# A cell-centred pressure-correction scheme for the compressible Euler equations

@article{Herbin2019ACP, title={A cell-centred pressure-correction scheme for the compressible Euler equations}, author={Rapha{\`e}le Herbin and Jean-Claude Latch{\'e} and Chady Zaza}, journal={IMA Journal of Numerical Analysis}, year={2019} }

We propose a robust pressure-correction scheme for the numerical solution of the compressible Euler equations discretized by a collocated finite volume method. The scheme is based on an internal energy formulation, which ensures that the internal energy is positive. More generally, the scheme enjoys fundamental stability properties: without restriction on the time step, both the density and the internal energy are positive, the integral of the total energy over the computational domain is…

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## 3 Citations

### Consistent Internal Energy Based Schemes for the Compressible Euler Equations

- Computer ScienceNumerical Simulation in Physics and Engineering: Trends and Applications
- 2021

Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct…

### Staggered Residual Distribution scheme for compressible flow

- PhysicsArXiv
- 2021

It is concluded that the approximation of the Euler equation of compressible fluid dynamics on a staggered mesh is general and can be used in a different setting as the specific one used here, for example finite volume, of discontinuous Galerkin methods.

### Conservativity And Weak Consistency Of A Class Of Staggered Finite Volume Methods For The Euler Equations

- Computer ScienceMath. Comput.
- 2021

The aim of the present paper is to derive a local total energy equation satisfied by the solutions, so that the schemes are in fact conservative, and to prove that they are consistent in the Lax-Wendroff sense.

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