Volume 7, Issue 4
Hyperbolic Moment Equations in Kinetic Gas Theory Based on Multi-variate Pearson-IV-distributions

Manuel Torrilhon

Commun. Comput. Phys., 7 (2010), pp. 639-673.

Published online: 2010-07

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In this paper we develop a new closure theory for moment approximations in kinetic gas theory and derive hyperbolic moment equations for 13 fluid variables including stress and heat flux. Classical equations have either restricted hyperbolicity regions like Grad’s moment equations or fail to include higher moments in a practical way like the entropy maximization approach. The new closure is based on Pearson-Type-IV distributions which reduce to Maxwellians in equilibrium, but allow anisotropies and skewness in non-equilibrium. The closure relations are essentially explicit and easy to evaluate. Hyperbolicity is shown numerically for a large range of values. Numerical solutions of Riemann problems demonstrate the capability of the new equations to handle strong non-equilibrium.

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@Article{CiCP-7-639, author = {Manuel Torrilhon}, title = {Hyperbolic Moment Equations in Kinetic Gas Theory Based on Multi-variate Pearson-IV-distributions}, journal = {Communications in Computational Physics}, year = {2010}, volume = {7}, number = {4}, pages = {639--673}, abstract = {

In this paper we develop a new closure theory for moment approximations in kinetic gas theory and derive hyperbolic moment equations for 13 fluid variables including stress and heat flux. Classical equations have either restricted hyperbolicity regions like Grad’s moment equations or fail to include higher moments in a practical way like the entropy maximization approach. The new closure is based on Pearson-Type-IV distributions which reduce to Maxwellians in equilibrium, but allow anisotropies and skewness in non-equilibrium. The closure relations are essentially explicit and easy to evaluate. Hyperbolicity is shown numerically for a large range of values. Numerical solutions of Riemann problems demonstrate the capability of the new equations to handle strong non-equilibrium.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2009.09.049}, url = {http://global-sci.org/intro/article_detail/cicp/7648.html} }
TY - JOUR T1 - Hyperbolic Moment Equations in Kinetic Gas Theory Based on Multi-variate Pearson-IV-distributions AU - Manuel Torrilhon JO - Communications in Computational Physics VL - 4 SP - 639 EP - 673 PY - 2010 DA - 2010/07 SN - 7 DO - http://dor.org/10.4208/cicp.2009.09.049 UR - https://global-sci.org/intro/cicp/7648.html KW - AB -

In this paper we develop a new closure theory for moment approximations in kinetic gas theory and derive hyperbolic moment equations for 13 fluid variables including stress and heat flux. Classical equations have either restricted hyperbolicity regions like Grad’s moment equations or fail to include higher moments in a practical way like the entropy maximization approach. The new closure is based on Pearson-Type-IV distributions which reduce to Maxwellians in equilibrium, but allow anisotropies and skewness in non-equilibrium. The closure relations are essentially explicit and easy to evaluate. Hyperbolicity is shown numerically for a large range of values. Numerical solutions of Riemann problems demonstrate the capability of the new equations to handle strong non-equilibrium.

Manuel Torrilhon. (1970). Hyperbolic Moment Equations in Kinetic Gas Theory Based on Multi-variate Pearson-IV-distributions. Communications in Computational Physics. 7 (4). 639-673. doi:10.4208/cicp.2009.09.049
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