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.
| Language | English |
|---|---|
| Article number | 124700 |
| Number of pages | 21 |
| Journal | Applied Mathematics and Computation |
| Volume | 365 |
| DOIs | |
| State | Published - 15 Jan 2020 |
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Keywords
- Computational Fluid Dynamics (CFD)
- ENATE
- Exponential scheme
- FV-CF
- Transport equation
Cite this
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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.
In: Applied Mathematics and Computation, Vol. 365, 124700, 15.01.2020.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - Similarities and differences of two exponential schemes for convection-diffusion problems
T2 - Applied Mathematics and Computation
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
VL - 365
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
M1 - 124700
ER -