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Positivity-Preserving Finite Difference WENO Scheme for Ten-Moment Equations with Source Term

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Abstract

We develop a positivity-preserving finite difference WENO scheme for the Ten-Moment equations with body forces acting as a source in the momentum and energy equations. A positive forward Euler scheme under a CFL condition is first constructed which is combined with an operator splitting approach together with an integrating factor, strong stability preserving Runge–Kutta scheme. The positivity of the forward Euler scheme is obtained under a CFL condition by using a scaling type limiter, while the solution of the source operator is performed exactly and is positive without any restriction on the time step. The proposed method can be used with any WENO reconstruction scheme and we demonstrate it with fifth order accurate WENO-JS, WENO-Z and WENO-AO schemes. An adaptive CFL strategy is developed which can be more efficient than the use of reduced CFL for positivity preservation. Numerical results show that high order accuracy and positivity preservation are achieved on a range of test problems.

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Acknowledgements

Rakesh Kumar would like to acknowledge funding support from the National Post-doctoral Fellowship (PDF/2018/002621) administered by SERB-DST, India.

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Correspondence to Praveen Chandrashekar.

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Meena, A.K., Kumar, R. & Chandrashekar, P. Positivity-Preserving Finite Difference WENO Scheme for Ten-Moment Equations with Source Term. J Sci Comput 82, 15 (2020) doi:10.1007/s10915-019-01110-1

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Keywords

  • Ten-moment equations
  • Finite difference
  • WENO scheme
  • Positivity scheme
  • Integrating factor SSPRK