Volume 13, Issue 5
A Conservative Enforcing Positivity-Preserving Algorithm for Diffusion Scheme on General Meshes

F.-J. Cao, Y.-Z. Yao, Y.-L. Yu & G.-W. Yuan

Int. J. Numer. Anal. Mod., 13 (2016), pp. 739-752

Published online: 2016-09

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  • Abstract

For a class of diffusion schemes not satisfying the property of positivity-preserving, we propose an enforcing positivity algorithm. It is locally conservative and easy to be implemented in existing codes. Moreover, this algorithm can be performed on both structured and unstructured meshes. Numerical experiments demonstrate that in terms of L_2 error and conservation this algorithm is much better than the trick of directly enforcing the negative values to zero (ENZ), which has been used in applications, meanwhile, in terms of L_∞ error it is approximate to ENZ and CEPA repairing algorithms.

  • Keywords

positivity correction conservation nonlinear diffusion equation general mesh

  • AMS Subject Headings

35R35 49J40 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-739, author = {F.-J. Cao, Y.-Z. Yao, Y.-L. Yu and G.-W. Yuan}, title = {A Conservative Enforcing Positivity-Preserving Algorithm for Diffusion Scheme on General Meshes}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {5}, pages = {739--752}, abstract = {For a class of diffusion schemes not satisfying the property of positivity-preserving, we propose an enforcing positivity algorithm. It is locally conservative and easy to be implemented in existing codes. Moreover, this algorithm can be performed on both structured and unstructured meshes. Numerical experiments demonstrate that in terms of L_2 error and conservation this algorithm is much better than the trick of directly enforcing the negative values to zero (ENZ), which has been used in applications, meanwhile, in terms of L_∞ error it is approximate to ENZ and CEPA repairing algorithms.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/462.html} }
TY - JOUR T1 - A Conservative Enforcing Positivity-Preserving Algorithm for Diffusion Scheme on General Meshes AU - F.-J. Cao, Y.-Z. Yao, Y.-L. Yu & G.-W. Yuan JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 739 EP - 752 PY - 2016 DA - 2016/09 SN - 13 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/462.html KW - positivity correction KW - conservation KW - nonlinear diffusion equation KW - general mesh AB - For a class of diffusion schemes not satisfying the property of positivity-preserving, we propose an enforcing positivity algorithm. It is locally conservative and easy to be implemented in existing codes. Moreover, this algorithm can be performed on both structured and unstructured meshes. Numerical experiments demonstrate that in terms of L_2 error and conservation this algorithm is much better than the trick of directly enforcing the negative values to zero (ENZ), which has been used in applications, meanwhile, in terms of L_∞ error it is approximate to ENZ and CEPA repairing algorithms.
F.-J. Cao, Y.-Z. Yao, Y.-L. Yu & G.-W. Yuan. (1970). A Conservative Enforcing Positivity-Preserving Algorithm for Diffusion Scheme on General Meshes. International Journal of Numerical Analysis and Modeling. 13 (5). 739-752. doi:
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