### Abstract

In this paper, we present a comparison of two novel exponential schemes for convection-diffusion problems. An exponential scheme uses in one way or another the analytical solution of the flux of a one-dimensional (1D) transport equation thereby improving the results of the simulation. In a multidimensional problem, the 1D solution is combined with operator splitting. The two approximations to be assessed are the Finite Volume-Complete Flux (FV-CF) and the Enhanced Numerical Approximation of a Transport Equation (ENATE) schemes. They were proposed by the two groups that co-author the current paper. Both schemes share many similarities in 1D but differ, especially in 2D, in some aspects that will be highlighted. In their derivation the algebraic coefficients of the computational stencil are integrals of flow parameters whose calculation is crucial for the accuracy of either method. These factors and their various approximations will be analysed. Some test cases will be used to check the ability of both schemes to provide accurate results.

Original language | English |
---|---|

Article number | 124700 |

Number of pages | 21 |

Journal | Applied Mathematics and Computation |

Volume | 365 |

DOIs | |

Publication status | Published - 15 Jan 2020 |

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### Keywords

- Computational Fluid Dynamics (CFD)
- ENATE
- Exponential scheme
- FV-CF
- Transport equation

### Cite this

*Applied Mathematics and Computation*,

*365*, [124700]. https://doi.org/10.1016/j.amc.2019.124700

}

**Similarities and differences of two exponential schemes for convection-diffusion problems : the FV-CF and ENATE schemes.** / Llorente, Víctor J. (Corresponding author); ten Thije Boonkkamp, Jan H.M.; Pascau, Antonio; Anthonissen, Martijn J.H.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Similarities and differences of two exponential schemes for convection-diffusion problems

T2 - the FV-CF and ENATE schemes

AU - Llorente, Víctor J.

AU - ten Thije Boonkkamp, Jan H.M.

AU - Pascau, Antonio

AU - Anthonissen, Martijn J.H.

PY - 2020/1/15

Y1 - 2020/1/15

N2 - In this paper, we present a comparison of two novel exponential schemes for convection-diffusion problems. An exponential scheme uses in one way or another the analytical solution of the flux of a one-dimensional (1D) transport equation thereby improving the results of the simulation. In a multidimensional problem, the 1D solution is combined with operator splitting. The two approximations to be assessed are the Finite Volume-Complete Flux (FV-CF) and the Enhanced Numerical Approximation of a Transport Equation (ENATE) schemes. They were proposed by the two groups that co-author the current paper. Both schemes share many similarities in 1D but differ, especially in 2D, in some aspects that will be highlighted. In their derivation the algebraic coefficients of the computational stencil are integrals of flow parameters whose calculation is crucial for the accuracy of either method. These factors and their various approximations will be analysed. Some test cases will be used to check the ability of both schemes to provide accurate results.

AB - In this paper, we present a comparison of two novel exponential schemes for convection-diffusion problems. An exponential scheme uses in one way or another the analytical solution of the flux of a one-dimensional (1D) transport equation thereby improving the results of the simulation. In a multidimensional problem, the 1D solution is combined with operator splitting. The two approximations to be assessed are the Finite Volume-Complete Flux (FV-CF) and the Enhanced Numerical Approximation of a Transport Equation (ENATE) schemes. They were proposed by the two groups that co-author the current paper. Both schemes share many similarities in 1D but differ, especially in 2D, in some aspects that will be highlighted. In their derivation the algebraic coefficients of the computational stencil are integrals of flow parameters whose calculation is crucial for the accuracy of either method. These factors and their various approximations will be analysed. Some test cases will be used to check the ability of both schemes to provide accurate results.

KW - Computational Fluid Dynamics (CFD)

KW - ENATE

KW - Exponential scheme

KW - FV-CF

KW - Transport equation

UR - http://www.scopus.com/inward/record.url?scp=85071992213&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2019.124700

DO - 10.1016/j.amc.2019.124700

M3 - Article

AN - SCOPUS:85071992213

VL - 365

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

M1 - 124700

ER -