TY - JOUR
T1 - Study of numerical error of a Eulerian–Lagrangian scheme in the presence of particle source
AU - Tatsumi, Ryoko
AU - Hoshino, Kazuo
AU - Hatayama, Akiyoshi
N1 - Funding Information:
The author would like to thank Prof. Dr. R. Schneider (University of Greifswald), Dr. A. Runov (IPP Greifswald), and Dr. R. Kanno (NIFS) for dedicated support and thoughtful discussions. This work was performed with the support and under the auspices of the NIFS Collaborative Research Program ‘ NIFS19KNTT052 ’. This work was supported by Grant-in-Aid for JSPS (Japan Society for the Promotion of Science) Research Fellows, Grant Number 18J12692 .
Publisher Copyright:
© 2021
PY - 2021/7
Y1 - 2021/7
N2 - Eulerian–Lagrangian (EL–LG) scheme is a numerical scheme that tracks pseudo particles in Eulerian cells. It is widely used in the computational fluid dynamics, however, numerical errors associated with a particle source term has not yet been investigated much. Hence this study focuses on numerical errors of EL–LG caused by particle sources. The purposes are: (i) to clarify causes and situations that bring larger numerical errors by source terms and (ii) to suggest an idea to reduce them. For those purposes, we focus on the particle continuity equation and carry out systematic analysis of the numerical error by setting the following three simple cases: Case (A) No source, Case (B) Constant source, and Case (C) source with arbitrary spatial profile. For each case, we have obtained a theoretical expression of the numerical error. It has been clarified that the errors become relatively large when (i) the spatial profile of the particle source has a large gradient and (ii) the source is localized in the region with high flow-velocity. These were caused by the treatment of the particle source: If pseudo particles due to the source are added in a simple way at the start or the end of the time step, this can lead to larger numerical errors. To reduce those errors, a time-averaging scheme has been suggested. Although the analyzed cases are simple, the results obtained in this study would give important knowledge and insight into numerical errors associated with particle sources in EL–LG schemes.
AB - Eulerian–Lagrangian (EL–LG) scheme is a numerical scheme that tracks pseudo particles in Eulerian cells. It is widely used in the computational fluid dynamics, however, numerical errors associated with a particle source term has not yet been investigated much. Hence this study focuses on numerical errors of EL–LG caused by particle sources. The purposes are: (i) to clarify causes and situations that bring larger numerical errors by source terms and (ii) to suggest an idea to reduce them. For those purposes, we focus on the particle continuity equation and carry out systematic analysis of the numerical error by setting the following three simple cases: Case (A) No source, Case (B) Constant source, and Case (C) source with arbitrary spatial profile. For each case, we have obtained a theoretical expression of the numerical error. It has been clarified that the errors become relatively large when (i) the spatial profile of the particle source has a large gradient and (ii) the source is localized in the region with high flow-velocity. These were caused by the treatment of the particle source: If pseudo particles due to the source are added in a simple way at the start or the end of the time step, this can lead to larger numerical errors. To reduce those errors, a time-averaging scheme has been suggested. Although the analyzed cases are simple, the results obtained in this study would give important knowledge and insight into numerical errors associated with particle sources in EL–LG schemes.
KW - CFD
KW - Eulerian–Lagrangian scheme
KW - Numerical error
KW - Particle source
KW - Plasma fluid simulation
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U2 - 10.1016/j.cpc.2021.107960
DO - 10.1016/j.cpc.2021.107960
M3 - Article
AN - SCOPUS:85104675593
VL - 264
JO - Computer Physics Communications
JF - Computer Physics Communications
SN - 0010-4655
M1 - 107960
ER -