Volume 9, Issue 3
Constraint Preserving Schemes Using Potential-Based Fluxes I Multidimensional Transport Equations

Siddhartha Mishra & Eitan Tadmor

Commun. Comput. Phys., 9 (2011), pp. 688-710.

Published online: 2011-03

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  • Abstract

We consider constraint preserving multidimensional evolution equations. A prototypical example is provided by the magnetic induction equation of plasma physics. The constraint of interest is the divergence of the magnetic field. We design finite volume schemes which approximate these equations in a stable manner and preserve a discrete version of the constraint. The schemes are based on reformulating standard edge centered finite volume fluxes in terms of vertex centered potentials. The potential-based approach provides a general framework for faithful discretizations of constraint transport and we apply it to both divergence preserving as well as curl preserving equations. We present benchmark numerical tests which confirm that our potential-based schemes achieve high resolution, while being constraint preserving.

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@Article{CiCP-9-688, author = {}, title = {Constraint Preserving Schemes Using Potential-Based Fluxes I Multidimensional Transport Equations}, journal = {Communications in Computational Physics}, year = {2011}, volume = {9}, number = {3}, pages = {688--710}, abstract = {

We consider constraint preserving multidimensional evolution equations. A prototypical example is provided by the magnetic induction equation of plasma physics. The constraint of interest is the divergence of the magnetic field. We design finite volume schemes which approximate these equations in a stable manner and preserve a discrete version of the constraint. The schemes are based on reformulating standard edge centered finite volume fluxes in terms of vertex centered potentials. The potential-based approach provides a general framework for faithful discretizations of constraint transport and we apply it to both divergence preserving as well as curl preserving equations. We present benchmark numerical tests which confirm that our potential-based schemes achieve high resolution, while being constraint preserving.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.030909.091109s}, url = {http://global-sci.org/intro/article_detail/cicp/7517.html} }
TY - JOUR T1 - Constraint Preserving Schemes Using Potential-Based Fluxes I Multidimensional Transport Equations JO - Communications in Computational Physics VL - 3 SP - 688 EP - 710 PY - 2011 DA - 2011/03 SN - 9 DO - http://doi.org/10.4208/cicp.030909.091109s UR - https://global-sci.org/intro/article_detail/cicp/7517.html KW - AB -

We consider constraint preserving multidimensional evolution equations. A prototypical example is provided by the magnetic induction equation of plasma physics. The constraint of interest is the divergence of the magnetic field. We design finite volume schemes which approximate these equations in a stable manner and preserve a discrete version of the constraint. The schemes are based on reformulating standard edge centered finite volume fluxes in terms of vertex centered potentials. The potential-based approach provides a general framework for faithful discretizations of constraint transport and we apply it to both divergence preserving as well as curl preserving equations. We present benchmark numerical tests which confirm that our potential-based schemes achieve high resolution, while being constraint preserving.

Siddhartha Mishra & Eitan Tadmor. (2020). Constraint Preserving Schemes Using Potential-Based Fluxes I Multidimensional Transport Equations. Communications in Computational Physics. 9 (3). 688-710. doi:10.4208/cicp.030909.091109s
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