High-order upwind and non-oscillatory approach for steady state diffusion, advection–diffusion and application to magnetized electrons

Amareshwara Sainadh Chamarthi, Kimiya Komurasaki, Rei Kawashima

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

Steady state simulations of magnetized electron fluid equations with strong anisotropic diffusion based on the first-order hyperbolic approach is carried out using cell-centered higher order upwind schemes, linear and weighted essentially non-oscillatory (WENO). Along with the magnetized electrons, the diffusion equation is also simulated to demonstrate the implementation and design order of the accuracy of the approach due to their similar upwind structure. We show the adequacy of linear upwind schemes for diffusion equation and the use of shock-capturing scheme like WENO does not have any adverse effect on the solution, unlike the total-variation diminishing (TVD) methods. We further extended the approach to advection–diffusion equation, and appropriate boundary conditions have obtained a consistent design accuracy of the third and fifth order. We implemented the WENO approach to advection–diffusion equation by using the split hyperbolic method to demonstrate the advantage of non-oscillatory schemes to capture sharp gradients in boundary layer type problems without spurious oscillations. Finally, numerical results for magnetized electrons simulations indicate that with increasing strength of magnetic confinement it is possible to capture sharp gradients without oscillations by WENO scheme.

Original languageEnglish
Pages (from-to)1120-1151
Number of pages32
JournalJournal of Computational Physics
Volume374
DOIs
Publication statusPublished - 2018 Dec 1
Externally publishedYes

Keywords

  • Diffusion and advection–diffusion equations
  • Higher order methods
  • Magnetized electron fluid
  • Weighted essentially non-oscillatory (WENO)

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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