Volume 29, Issue 6
A Non-Oscillatory Kinetic Scheme for Multi-Component Flows with the Equation of State for a Stiffend Gas

Yibing Chen & Song Jiang

J. Comp. Math., 29 (2011), pp. 661-683

Published online: 2011-12

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  • Abstract

We extend the traditional kinetic scheme for ideal gases to the Euler equations with the equation of state for a multi-component stiffened gas. Based on a careful analysis of the oscillation mechanism of the traditional kinetic scheme across contact discontinuities, we propose a new non-oscillatory kinetic (NOK) scheme for multi-component stiffened gases. The basic idea in the construction is to use a flux splitting technique to construct numerical fluxes which do not depend on the concrete form of the equilibrium state. The new scheme can not only can avoid spurious oscillations of the pressure and velocity near a material interface which are observed in the traditional kinetic schemes such as the kinetic flux vector splitting (KFVS) and BGK schemes, but also can deal with the stiffened gas equation of state. Moreover, we also carry out a careful analysis on the consistency condition, truncation error and positivity of the NOK scheme. A number of 1D and 2D numerical tests are presented which demonstrate the accuracy and robustness of the new scheme in the simulation of problems with smooth, weak and strong shock wave regions.

  • Keywords

Kinetic scheme Non-oscillation Multi-component Stiffened gases

  • AMS Subject Headings

65M06 82C40 35L64 76N10.

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COPYRIGHT: © Global Science Press

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@Article{JCM-29-661, author = {Yibing Chen and Song Jiang}, title = {A Non-Oscillatory Kinetic Scheme for Multi-Component Flows with the Equation of State for a Stiffend Gas}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {6}, pages = {661--683}, abstract = { We extend the traditional kinetic scheme for ideal gases to the Euler equations with the equation of state for a multi-component stiffened gas. Based on a careful analysis of the oscillation mechanism of the traditional kinetic scheme across contact discontinuities, we propose a new non-oscillatory kinetic (NOK) scheme for multi-component stiffened gases. The basic idea in the construction is to use a flux splitting technique to construct numerical fluxes which do not depend on the concrete form of the equilibrium state. The new scheme can not only can avoid spurious oscillations of the pressure and velocity near a material interface which are observed in the traditional kinetic schemes such as the kinetic flux vector splitting (KFVS) and BGK schemes, but also can deal with the stiffened gas equation of state. Moreover, we also carry out a careful analysis on the consistency condition, truncation error and positivity of the NOK scheme. A number of 1D and 2D numerical tests are presented which demonstrate the accuracy and robustness of the new scheme in the simulation of problems with smooth, weak and strong shock wave regions.}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1109-m11si04}, url = {http://global-sci.org/intro/article_detail/jcm/8499.html} }
TY - JOUR T1 - A Non-Oscillatory Kinetic Scheme for Multi-Component Flows with the Equation of State for a Stiffend Gas AU - Yibing Chen & Song Jiang JO - Journal of Computational Mathematics VL - 6 SP - 661 EP - 683 PY - 2011 DA - 2011/12 SN - 29 DO - http://doi.org/10.4208/jcm.1109-m11si04 UR - https://global-sci.org/intro/article_detail/jcm/8499.html KW - Kinetic scheme KW - Non-oscillation KW - Multi-component KW - Stiffened gases AB - We extend the traditional kinetic scheme for ideal gases to the Euler equations with the equation of state for a multi-component stiffened gas. Based on a careful analysis of the oscillation mechanism of the traditional kinetic scheme across contact discontinuities, we propose a new non-oscillatory kinetic (NOK) scheme for multi-component stiffened gases. The basic idea in the construction is to use a flux splitting technique to construct numerical fluxes which do not depend on the concrete form of the equilibrium state. The new scheme can not only can avoid spurious oscillations of the pressure and velocity near a material interface which are observed in the traditional kinetic schemes such as the kinetic flux vector splitting (KFVS) and BGK schemes, but also can deal with the stiffened gas equation of state. Moreover, we also carry out a careful analysis on the consistency condition, truncation error and positivity of the NOK scheme. A number of 1D and 2D numerical tests are presented which demonstrate the accuracy and robustness of the new scheme in the simulation of problems with smooth, weak and strong shock wave regions.
Yibing Chen & Song Jiang. (1970). A Non-Oscillatory Kinetic Scheme for Multi-Component Flows with the Equation of State for a Stiffend Gas. Journal of Computational Mathematics. 29 (6). 661-683. doi:10.4208/jcm.1109-m11si04
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