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

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.

35R35, 49J40, 60G40

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@Article{IJNAM-13-739, author = {}, 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 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, conservation, nonlinear diffusion equation, 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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