, a predictor-corrector method which consists of two steps, which proves that the scheme satisfies the scalar maximum principle, and demonstrates the application of the central scheme to several prototype two- dimensional Euler problems.

### Second-Order Fully Discrete Central-Upwind Scheme for Two-Dimensional Hyperbolic Systems of Conservation Laws

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- 2017

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### A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations

- Computer Science, MathematicsSIAM J. Sci. Comput.
- 2000

A high-order extension of the recently proposed second-order, semidiscrete method for approximating solutions to multidimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems.

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- Mathematics, Computer ScienceSIAM J. Sci. Comput.
- 2000

A new third-order central scheme for approximating solutions of systems of conservation laws in one and two space dimensions is presented, based on reconstructing a piecewise-polynomial interpolant from cell-averages which is then advanced exactly in time.

### A Fourth-Order Central WENO Scheme for Multidimensional Hyperbolic Systems of Conservation Laws

- MathematicsSIAM J. Sci. Comput.
- 2002

The heart of the method is the reconstruction step, in which a genuinely two-dimensional interpolant is reconstructed from cell averages by taking a convex combination of building blocks in the form of biquadratic polynomials.

### A third-order semi-discrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems

- MathematicsNumerische Mathematik
- 2001

A new third-order semi-discrete genuinely multidimensional central scheme for systems of conservation laws and related convection-diffusion equations, which makes it a universal method, which can be easily implemented to a wide variety of problems.

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- Computer ScienceSIAM J. Numer. Anal.
- 2005

A fourth-order scheme is obtained that satisfies the total variation bounded (TVB) property and is carried out by componentwise application of the scalar framework.

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- 2011

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- Mathematics
- 2017

In this paper, we derive a new second-order fully discrete Godunov-type centralupwind scheme for two-dimensional hyperbolic systems of conservation laws. The scheme is derived in three steps:…

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